# Simplification MCQ Questions & Answers

Simplification MCQs : This section focuses on the "Simplification". These Multiple Choice Questions (MCQs) should be practiced to improve the Simplification skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

A. 20
B. 80
C. 100
D. 120

Question 2

If a - b = 3 and a^2 + b^2 = 29, find the value of ab.

A. 10
B. 12
C. 15
D. 18

Question 3

A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

A. 45
B. 60
C. 75
D. 90

Question 4

There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

A. 20
B. 80
C. 100
D. 200

Question 5

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900

Question 6

The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

A. Rs. 1200
B. Rs. 2400
C. Rs. 4800
D. Cannot be determined

Question 7

A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is:

A. Rs. 120
B. Rs. 160
C. Rs. 240
D. Rs. 300

Question 8

One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

A. Rs. 30,000
B. Rs. 50,000
C. Rs. 60,000
D. Rs. 90,000

Question 9

A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:

A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds

Question 10

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

A. 1/7
B. 1/8
C. 1/9
D. 7/8

Question 11

To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?

A. 10
B. 35
C. 62.5
D. Cannot be determined

Question 12

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

A. 160
B. 175
C. 180
D. 195

Question 13

Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?

A. 256
B. 432
C. 512
D. 640

Question 14

A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

A. 22
B. 23
C. 24
D. 26

Question 15

David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

A. 19
B. 28
C. 30
D. 37

Question 16

(0.2 x 0.2 x 0.2)(0.06 x 0.06 x 0.06) / (0.12 x 0.12 x 0.12) = ?

A. 0.008
B. 0.001
C. 0.002
D. 0.006

Question 17

(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

A. 0
B. 1
C. 2
D. 3

Question 18

(1155) +(18 − 6) × 9 =?

A. 113
B. 115
C. 100
D. 110

Question 19

(798+579)2- (798-579)2798 x 579 =

A. 2
B. 6
C. 4
D. 8

Question 20

(secA - 1)/(secA + 1) is equal to?

A. (1 - sinA)/(1 + sinA)
B. (1 + cosA)/(1 - cosA)
C. (1 + sinA)/(1 - sinA)
D. (1 - cosA)/(1 + cosA)

Question 21

(secA ­- tanA)/(cosecA + cotA) is equal to

A. (secA -­ cotA) / (cosecA + tanA)
B. (secA -­ cosA) / (cosecA + sinA)
C. (cosecA -­ cotA) / (secA + tanA)
D. (secA + cosA) / (cosecA -­ sinA)

Question 22

[15% of 300% of 560] × 2 ÷ 5 =

A. 100
B. 90
C. 85
D. 105

Question 23

[63 - (-3){-2 - 8 - 3}] / 3{6 + (-2) (-1)} = ?

A. 0
B. 3
C. 1
D. 2

Question 24

[sinA/(1 + cosA)] + [(1 + cosA)/sinA] is equal to

A. 2secA
B. 2cosecA
C. 2tanA
D. 2cotA

Question 25

∆ABC is right angled at B. If m∠A = 30°, then find the value of (sinC + 1/3).

A. 4/3
B. (√3+1)/2
C. (√3+2)/√3
D. (3√3+2)/6

Question 26

∆ABC is right angled at B. If m∠A = 30°., then Sec C =?

A. 1/2
B. 1/√2
C. 2
D. 1/√3

Question 27

∆ABC is right angled at B. If m∠A = 45°, then find the value of (coseC + 1/√3).

A. (3√2+1)/3
B. (2+√3)/2
C. 5/√3
D. (√6+1)/√3

Question 28

∆DEF is right angled at E. If cosD = 5/13, then what is the value of tanF?

A. 5/13
B. 5/12
C. 13/5
D. 13/12

Question 29

∆LMN is right angled at M. If m ∠N = 45°. What is the length (in cm) of MN, if NL = 6√2 cm?

A. 3
B. 4
C. 2
D. 6

Question 30

∆PQR is right angled at Q. If m∠R = 45°, then find the value of (cosecP - √3/2)

A. (3√3-1)/3
B. 2/√3
C. (2-√3)/√3
D. (2√2-√3)/2

Question 31

∆PQR is right angled at Q. If sinP = 12/13, then what is the value of tanR?

A. 5/13
B. 13/5
C. 13/12
D. 5/12

Question 32

∆XYZ is right angled at Y. If CosecX = 17/15, then what is the value of CotZ?

A. 17/15
B. 8/17
C. 17/8
D. 15/8

Question 33

∆XYZ is right angled at Y. If m ∠Z = 60. What is the length (in cm) of YZ, if ZX = 9√3 cm?

A. 3√3
B. 3√3/2
C. 9√3/2
D. √3

Question 34

∆XYZ is right angled at Y. If tanX = 15/8, then what is the value of sinZ ?

A. 15/17
B. 17/8
C. 17/15
D. 8/17

Question 35

∆XYZ is right angled at Y. If tanX = 24/7, then what is the value of cotZ ?

A. 25/7
B. 24/25
C. 7/24

Question 36

√(1 + tan2A)/tanA is equal to

A. secA
B. sinA
C. cosecA
D. cosA

Question 37

√[(1 ­ sinA)/(1 + sinA)] is equal to?

A. secA -­ tanA
B. cosecA -­ cotA
C. secA + tanA
D. cosecA + cotA

Question 38

0 is the circumference of a triangle ∆ABC. The point A and the chord BC are on the opposite side of O. If ∠BOC=150° then the value of ∠BAC is

A. 65°
B. 60°
C. 70°
D. 75°

Question 39

0.196 + 1.96 + 19.6 + 196 = ?

A. 217.756
B. 216.856
C. 216.756
D. 217.676

Question 40

0.296 + 2.96 + 29.6 + 296 = ?

A. 327.856
B. 328.756
C. 328.856
D. 327.756

Question 41

1\$ = Rs.67.89. Money changer adds a margin of RS. 1.11. What will be the cost of \$150?

A. RS. 10,183
B. RS. 10,350
C. RS. 10,330
D. RS. 10,450

Question 42

1.004 - 0.4 is equal to

A. 0.604
B. 0.006
C. 0.64
D. 1

Question 43

1/(secA + tanA) is equal to

A. cosecA - cotA
B. sinA - cosA
C. secA - tanA
D. sinA + cosA

Question 44

1/(tanA + cotA) is equal to

A. (cosecA + sinA)(secA - cosA)
B. √[(cosecA - sinA)(secA - cosA)]
C. √[(cosecA + sinA)(secA - cosA)]
D. (cosecA - sinA)(secA - cosA)

Question 45

10 dozen apples, 15 dozen mangoes & 20 dozen oranges are kept for sale. 1/2, 1/3rd & 1/4th of each item respectively have been added. What is the total number of fruits kept for sale now?

A. 720
B. 600
C. 580
D. 820

Question 46

10+10(9) =

A. 180
B. 110
C. 100
D. 19

Question 47

112 × 54 =

A. 68947
B. 69874
C. 70000
D. 76000

Question 48

125 - 73 + 48 - 137 + 99 = ?

A. 237
B. 62
C. -37
D. 52

Question 49

1422 ÷ 1260.25 = ?

A. 586
B. 578
C. 568
D. 566

Question 50

1747 + 13212 - ? = 1123

A. 16
B. 17
C. 18
D. 19

Question 51

18800÷470÷20=?

A. 1
B. 2
C. 3
D. 4

Question 52

19 x 23 = 437. Then 190 x 0.023 = ?

A. 43.7
B. 4.37
C. 0.0437
D. 0.437

Question 53

199994 x 200006 = ?

A. 39999799964
B. 39999999864
C. 39999999954
D. 39999999964

Question 54

2 ­- (cosA + sinA)2 is equal to

A. (cosecA -­ sinA)2
B. cosA ­- sinA
C. cosecA ­- sinA
D. (cosA -­ sinA)2

Question 55

2 sec2A is equal to

A. (1 - tanA)2 - (1 + tanA)2
B. √[(1 - tanA)2 + (1 + tanA)2 ]
C. √[(1 - tanA)2 - (1 + tanA)2]
D. (1 - tanA)2 + (1 + tanA)2

Question 56

2*[­0.3(1.3 + 3.7)] of 0.8 = ?

A. ­1.92
B. -0.72
C. 2.16
D. -­2.4

Question 57

217 x 217 + 183 x 183 = ?

A. 84521
B. 87487
C. 80578
D. 78458

Question 58

23 x 19 = 437. How much is 0.0437 / 1.9 = ?

A. 0.0023
B. 0.23
C. 0.023
D. 2.3

Question 59

23 x 31 = 713. How much is 0.0713 / 3.1?

A. 0.23
B. 0.0023
C. 2.3
D. 0.023

Question 60

23x12+49x15312+50 = ?

A. 0.5
B. 1
C. 2
D. 3

Question 61

25 - 1/2{5 + 4 - (3 + 2 - 1 + 3)} = ?

A. 21
B. 23
C. 22
D. 24

Question 62

2660 of 17 of 12 of 19.5 of 12 = ?

A. 1
B. 10
C. 0.1
D. 100

Question 63

2cos[(C+D)/2]sin[(C-D)/2] is equal to

A. sinC + sinD
B. sinC - sinD
C. cosC - cosD
D. cosC + cosD

Question 64

2sin[(C+D)/2].cos[(C­-D)/2] is equal to

A. sinC ­-  sinD
B. cosC + cosD
C. cosC -­ cosD
D. sinC + sinD

Question 65

2sin[(C+D)/2].sin[(D­-C)/2] is equal to

A. cosC + cosD
B. cosC ­- cosD
C. sinC ­- sinD
D. sinC + sinD

Question 66

2sinAsinB is equal to

A. sin(A+B) + sin(A­-B)
B. cos(A-­B) -­ cos(A+B)
C. sin(A+B) -­ sin(A-­B)
D. cos(A+B) + cos(A-­B)

Question 67

38% of 7500 +  ?% of 375 = 50% of 6000

A. 50
B. 40
C. 60
D. 45

Question 68

3cosA is equal to

A. 4cos3A + 3cosA
B. 4cos3A - 3cosA
C. 3cos3A + 3cosA
D. 3cos3A - 3cosA

Question 69

3x2-14x+16=05y2-16y+12=0

A. x > y
B. x < y
C. x=y or relation cannot be established between x and y
D. x ≥ y

Question 70

4 + 16 x -12 x 24 - 13 - 3 ÷ 20 - 4 = ?

A. 4
B. 6
C. 5
D. 3

Question 71

40.36 ­- (9.347 -­ x ) -­ 29.02 = 3.68. Find x.

A. -56.353
B. 1.687
C. -17.007
D. 82.407

Question 72

43% of 616.6 + 37% of 217 =?

A. 345.428
B. 354.428
C. 344.428
D. 364.428

Question 73

45 - [38 - {60 / 3 - (6 - 9 / 3)/ 3}]= ?

A. 24
B. 25
C. 26
D. 21

Question 74

5 + 2 x 10/2 = ?

A. 15
B. 35
C. 10
D. 20

Question 75

5 bottles cost as much as 2 bags. The cost of 15 bottles and 4 bags is Rs 2,000. What is the price (in Rs.) of a single bag?

A. 200
B. 215
C. 240
D. 250

Question 76

5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

A. -13
B. 11
C. 13
D. -11

Question 77

5 + 2 x 10 =

A. 70
B. 20
C. 25
D. 52

Question 78

5.16 x 3.2 =

A. 15.502
B. 16.512
C. 17.772
D. 17.52

Question 79

50.003% of 99.8÷49.988 = ?

A. 2
B. 0
C. 1
D. 50

Question 80

56/32 simplified value?

A. 1.705
B. 1.45
C. 1.75
D. 7.5

Question 81

6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?

A. 5/3
B. 7/3
C. 5/4
D. 4/5

Question 82

6.651 -­ (148.6 ­- x ) -­ 57.22 = 6.098. Find x.

A. 205.267
B. 90.827
C. -­91.933
D. 218.569

Question 83

64/12 in simplest form?

A. 19/6
B. 32/4
C. 16/3
D. None of the above

Question 84

-70 + 28 / (7 - 3) = ?

A. -9
B. -69
C. -10.5
D. -63

Question 85

72 ÷ 52 × 3272 ÷ 52 of 32 ÷ 5.25

A. 3/5
B. 3/6
C. 3/7
D. 3/8

Question 86

78 books, 114 crayons and 141 notebooks were distributed to school children equally. It was found that 6 were left undistributed in each. What was the total number of children?

A. 9
B. 8
C. 13
D. 12

Question 87

78 of 448 + 67 of 3374 = ?

A. 3084
B. 3184
C. 3584
D. None of these

Question 88

8 x {5 - (-2) x (-3)} = ?

A. 8
B. -168
C. 88
D. -8

Question 89

97 x 97 = ?

A. 9391
B. 9409
C. 9049
D. 9309

Question 90

9876-?+5431=5553

A. 9754
B. 9765
C. 8754
D. 9854

Question 91

9997 x 10003 = ?

A. 9999991
B. 99999911
C. 99999991
D. 9999911

Question 92

A 1.6 m tall observer is 45 meters away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in meters is

A. 25.98
B. 26.58
C. 27.58
D. 27.98

Question 93

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A. 12/π+4
B. 6/π+4
C. 3/π+4
D. 6/π+2√2

Question 94

A 8 cm long perpendicular is drawn from the centre of a circle to a 12 cm long chord. The diameter of the circle is

A. 10 cm
B. 12 cm
C. 16 cm
D. 20 cm

Question 95

A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?

A. 3
B. 4
C. 5
D. 6

Question 96

A and B together have Rs. 6300. If 5/19 of A's amount is equal to 2/5 of B's amount. The amount of 'B' is

A. Rs. 2500
B. Rs. 3800
C. Rs.2300
D. Rs. 4000

Question 97

A bag contain equal number of 1 rupee, 50 paisa and 25 paisa coins. If the total amount is Rs 105, then how many coins of each type are there?

A. 15
B. 45
C. 60
D. 80

Question 98

A bag contains 25 paise, 50 paise and 1 Rs coins. There are 220 coinsinall and the total amount in the bag is Rs. 160. If there arethrice as many 1 Rs. coins as there are 25 paise coins, then what is the number of 50 paise coins?

A. 60
B. 40
C. 120
D. 80

Question 99

A bag contains coins of denominations Rs.1, Rs.5 and Rs.10. Assuming there are equal number of Rs.1, Rs.5 and Rs.10, what will be the total number of coins in the bag be if the total money is Rs. 368?

A. 69
B. 96
C. 56
D. 65

Question 100

A bag has Rs 30.8 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio of 6:3:2. What is the number of 50 paise coins?

A. 8
B. 24
C. 12
D. 4

Question 101

A box weighs 8.5 kg when full of sand and weighs 5.5 kg when it is half filled with sand . Weight of the empty box is

A. 5 kg
B. 6 kg
C. 2.5 kg
D. 4.5 kg

Question 102

A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area of the circle?

A. 308 sq cm
B. 462 sq cm
C. 154 sq cm
D. 616 sq cm

Question 103

A class consists of both boys and girls along with a teacher. After a class, the teacher drinks 9 litres of water, a boy drinks 7 litres of water and a girl drinks 4 litres of water. If after a class 42 litres of water was consumed, find the number of girls in the class ?

A. 8
B. 6
C. 5
D. 3

Question 104

A complete factorisation of x4 + 64 is

A. (x2 + 8)2
B. (x2 + 8)(x2 - 8)
C. (x2 - 4x + 8)(x2 -4x - 8)
D. (x2 + 4x + 8)(x2 - 4x + 8)

Question 105

A factory produced 18,58,509 cassettes in the month of January, 7623 more cassettes in the month of February and owing to short supply of electricity produced 25,838 less cassettes in March than in February. Find the total production in all?

A. 55,57,312
B. 59,83,245
C. 55,64,935
D. 56,08,988

Question 106

A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :

A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds

Question 107

A fraction is greater than its reciprocal by (72)/(77). What is the fraction?

A. 7/11
B. 11/7
C. 4/7
D. 7/4

Question 108

A fraction, when taken away from 1/3 gives 1/12. The fraction is

A. 5/12
B. 1/4
C. 3/4
D. 1/9

Question 109

A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to

A. 7 km/hr
B. 11 km/ hr
C. 26 km/hr.
D. 33 km/hr

Question 110

A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?

A. (6/11, 9/11)
B. (6/7, 9/7)
C. (6/11, -9/11)
D. (-6/7, 9/7)

Question 111

A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?

A. (18/13, 12/13)
B. (18/13, -12/13)
C. (-18/13, -12/13)
D. (-18/13, 12/13)

Question 112

A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5 Km/hr. If he covers the same distance on cycle at the rate of 24 Km/hr, then the time taken by him in minutes is

A. 40
B. 45
C. 50
D. 55

Question 113

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?

A. 15
B. 20
C. 10
D. 8

Question 114

A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.10.25, then the number of 20-paise coins is

A. 42
B. 45
C. 38
D. 36

Question 115

A man spends in 8 months as much as he earns in 6 months. He saves Rs. 6000 in a year. His average monthly income is

A. Rs. 2400
B. Rs. 2000
C. Rs. 2150
D. Rs. 1800

Question 116

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?

A. 10 m
B. 14 m
C. 12 m
D. 8 m

Question 117

A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?

A. 35/3
B. 37/3
C. – 105/11
D. – 105/13

Question 118

A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?

A. 88572
B. 77854
C. 99584
D. 55654

Question 119

A ship is full of cargo containers. It drops 2/3 of cargo containers at the first port and takes 60 more, at the second port it drops two third of the new total and takes eleven more. On arriving at the third port it is found that it have 48 cargo containers. Find the number of cargo containers in the ship at the starting?

A. 189
B. 159
C. 161
D. 153

Question 120

A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is

A. 5
B. 10
C. 20
D. 22

Question 121

A. 4250
B. 4000
C. 8005
D. 8000

Question 122

A T.V was sold at a profit of 5% If it had been sold at a profit of 10% , the profit would have been Rs. 1000 more. What is its cost price ?

A. Rs.20000
B. Rs.5000
C. Rs.10000
D. Rs.15000

Question 123

A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?

A. 300
B. 150
C. 175
D. 200

Question 124

A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:

A. 28 litres
B. 32 litres
C. 35 litres
D. 42 litres

Question 125

A telephone bill costs Rs.13 for 19 minutes. What is the cost in rupees for 15 minutes 50 seconds?(rounded to one decimal)

A. 10.8
B. 10.7
C. 10.6
D. 10.9

Question 126

A tetrahedron has 4 vertices. How many edges does it have?

A. 8
B. 12
C. 6
D. 10

Question 127

A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60 and 45 deg respectively. What is the height (in metres) of tower?

A. 20√3
B. 30(√3 + 1)
C. 40(√3 – 1)
D. 50(√3 – 1)

Question 128

A triangular prism has 9 edges. How many vertices does it have?

A. 8
B. 6
C. 12
D. 10

Question 129

A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value ofA2 + 2AB + AB2?

A. 96475
B. 98625
C. 92425
D. 89125

Question 130

A, B and C are three points on a circle with centre O. The tangent at C meets BA produced at T. If ∠ATC = 30° and ∠ACT = 48°,then what is the value of ∠AOB ?

A. 78°
B. 96°
C. 102°
D. 108°

Question 131

A, B and C can finish a job working alone in 72, 24 and 36 days respectively. In how many days they can finish the job if they worked together?

A. 12
B. 9
C. 15
D. 18

Question 132

AB is a diameter of a circle. C is a point on the tangent drawn at A . If AB = 8 cm and AC = 6 cm , then the length of BC is

A. 10 cm
B. 14 cm
C. 5 cm
D. 7 cm

Question 133

AB is the diameter of a circle with center O and P be a point on its circumference. If ∡POA = 120°, then the value of ∡PBO is

A. 30°
B. 60°
C. 50°
D. 40°

Question 134

ABC is a right angled triangle. ∠BAC = 90 deg and ∠ACB = 60 deg. What is the ratio of the circum radius of the triangle to the side AB?

A. 1 : 2
B. 1 : √3
C. 2 : √3
D. 2 : 3

Question 135

ABCD is a parallelogram. Co-ordinates of A, B and C are (5,0), (-2,3) and (-1,4) respectively. What will be the equation of line AD?

A. y = 2x - 5
B. y = x + 5
C. y = 2x + 5
D. y = x - 5

Question 136

Along a yard 225 metres long, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees

A. 8
B. 9
C. 10
D. 11

Question 137

An aeroplane flying horizontally at a height of 3 Km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is

A. 230.63 m/sec
B. 230.93 m/sec
C. 235.85 m/sec
D. 236.25 m/sec

Question 138

An angle is four times its complementary angle. What is the measure of the angle?

A. 72°
B. 108°
C. 54°
D. 36°

Question 139

An angle is greater than its complementary angle by 30°. Find the measure of the angle?

A. 30°
B. 90°
C. 60°
D. 120°

Question 140

An angle is thrice its complementary angle. What is the measure of the angle?

A. 22.5°
B. 135°
C. 45°
D. 67.5°

Question 141

An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was

A. 1500000
B. 1000000
C. 1200000
D. 1100000

Question 142

An owner of a Dry fruits shop sold small packets of mixed nuts for Rs. 150 each and large packets for Rs. 250 each. One day he sold 5000 packets, for a total of Rs. 10.50 lakh. How many small packets were sold ?

A. 2000
B. 3000
C. 2500
D. 3500

Question 143

Anuj runs 1 2/3 laps of 7 laps race, find the remaining laps to be run.

A. 16/3
B. 14/3
C. 11/3
D. 10/3

Question 144

Arrange them in ascending order 64, 33 and 43

A. 33 < 64 > 43
B. 33 > 64 > 43
C. 33 > 43 > 64
D. 33 < 64 < 43

Question 145

At what point does the line 2x - 3y = 6 cuts the Y axis?

A. (0, 2)
B. (-2, 0)
C. (2, 0)
D. (0, -2)

Question 146

At what point does the line 2x + 5y = -6 cuts the X-axis?

A. (3, 0)
B. (0, 3)
C. (-3, 0)
D. (0, -3)

Question 147

At what point does the line 3x + 2y = 12 cuts the Y-axis?

A. (0, 6)
B. (0, -6)
C. (6, 0)
D. (-6, 0)

Question 148

At what point does the line 3x + 2y = -12 intercept the Y-axis?

A. (0,6)
B. (0,-6)
C. (-4,0)
D. (4,0)

Question 149

ax + 3y = 6 has slope -2/3. What is the value of a?

A. -2
B. 2
C. 3
D. -3

Question 150

By how much is three-fifth of 350  greater than four-seventh of 210 ?

A. 90
B. 100
C. 110
D. 120

Question 151

CAlculate : 72-6-45÷5-72-2×2÷2+2

A. -16/18
B. -14/7
C. -12/7
D. -12/18

Question 152

Calculate the angle subtended by the chord at the point on the major arc if the radius and the chord of the circle are equal in length.

A. 30°
B. 120°
C. 200°
D. 300°

Question 153

Calculate the sum of squares from 1 to 9.

A. 284
B. 285
C. 385
D. 380

Question 154

Calculate the value of 0.77777 + 0.7777 + 0.777 + 0.77 + 0.7 + 0.07.

A. 3.86274
B. 3.80247
C. 3.85274
D. 3.87247

Question 155

Calculate the value of √3√3 + 3, if √3 = 1.732

A. 0.366
B. 0.566
C. 0.356
D. 0.346

Question 156

Calculate the value of 55-5, if the value of √5 = 2.236.

A. 0.809
B. 0.89
C. 0.089
D. 0.807

Question 157

Calculate the value of 61681 x 61681 - 31681 x 3168130000?

A. 93352
B. 94362
C. 93362
D. 95362

Question 158

Calculate the value of 61681x61681-31681x3168130000

A. 93352
B. 94362
C. 93362
D. 95362

Question 159

A crate of egg holds one rotten egg out of every 25 egg in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate,then calculate the number of eggs in the crate.

A. 380
B. 400
C. 420
D. 440

Question 160

Divya and Kriti have total 46 candies. If Divya has 10 candies more than kriti, then find the total number of candies Divya have?

A. 20
B. 24
C. 28
D. 32

Question 161

Expand : S + 23

A. S3+3S2+12S+8
B. S3+3S2+6S+8
C. S3+6S2+12S+8
D. S3+6S2+6S+8

Question 162

Expand and simplify (3x + 2)2*(4x -­ 3) -­ (2x3 - 9x2 + 12x -­ 24)

A. 34x3 + 30x2 -­ 32x -­ 12
B. 34x3 + 30x2 -­ 32x + 12
C. 34x3 -­ 30x2 -­ 32x + 12
D. 34x3 -­ 30x2 + 32x -­ 12

Question 163

Expand and simplify (x + 4)2 + (x -­ 2)2

A. 2(x2 + 2x + 10)
B. 2(x2 + 2x -­ 10)
C. 2(x2 -­ 2x + 10)
D. 2(x2 -­ 2x ­- 10)

Question 164

Expand and simplify (x + 5)2 + (x - 3)2

A. 2(x2 + 2x - 17)
B. 2(x2 - 2x + 17)
C. 2(x2 - 2x - 17)
D. 2(x2 + 2x + 17)

Question 165

Expanded and simplification of (x + 3)(x - 1) will be equal to

A. x2+ 2x - 3
B. x2 + 3x + 2
C. x2 - 2x + 3
D. x2 + 3x - 2

Question 166

Factorise 24x2 - 54x - 15

A. 3(2x + 5)(4x - 1)
B. 3(2x - 5)(4x + 1)
C. 2(3x - 5)(4x + 1)
D. 4(2x - 5)(3x + 1)

Question 167

Factorise x2 + 3x -­ 18

A. (x+18)(x-­1)
B. (x­-1)(x+18)
C. (x+6)(x-­3)
D. (x-­6)(x+3)

Question 168

Factors of 48x3- 8x2- 93x- 45 are

A. (4x + 3)(4x ­- 3)(3x ­- 5)
B. (4x -­ 3)(4x -­ 3)(3x-­ 5)
C. (4x + 3)(4x + 3)(3x -­ 5)
D. (4x -­ 3)(4x + 3)(3x + 5)

Question 169

Factors of  x2 + 7x + 10 are

A. (x-5)(x-2)
B. (x+5)(x+2)
C. (x-5)(x+2)
D. (x-4)(x+2)

Question 170

Find co-ordinates of the mid point of the segment joining points C (3,-5) and D (-7,3).

A. (-2, -1)
B. (5, -4)
C. (-5, 4)
D. (2, 1)

Question 171

Find equation of the perpendicular bisector of segment joining the points (2,­6) and (4,0)?

A. x + 3y = 6
B. x + 3y = -­6
C. x -­ 3y = -­6
D. x ­- 3y = 6

Question 172

Find k, if the line 2x- ­3y = 11 is perpendicular to the line 3x + ky = -­4?

A. -2
B. 1
C. -1
D. 2

Question 173

Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?

A. 20
B. -20
C. 4
D. -4

Question 174

Find length of the arc whose central angle is 45° and radius of the circle is 28 cm?

A. 11 cm
B. 33 cm
C. 44 cm
D. 22 cm

Question 175

Find the common factor of (3757+4357) and (3737+4337) ?

A. (43 - 37)
B. (43 + 37)
C. (37 + 37)
D. 10

Question 176

Find the common factor of 3757+ 4357 and 3737+ 4337

A. (43 - 37)
B. (43 + 37)
C. 37
D. 10

Question 177

Find the degree of the polynomial 8x4 + 2x2y3 + 4

A. 4
B. 5
C. 0
D. 1

Question 178

Find the greatest number that will divide 390, 495 and 300 without leaving a remainder

A. 5
B. 15
C. 25
D. 35

Question 179

Find the products : 0.5 x 0.05 x 0.005 x 500

A. 0.0625
B. 0.00625
C. 0.06255
D. 0.625

Question 180

Find the roots of the quadratic equation 27x2 + 57x  -­ 14 = 0

A. ­2/9, 7/3
B. 2/9, ­-7/3
C. 9/2, ­-3/7
D. -9/2, 3/7

Question 181

Find the sum of interior angles of a dodecagon?

A. 1620°
B. 1800°
C. 1440°
D. 1260°

Question 182

Find the unit digit in the given product (4211)102 x (361)52.

A. 3
B. 1
C. 4
D. 7

Question 183

Find the unit place digit in 192102 + 193103

A. 0
B. 1
C. 3
D. 5

Question 184

Find the unit place in 194102+294103

A. 0
B. 6
C. 8
D. 2

Question 185

Find the value of '?' in 512 × 125 ÷ 15625 = 3125 × 25?

A. 4
B. 3
C. 2
D. 1

Question 186

Find the value of 0.0112 - 0.0012 of 0.14 + 0.25 × 0.20.02 × 0.01

A. 257
B. 25.7
C. 2.57
D. 0.0257

Question 187

Find the value of 1006×994?

A. 999932
B. 999964
C. 1000032
D. 1000064

Question 188

Find the value of 200 x 20 x 2 x 0.2 x 0.02 x 0.002 = ?

A. 0.064
B. 0.64
C. 64
D. 640

Question 189

Find the value of 6732.8 + 673.28 + 67.328 + 6.7328 + 0.67328 ?

A. 74808.1408
B. 7480.78408
C. 74808.2408
D. 7480.81408

Question 190

Find the value of 'a' for which x+3x+a24 is a perfect square.

A. √3
B. 2√3
C. 3√3
D. 4√3

Question 191

Find the value of p if ­-3x -­ 11, x + p and 5x + 7 are in arithmetic progression.

A. 9
B. 2
C. -9
D. -2

Question 192

Find the value of x if 0.08x + 0.04y = 10 and 0.2(x-1) + 0.4y = 24.8

A. 125
B. 150
C. 1.25
D. 12.5

Question 193

Find the value of x if 1-x24 = 1318

A. 155
B. 157
C. 159
D. 161

Question 194

Find the value of 'y' if y84 = 225

A. 10
B. 12
C. 15
D. 18

Question 195

Find the value of  x3 - y3, if x - y = 4 and xy = 12.

A. 198
B. 208
C. 218
D. 228

Question 196

Find the value of  y(y4 - y2 - y) when y = 5.

A. 2900
B. 2975
C. 2925
D. 2995

Question 197

Find the value of 27a3 + 1a3, if 9a2 + 1a2 = 43

A. 240
B. 280
C. 320
D. 360

Question 198

Find the value of 491321973

A. 17/13
B. 13/17
C. 13/7
D. 17/7

Question 199

Find the value of 532+108

A. 732
B. 1732
C. 2732
D. 3732

Question 200

Find the value of 62532+18

A. 1635
B. 2635
C. 3635
D. 4635

Question 201

Find the value of 64344?

A. 1
B. 2
C. 3
D. 4

Question 202

Find the value of 6813+6413314

A. 5
B. 6
C. 36
D. 216

Question 203

Find the value of 777777?

A. 73164
B. 7164
C. 76364
D. 7764

Question 204

Find the value of sin230 cos245 + 4 tan230 + 1/2sin290 - 2 cos290 + 1/24

A. 3
B. 4
C. 2
D. 1

Question 205

Find x, if 5x-6+5x+6 = 6

A. -4
B. 0
C. 2
D. 4

Question 206

For real a, b and c if a2 + b2 + c2 = ab + bc + ca, then find the value of a+b+c2.

A. 9a2
B. 81a2
C. 27a2
D. 243a2

Question 207

For the inequation x^2–7x + 12 > 0, which one of the following is correct ?

A. 3 < x < 4
B. –∞ < x < 3 only
C. 4 < x < ∞ only
D. –∞ < x < 3 or 4 < x < ∞

Question 208

For triangle ABC, find equation of median AD if co­ordinates of points A, B and C are (2,­4), (3,0) and (5,­2) respectively?

A. 3x ­- 2y = 14
B. 3x -­ 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2

Question 209

For triangle ABC, find equation of median AD if co­-ordinates of points A, B and C are (2,­4), (3,0) and (5,­2) respectively?

A. 3x -­ 2y = 14
B. 3x -­ 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2

Question 210

For triangle ABC, what would be the equation of median AD if co-ordinates of A, B and C are (-5,4), (-4,0) and (-2,2) respectively?

A. 3x - 2y = -11
B. 3x + 2y = 7
C. 3x + 2y = -7
D. 3x - 2y = 11

Question 211

For triangle PQR, find equation of altitude PS if co-­ordinates of P, Q and R are (1,2), (2,­-1) and (0,5) respectively?

A. x ­- 3y = ­-7
B. x -­ 3y = -­5
C. x + 3y = ­4
D. x + 3y = ­7

Question 212

For triangle PQR, find equation of altitude PS if co­-ordinates of P, Q and R are (6,2), (0,3) and (­-4,5) respectively?

A. 2x -­ y = 14
B. 2x + y = 10
C. 2x -­ y = 10
D. 2x + y = 14

Question 213

For triangle PQR, what is the equation of altitude PS if co­ordinates of P, Q and R are (5,1), (0,­4) and (­2,3) respectively?

A. 7x + 2y = 33
B. 2x -­ 7y = 9
C. 2x -­ 7y = ­-3
D. 7x + 2y = -­33

Question 214

For what value of C, the system of equation 6x + 2y = 2 & 3x + y = C will be coincident?

A. 4
B. 0
C. 2
D. 1

Question 215

For what value of k, the expression x6– 18x3 + k will be a perfect square?

A. -9
B. 81
C. 9
D. -81

Question 216

For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 = 0 has infinite number of solutions?

A. 3
B. 4
C. 6
D. 9

Question 217

For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?

A. 3
B. 4
C. 6
D. 9

Question 218

For x > 0, what is the minimum value of  x + x+22x?

A. 1
B. 2
C. 2.5
D. 1.5

Question 219

For x = 462+3, what is the value of x+22x-22+x+23x-23

A. 1
B. √2
C. √3
D. 2

Question 220

Geetha weighs 11.235 kg. Her sister weighs 1.4 times her weight. Find their combined weight?

A. 15.729 kg
B. 25.964 kg
C. 26.964 kg
D. 26.946 kg

Question 221

Given 17 x 29 = 493, then 170 x 0.029 = ?

A. 0.0493
B. 4.93
C. 0.493
D. 49.3

Question 222

Given a -­ b = 2, a3 - b3=26 then (a + b)2 is

A. 9
B. 4
C. 16
D. 12

Question 223

Given that 100.48 = x,  100.70 = y and xz = y2,  then the value of z is close to ___ ?

A. 3.7
B. 2.7
C. 3.6
D. 2.9

Question 224

Given that tan(θ + 15°) = √3. Then the value of θ is?

A. 15°
B. 75°
C. 45°
D. 65°

Question 225

Given w = -2, x = 3, y = 0 & z = -1/2. Find the value of (z/w) + x.

A. 13/4
B. -13/4
C. 3.2
D. 3.5

Question 226

Given: 2x - 4 ≤ 2 - x/3 and 2(2x + 5) > 3x - 5, then x can take which of the following values?

A. -14
B. 3
C. 4
D. 14

Question 227

Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

A. 23
B. 24
C. 25
D. 26

Question 228

How many  18' s are there in  3712?

A. 300
B. 400
C. 500
D. 600

Question 229

How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346?

A. 3675
B. 4018
C. 4021
D. 4025

Question 230

If ( x - 5)2 + (y - 2)2 + (z - 9)2 = 0 , then value of (x + y - z) is

A. 16
B. -1
C. -2
D. 12

Question 231

If (1 -­ cosA)/(1 + cosA) = x, then the value of x is

A. (cotA + cosecA)2
B. (cotA -­ cosecA)2
C. cotA -  cosecA
D. cotA + cosecA

Question 232

If (1 - sinA)/(1 + sinA) = x, then x is

A. (cosecA - cotA)2
B. secA - tanA
C. (secA - tanA)2
D. cosecA - cotA

Question 233

If (1 + cosA)/(1 - cosA) = x, then x is

A. cot2A/(secA - 1)2
B. cot2A/(secA + 1)2
C. tan2A/(secA + 1)2
D. tan2A/(secA - 1)2

Question 234

If (1 + cosA)/2 = x, then the value of x is

A. sin(A/2)
B. √sin(A/2)
C. √cos(A/2)
D. cos2(A/2)

Question 235

If (1 + secA)/tanA = x, then x is

A. cot(A/2)
B. tan(A/2)
C. cosec(A/2)
D. sec(A/2)

Question 236

If (1 + sinA)/cosA + cosA/(1 + sinA) = x, then the value of x is

A. 2cosecA
B. 2cosec2A
C. 2sec2A
D. 2secA

Question 237

If (-1/2) * ( x - 5) + 3 = -5/2, then what is the value of x?

A. 16
B. 4
C. -6
D. -4

Question 238

If (1/4 of x) - (4/5 of 6/7) equals - 9/7, then value of x is

A. -12
B. -2.4
C. -3.6
D. -14

Question 239

If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ?

A. (P + 1)/(P – 1)
B. (P2+ 1)/2P
C. 2(P2+ 1)/P
D. 2P/(P2+ 1)

Question 240

If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?

A. 81
B. 361
C. 729
D. 6561

Question 241

If (23)2= 4x then 3x is equal to

A. 3
B. 6
C. 9
D. 27

Question 242

If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?

A. 34
B. 35
C. 33
D. 33.5

Question 243

If (36 - 16x) - (4x - 8) = 4, then the value of x is

A. 4
B. 2
C. 6
D. 3

Question 244

If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct ?

A. a/b = c/d
B. a/d = c/b
C. a/b = d/c
D. none

Question 245

If (4x - 3) - (2x + 1) = 4, then the value of x is

A. 0
B. 1
C. 2
D. 3

Question 246

If (4x - 3) = (3x + 8), then the numerical value of(x + 1)3  is

A. 1331
B. 1000
C. 1728
D. 729

Question 247

If (4x -­ 5) = (3x ­- 1), then the numerical value of (x + 4)2

A. 16
B. 64
C. 32
D. 8

Question 248

If (5/9 of x) ­- (2/5 of 9/4) equals ­ -4/5 then find x.

A. 0.18
B. 0.12
C. 2
D. 0.54

Question 249

If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2 – 4xy)/(9x2 + 16y2 + 24xy) ?

A. 0
B. 3/7
C. 18/49
D. 1/6

Question 250

If (6 ­- 18x) -­ (x ­- 7) = 8, then the value of x is ______.

A. -5/19
B. -2/13
C. 2/13
D. 5/19

Question 251

If (6x ­- 1) -­ (8x -­ 5) = 7, then the value of x is _______ .

A. -3/2
B. 3/2
C. 11/2
D. -11/2

Question 252

If (6x ­- 5) = (4x + 7), then the numerical value of (x + 1)3  is

A. 216
B. 125
C. 64
D. 343

Question 253

If (7x -­ 13) ­ (12x + 3) = 14, then the value of x is ______ .

A. -6
B. 6
C. -2/5
D. 2/5

Question 254

If (8 - 10x) - (13x - 2) = -9, then the value of x is

A. -19/23
B. 19/23
C. -1/23
D. 1/23

Question 255

If (8x ­- 4) = (3x + 6), then the numerical value of (x + 1)3 is

A. 3
B. 9
C. 27
D. 81

Question 256

If (9 - 3x) - (17x - 10) = -1, then the value of x is

A. 1
B. -1
C. 9/10
D. -0.9

Question 257

If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?

A. 9/5
B. 11/7
C. 7/11
D. 7/4

Question 258

If (cosecA -­ 1)/(cosecA + 1) = x, then the value of x is

A. (sinA/(1 + cosA))2
B. cosA/(1 + sinA)
C. (cosA/(1 + sinA))2
D. sinA/(1 + cosA)

Question 259

If (cotA - cosecA)2 = x, then the value of x is

A. (1 - cosA)/(1 + cosA)
B. (1 - sinA)/(1 + sinA)
C. (1 - secA)/(1 + secA)
D. (1 - cosecA)/(1 + cosecA)

Question 260

If (cotAcotB - 1) / (cotB + cotA) = x, then the value of x is

A. cot(A - B)
B. tan(A + B)
C. cot(A + B)
D. tan(A - B)

Question 261

If (sinA + CosA)/(sin A - cos A) = 5/4, the value of (tan2A + 1)/(tan2A - 1) = ?

A. 41/40
B. 12/13
C. 40/41
D. -31/49

Question 262

If (tanA ­- tanB)/(1 + tanAtanB) = x, then the value of x is

A. tan(A -­ B)
B. tan(A + B)
C. cot(A ­- B)
D. cot(A + B)

Question 263

If (tanA + tanB)/(1 ­ tanAtanB) = x, then the value of x is

A. tan(A + B)
B. tan(A -­ B)
C. cot(A + B)
D. cot(A ­- B)

Question 264

If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?

A. k1 = 6, k2 = – 1
B. k 1 = 1, k 2 = – 6
C. k 1 = 1, k2 = 6
D. k1 = – 6, k2 = 1

Question 265

If (x – y) = 7, then what is the value of (x – 15)3 – (y – 8)3?

A. 0
B. 343
C. 392
D. 399

Question 266

If (x + 1/x) = 3, then x8+1x8 is equal to

A. 2201
B. 2203
C. 2207
D. 2213

Question 267

If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x3 + y3+ z3?

A. 104
B. 144
C. 196
D. 288

Question 268

If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?

A. 0
B. 1
C. 2
D. – 1

Question 269

If (x ­- 2) (x -­ p) = x2 - ax + 6, then the value of (a -­ p) is

A. 0
B. 1
C. 2
D. 3

Question 270

If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?

A. 5
B. 9
C. 15
D. 20

Question 271

If (x - 4) (x2 + 4x + 16) = x3 - P, then P is equal to

A. 27
B. 8
C. 64
D. 0

Question 272

If (x/5) + (5/x) = – 2, then what is the value of x3?

A. –125
B. 5
C. 1/125
D. 625

Question 273

If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?

A. ( b + 3 a)/( a – 3 b)
B. ( a + 3 b)/( b – 3 a)
C. (1 + 3 a)/( a + 3 b)
D. ( a + 3 b2)/( b – 3 a2)

Question 274

If (x/y)a-4 = (y/x)2a-5, then what is the relation between x and y?

A. x > y
B. Cannot be determined
C. x < y
D. x = y

Question 275

If (x+1/x) = 5, then the value of 5xx2+5x+1?

A. 1/3
B. 1/4
C. 1/2
D. 1/5

Question 276

If (x+a) is the H.C.F of 2x2+5x-12 and x2+x-12 then find the value of a.

A. -3
B. -2
C. 4
D. 5

Question 277

If (x2/yz) + (y2/zx) + (z2/xy) = 3, then what is the value of (x + y + z)3?

A. 0
B. 1
C. 2
D. 3

Question 278

If [2(4x/5 - 3/4)]/3 - 5/3 = -1/6, then the value of x is?

A. 4/15
B. -15/4
C. -4/15
D. 15/4

Question 279

If [4(2x/5 - 3/2)]/3 + 7/5 = 37/5, then what is the value of x?

A. -15
B. 7/5
C. 15
D. -7/5

Question 280

If [7(5x/3 - 3/2)]/2 + 3/2 = 1/4, then what is the value of x?

A. 35/24
B. 24/35
C. -24/35
D. -35/24

Question 281

If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?

A. – 8 + √3
B. – 8 – √3
C. – 8 + √5
D. None of these

Question 282

If √(1 - cos2A) = x, then the value of x is

A. cosecA
B. sinA
C. tanA
D. secA

Question 283

If √(1 - sin2A) = x, then the value of x is

A. tanA
B. cosA
C. cosecA
D. secA

Question 284

If √(1 + cot2A) = x, then the value of x is

A. secA
B. sinA
C. cosecA
D. cosA

Question 285

If √(1 + cot2A)/cotA = x, then the value of x is

A. sinA
B. cosecA
C. secA
D. cosA

Question 286

If √(1+tan2A) = x, then the value of x is

A. sinA
B. cosecA
C. secA
D. cosA

Question 287

If √(cosec2A - 1) = x, then the value of x is

A. tanA
B. sinA
C. cosA
D. cotA

Question 288

If √(sec2A ­ 1) = x, then the value of x is

A. cotA
B. tanA
C. cosecA
D. cosA

Question 289

If √[(1 - cosA)/2] = x, then the value of x is

A. cos(A/2)
B. tan(A/2)
C. sin(A/2)
D. cot(A/2)

Question 290

If √[(1 + cosA)/2] = x, then find the value of x.

A. sin(A/2)
B. tan(A/2)
C. cot(A/2)
D. cos(A/2)

Question 291

If √20 + √125 = 15.65, then what is the value of √45 + √5?

A. 6.98
B. 8.94
C. 9.98
D. 11.27

Question 292

If √3 = 1.732, then the value of 9+233?

A. 7.169
B. 7.196
C. 5.198
D. 7.296

Question 293

If √5 = 2.236, then √5/2 is

A. 1.851
B. 1.118
C. 2.236
D. 1.782

Question 294

If √x ­- √y = 1 , √x + √y = 17 then √xy = ?

A. √72
B. 72
C. 32
D. 24

Question 295

If 1 + (1/2) + (1/3) + ... + (1/20) = k, then what is the value of (1/4) + (1/6) + (1/8) + ... + (1/40)?

A. k/2
B. 2k
C. (k – 1)/2
D. (k + 1)/2

Question 296

If 1 + secA = x, then the value of x is

A. sinAtanA/(1 + cosA)
B. √[sinAtanA/(1 - cosA)]
C. sinAtanA/(1 - cosA)
D. √[sinAtanA/(1 + cosA)]

Question 297

If 1 = 2, 3 = 6, 4 = 8, and + = -, what would be the value of 41 + 34 + 13 = ?

A. -88
B. 88
C. 12
D. -12

Question 298

If 1/(1 + cosA) + 1/(1 ­- cosA) = x , then value of x is

A. 2sec2A
B. 2cosecA
C. 2cosec2A
D. 2secA

Question 299

If 1/(cosecA ­ cotA) = x, then the value of x is

A. cosecA + cotA
B. cosecA­ - cotA
C. cosec2A + cot2A
D. √[cosec2A + cot2A]

Question 300

If 1/(tanA + cotA) = x, then value of x is

A. cosAsinA
B. cos2Asin2A
C. cosecAsecA
D. cosec2Asec2A

Question 301

If 1/√(1 -­ sin2A) = x, then the value of x is

A. tanA
B. cosecA
C. secA
D. cosA

Question 302

If 1/√(1 + cot2A) = x, then value of x is

A. sinA
B. cosecA
C. cosA
D. secA

Question 303

If 1/√(1+tan2A) = x, then value of x is

A. cosA
B. sinA
C. cosecA
D. secA

Question 304

If 1/√(cosec2A - 1) = x, then value of x is

A. cotA
B. tanA
C. sinA
D. cosA

Question 305

If 1/2 is added to a number and the sum is multipled by 3, the result is 21. Then the number is

A. 6.5
B. 5.5
C. 4.5
D. -6.5

Question 306

If 1/3(12x/5 - 1/2) + 6/5 = 7/6, then what is the value of x?

A. 1/6
B. -1/6
C. 1/5
D. -1/5

Question 307

If 1/6 of x - 7/2 of 3/7 equals - 7/4, then the value of x is

A. -1.5
B. 3
C. -2.5
D. 6

Question 308

If 10x/3 + 5/2(2 - x/3) = 7/2, then the value of x is?

A. 3/5
B. -5/3
C. 5/3
D. -3/5

Question 309

If 123 x 356 = 43788, then 1.23 x 0.356 = ?

A. 437.88
B. 4.3788
C. 0.43788
D. 0.043788

Question 310

If 12x = 192- 112, what is the value of x?

A. 20
B. 17
C. 13
D. 11

Question 311

If 13x2 = 172 - 92, find the value of x?

A. 16
B. 12
C. 8
D. 4

Question 312

If 14.35 - (1.956 - x ) - 83.92 = 3.858 then what is the value of x?

A. -92.456
B. 75.384
C. 71.472
D. 104.084

Question 313

If 14/3 + (1/2)(x - 7/3) = -2x/3, then the value of x is?

A. -3
B. 3
C. -6
D. 6

Question 314

If 16% of an electricity bill is deducted, Rs 1806 is still to be paid. How much was the bill?

A. Rs 1557
B. Rs 2186
C. Rs 1593
D. Rs 2150

Question 315

If 17/3 + [3(2x - 5/3)]/2 = 1/6, then what is the value of x?

A. 1
B. 3
C. -3
D. -1

Question 316

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

A. 1 or 3/5
B. 1 or –1/2
C. –1 or–1/2
D. –1 or 3/5

Question 317

If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?

A. 500
B. 1000
C. 1500
D. 2000

Question 318

If 2(3x-2) < 6-3x and 6x + 2(6-x) > 2x-2, then x can take which of the following values?

A. -8
B. 5
C. 8
D. -5

Question 319

If 2/3(6x/5 - 1/4) + 1/3 = 9x/5, then what is the value of x?

A. 1/6
B. -1/6
C. 1/5
D. -1/5

Question 320

If 22x - 40 = 207 + 3x, then x = ?

A. 14
B. 13
C. 12
D. 11

Question 321

If 23x + 23y = 184, then what is the average of x and y?

A. 2
B. 4
C. 3
D. 2.5

Question 322

If 2560.256 = 25.6x, then what will be the value of x?

A. 2.56
B. 25.6
C. 0.256
D. 0.0256

Question 323

If 27x + 27[x–(1/3)] = 972, then what is the value of x?

A. 2
B. 3
C. 4
D. 5

Question 324

If 2cos2A - 1 = x, then the value of x is

A. cosec4A - sin4A
B. cos4A - sin4A
C. cos4A - tan4A
D. cosec4A - tan4A

Question 325

If 2cosAsinB = x, then the value of x is?

A. sin(A+B) + sin(A­-B)
B. cos(A+B) + cos(A­-B)
C. sin(A+B) ­- sin(A-­B)
D. cos(A­-B) -­ cos(A+B)

Question 326

If 2cosec2A = x, then the value of x is

A. 1/(1 - cosecA) - 1/(1 + cosecA)
B. 1/(1 + sinA) + 1/(1 - tanA)
C. 1/(1 + cosA) + 1/(1 - cosA)
D. 1/(1 - tanA) - 1/(1 + sinA)

Question 327

If 2secA - (1 + sinA)/cosA = x, then the value of x is

A. cosecA/(1+sinA)
B. cosA/(1+sinA)
C. cosA(1+sinA)
D. cosecA(1+sinA)

Question 328

If 2x - 3 = 3x - 5, then the numerical value of  (x - 3)2 is

A. 5
B. 1
C. -5
D. -1

Question 329

If 2x - 5y = 5 and 2x - y = 9, then x - y is ______.

A. 2
B. 4
C. 6
D. 3

Question 330

If 2x - 6 ≤ x - 3 and 1+3x < 4x + 4, then x can take which of the following values?

A. 4
B. -4
C. -6
D. 2

Question 331

If 2x + (9/x) = 9, then what is the minimum value of x2+1x2 = ?

A. 95/36
B. 97/36
C. 87/25
D. 623/27

Question 332

If 2x + 3 = 9 then find the value of 3x + 2

A. 12
B. 16
C. 13
D. 11

Question 333

If 2x + 3(5-2x) > 2 - 3x < 2x - x/3, then x can take which of the following values?

A. 0
B. -2
C. -4
D. 2

Question 334

If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?

A. 32
B. 52
C. 64
D. 46

Question 335

If 2x + 3y = 0 and 3x ­- 4y = 34, then x ­- y = ______

A. 10
B. -10
C. 2
D. -2

Question 336

If 2x + 5 > 2 + 3x and 2x -­ 3 ≤ 4x -­ 5, then x can take which of the following values?

A. -2
B. 2
C. -4
D. 4

Question 337

If 2x + 6y = 3xy and 10x -­ 3y = 4xy, find x, y.

A. 3, 2
B. 2, 3
C. 4, 6
D. 6, 4

Question 338

If 2x- 3(4-2x) < 4x - 5 < 4x + 2x/3, then x can take which of the following values?

A. 2
B. 8
C. 0
D. -8

Question 339

If 2x -3(x + 2) < 5 - 2x < -x + 2, then find the value of x.

A. 2
B. 0
C. 10
D. 12

Question 340

If 2x + 3y3x - 4y = 117, then the value of x/y is __

A. 65/19
B. 68/19
C. 67/19
D. 64/19

Question 341

If 2x/3 - [5(4x/5 - 4/3)]/2 = 1/3, then what is the value of x?

A. 9/4
B. 4/9
C. -9/4
D. -4/9

Question 342

If 2x+ 4(x - 3) < -2 - x < 2x - 1, then find the value of x.

A. -1
B. 1
C. 2
D. -2

Question 343

If 3 dozen guavas cost Rs. 90, how many guavas can be bought for Rs. 240?

A. 98
B. 96
C. 102
D. 90

Question 344

If 3 tan θ = cot θ where 0 < θ < π/2, then what is the value of θ ?

A. π/6
B. π/4
C. π/2
D. 1

Question 345

If 3.352 -­ (9.759 -­ x ) -­ 19.64 = 7.052, then what is the value of x?

A. -6.181
B. 13.581
C. 33.099
D. 39.803

Question 346

If 3.5x = 0.07y, then find the result of [y-x / y+x]

A. 51/49
B. 49/53
C. 49/51
D. 53/57

Question 347

If -3/2 + (2/3)(3x + 9) = x/2, then what is the value of x?

A. -9
B. 11
C. 9
D. -3

Question 348

If -3[1-(x/2)] + 5x/3 = 1/6, then what is the value of x?

A. 2
B. -1
C. 1
D. -2

Question 349

If 3√2 + √18 + √50 = 15.55, then what is the value of √32 + √72?

A. 13.22
B. 10.83
C. 14.13
D. 16.54

Question 350

If 3√7 + √343 = 19.21, then find the value of √252 + 20√7.

A. 39.4
B. 49.9
C. 56.8
D. 92.3

Question 351

If 31x + 31y = 403, then what is the average of x and y?

A. 3.5
B. 5
C. 6.5
D. 13

Question 352

If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2?

A. 0
B. 2
C. 4
D. 6

Question 353

If 3P/5 = 7Q/2 = 7R/5, then what is the ratio of p, Q and R respectively?

A. 3 : 2 : 5
B. 3 : 35 : 14
C. 5 : 7 : 5
D. 35 : 6 : 15

Question 354

If 3x - 10 = -(2x + 5), then the numerical value of (x - 4)3 is

A. 27
B. 125
C. -125
D. -27

Question 355

If 3x -­ 7 = 5x ­- 1, then the numerical value of (x ­- 4)2 is

A. 1
B. 49
C. -1
D. -49

Question 356

If 3x - 8(2 - x) = -19, then the value of x is

A. -3/11
B. -33/11
C. -3/5
D. -33/5

Question 357

If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2+ 15x + 1)?

A. 1/5
B. 1/10
C. 2/5
D. 10

Question 358

If 3x + 2y = 7 and 4x - y = 24, then x - y = ______.

A. 9
B. 1
C. -9
D. -1

Question 359

If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9?

A. 18
B. – 9
C. – 27
D. – 18

Question 360

If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?

A. – 28
B. – 14
C. – 31
D. – 45

Question 361

If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

A. 4
B. 2
C. 3
D. 5

Question 362

If 3x^2 + ax + 4 is perectly divisible by x - 5, then the value of a is :

A. -5
B. -15.8
C. -12
D. -15.6

Question 363

If 3x= 4y= 12, then z is equal to

A. xy
B. x + y
C. xy/x+Y
D. 4x +3y

Question 364

If 3x2 - ax + 6 = ax2 + 2x + 2 has only one (repeated) solution, then the positive integral solution of a is

A. 4
B. 5
C. 2
D. 3

Question 365

If 3x2 = 102 - 52, find the value of x?

A. 7
B. 5
C. 9
D. 11

Question 366

If 4(2x - ­4) -­ 2 > 3x -­ 1 ≥ 4x - ­7, then x can take which of the following values?

A. 7
B. 6
C. 2
D. 0

Question 367

If 4(2x + 3) > 5 -­ x and 5x - ­3(2x­ - 7) > 3x -­ 1, then x can take which of the following values?

A. 6
B. -1
C. 5
D. -6

Question 368

If 4(4x + 5) > 2x - 1 > 4x - 3, then the value of x is

A. 2
B. 3
C. -2
D. 0

Question 369

If 4(x+y) = 256 and (256)(x-y) = 4, then what is the value of x and y?

A. 17/8, 15/8
B. 17/4, 15/4
C. 9/17, 15/17
D. 8/17, 8/15

Question 370

If 493/29 = 17, then 4.93/0.0017 = ?

A. 290
B. 0.29
C. 2.9
D. 2900

Question 371

If 4x - 7y = 3 and 2x - y = 9, then x - y is.

A. 3
B. 4
C. 5
D. 6

Question 372

If 4x + 3y = 11 and 3x + 2y = 8, then (x,y) is

A. 2, 0
B. 1, 6
C. 2, 1
D. 5, 6

Question 373

If 4x + 5y = 14 and x - 5y = 16 then the value of x and y are

A. 10 and -6/5
B. 6 and 2
C. 10 and 6/5
D. 6 and -2

Question 374

If 4x = √5+ 2, then the value of x - 1/16x is

A. 1
B. -1
C. 4
D. 2√5

Question 375

If 4x2= 152- 92, then value of x is

A. 9
B. 6
C. 3
D. 12

Question 376

If 5 ­ 3x < 4 ­ x and 5(2 ­ x) > 2 ­ 2x, then x can take which of the following values?

A. 0
B. 1
C. 3
D. -1

Question 377

If 5 -­ 5x < 4 -­ x and 2 -­ x < 6 -­ 4x, then x can take which of the following values?

A. 1
B. 2
C. -1
D. -2

Question 378

If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?

A. 1
B. 2
C. 3
D. 4

Question 379

If 5 sin2θ+ 4 cos2θ= 9/2 and 0 <θ<Π/2 then tanθ is equal to?

A. 1
B. 0
C. -1
D. 1/4

Question 380

If 5(4 - x) - 4 > 5x -2 > 2x - 6, then the value of x is

A. -2
B. 2
C. -1
D. 3

Question 381

If 5/2 - (6/5)(x - 15/2) = -x/5, then what is the value of x?

A. -23/2
B. 13/2
C. -13/2
D. 23/2

Question 382

If 51.97 ­ (81.18 -­ x ) ­- 59.39 = 5.268, then value of x will be

A. - 24.912
B. - 68.492
C. 93.868
D. 197.808

Question 383

If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?

A. 6
B. 8
C. 12
D. 10

Question 384

If 5x - (1/2)(2x -7) = 5.5, then what is the value of x?

A. 3/2
B. 1/2
C. -1/2
D. -3/2

Question 385

If 5x - 4 ≤ 2 - x and 4x + 5 > 2x - 5, then x can take which of the following values?

A. 3
B. 6
C. -7
D. -1

Question 386

If 5x ­- 40 = 3x, then the numerical value of 2x -­ 11 is

A. 29
B. 39
C. 19
D. 9

Question 387

If 5x - ­5(3x ­- 2) < 4x -­ 1 < 2 + 2x, then x can take which of the following values?

A. 2
B. 1
C. -1
D. -2

Question 388

If 5x + 1/x = 10, then x2 + 125x2 is equal to

A. 215
B. 335
C. 315
D. 235

Question 389

If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3  is equal to :

A. 22
B. 23
C. 24
D. 25

Question 390

If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2?

A. 1/600
B. 1/60
C. 1/36
D. 1/360

Question 391

If a + b + c + d = 4, then the value of 1(1-a)(1-b)(1-c) + 1(1-b)(1-c)(1-d) + 1(1-c)(1-d)(1-a) + 1(1-d)(1-a)(1-b)

A. 0
B. 1
C. 4
D. 1+ abcd

Question 392

If a + b + c = 0 , then the value of a3 + b3+ c3 is

A. abc
B. 2abc
C. 3abc
D. 0

Question 393

If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc?

A. 121
B. 168
C. 300
D. 770

Question 394

If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :

A. 10
B. 30
C. 50
D. 70

Question 395

If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)?

A. 0
B. 9
C. 27
D. 3

Question 396

If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?

A. 1/2
B. 5/12
C. 3/4
D. 1/4

Question 397

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?

A. 189
B. 243
C. 361
D. 486

Question 398

If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?

A. 48
B. 24
C. 36
D. 42

Question 399

If a + b = ­ 8 and a2 + b2 = 34, then value of ab is

A. 30
B. 64
C. 98
D. 15

Question 400

If a + b = 1 and ab = -6, then what is the value of a3+ b3?

A. 17
B. 15
C. 19
D. 13

Question 401

If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to

A. 1
B. 2
C. 4
D. 0

Question 402

If a + b = 10 and ab = 21, then the value of (a - b)2 is

A. 15
B. 16
C. 17
D. 18

Question 403

If a + b = 10 and ab = 24, then the value of a3 + b3 is

A. 280
B. 370
C. 520
D. 730

Question 404

If a + b = 10 and ab = 24, then what is the value of a3 + b3?

A. 280
B. 152
C. 140
D. 72

Question 405

If a + b = 10 and ab- 13 = -ba - 11, then what is the value of 3ab + 4a2 + 5b2 ?

A. 450
B. 300
C. 600
D. 750

Question 406

If a + b = 11 and a2+ b2= 61, then value of ab is

A. 12
B. 96
C. 24
D. 30

Question 407

If a + b = 3 and ab = -4, then what is the value of a3 + b3?

A. 36
B. 63
C. 12
D. -15

Question 408

If a + b = 4 and ab = 3, then what is the value of a3 + b3?

A. 21
B. 17
C. 28
D. 31

Question 409

If a + b = 4 and ab = -5, then what is the value of a3 + b3?

A. 34
B. 36
C. 124
D. 126

Question 410

If a + b = 5 and ab = 6, then what is the value of a3 + b3?

A. 32
B. 38
C. 35
D. 34

Question 411

If a + b = 8 and ab = 15, then what is the value of a3 + b3?

A. 98
B. 152
C. 124
D. 260

Question 412

If a + b = 9 and a2+ b2= 61, then ab is

A. 20
B. 10
C. 81
D. 142

Question 413

If A + B = 90 deg and Cos B = 1/3, then the value of Sin A is

A. 1/2
B. 1/4
C. 1/3
D. 2/3

Question 414

If A = (1/0.4) + (1/0.04) + (1/0.004) + ... upto 8 terms, then what is the value of A?

A. 27272727.5
B. 25252525.5
C. 27777777.5
D. 25555555.5

Question 415

If A = (-14 + 4) and B = 4 - 14, then AB =

A. 0
B. -100
C. 100
D. -1

Question 416

If a = √2 + 1 and b = √2 - 1, then the value of 1a+1+1b+1 will be

A. 0
B. 1
C. 2
D. -1

Question 417

If a = √2 + 1, b = √2 - 1 then the value of 1a+1+1b+1 ?

A. 0
B. 1
C. 2
D. 3

Question 418

If a = 1/a-5, then the value of a + 1/a = ?

A. √29
B. √-29
C. - √29
D. √27

Question 419

If a = 2 , b = ­3 then the value of 27a3 - 54a2b + 36ab2 - 8b3 is

A. 1562
B. 1616
C. 1676
D. 1728

Question 420

If a = 299, b = 298, c = 297 then the value of 2a3 + 2b3 + 2c3 - 6abc is

A. 5154
B. 5267
C. 5364
D. 5456

Question 421

If A = 30°, B = 60° and C = 135°, then what is the value of sin3A + cos3B + tan3C – 3sin A cos B tan C?

A. 0
B. 1
C. 8
D. 9

Question 422

If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 – 3abc?

A. 365
B. 444
C. 666
D. 999

Question 423

If A and B are the roots of the equation Ax2 – A2x + AB = 0, then what is the value of A and B respectively?

A. 1, 0
B. 1, 1
C. 0, 2
D. 0, 1

Question 424

If a and b are the roots of the equation Px2 – Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?

A. Q2-2P2R+PPR2
B. Q2-2PRR+PPR2
C. Q2-2R2P+RP2R2
D. Q2-2PR2R+2PP2R2

Question 425

If a rod of length 208 45 is cut into equal pieces of length 23 15 then the total number of rods obtained is

A. 5
B. 8
C. 9
D. 7

Question 426

If a sum of money deposited in a bank at simple interest is doubled in 6 years, then after 12 years, the amount will be

A. 5/2times the original amount
B. 3times the original amount
C. 7/2times the original amount
D. 4times the original amount

Question 427

If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2 )?

A. 75
B. 83
C. 217
D. 225

Question 428

If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2)

A. 2(a2 - b2)
B. 2(a2 + b2)
C. 4(a2 - b2)
D. 4(a2 + b2)

Question 429

If a.sin 45°.cos 45°.tan60° = tan 245° ­ cos60° then find the value of a ?

A. 13
B. 3
C. 1
D. 32

Question 430

If a/(a+b) = 15/21, what is (a+b)/(a-b) is equal to?

A. 13/9
B. 23/11
C. 14/5
D. 21/9

Question 431

If A/3 = B/2 = C/5, then what is the value of ratio (C + A)2 : (A + B)2 : (B + C)2?

A. 9 : 4 : 25
B. 25 : 4 : 9
C. 64 : 25 : 49
D. 49 : 25 : 64

Question 432

If a:b = 3:8, find the value of (5a ­ 3b)/(2a + b).

A. 9/14
B. 14/9
C. -9/14
D. -14/9

Question 433

If a+b+c = 0, then (a^3 + b^3 + c^3)^2 = ?

A. 27abc
B. 9abc
C. 3abc
D. 9a^2b^2c^2

Question 434

If a+b=2c then the value of aa-c+cb-c is equal to (where a≠b≠c)

A. -1
B. 1
C. 0
D. 1/2

Question 435

If a+b=3 then the value of a3+b3+9ab-­27 is

A. 24
B. 25
C. 0
D. 27

Question 436

If a+b=5 and a­b=3, then the value of (a2+b2) is

A. 17
B. 18
C. 19
D. 20

Question 437

If a+b=5 then the value of a-37+b-27 is

A. 27
B. 37
C. 1
D. 0

Question 438

If a=101 then the value of a(a2-3a+3) is

A. 1000000
B. 1010101
C. 1000001
D. 999999

Question 439

If a=x13y13+x-13y-13 then a3-3ay-x is equal to

A. y^2x
B. x^2y
C. a^2x
D. a^2y

Question 440

If a-1a=7,then a2+1a2=?

A. 54
B. 51
C. 53
D. 52

Question 441

If a2sec2x - b2tan2x = c2 then the value of sec2x + tan2x is equal to (assume b2 ≠ a2 )

A. b2-a2+2c2b2+a2
B. b2+a2-2c2b2-a2
C. b2-a2-2c2b2+a2
D. b2-a2b2+a2+2c2

Question 442

If a3 + b3 = 19 and ab = -6 , then what is the value of a + b?

A. 5
B. 7
C. 1
D. -5

Question 443

If a3 + b3 = 28 and a + b = 4, then what is the value of ab?

A. -3
B. 2
C. 8
D. 3

Question 444

If a3 + b3 = 35 and ab = 6, then what is the value of a + b?

A. 5
B. 8
C. 2
D. -8

Question 445

If a3- b3= 91 and a - b = 1, then what is the value of ab?

A. 27
B. 6
C. 9
D. 30

Question 446

If a3+ b3 = 19 and a + b = 1, then what is the value of ab?

A. 5
B. -6
C. 7
D. -9

Question 447

If a3+ b3 = 341 and ab = 30, then what is the value of a + b?

A. 1
B. 9
C. 7
D. 11

Question 448

If a4 + 1 = [a2 /b2 ] (4b2 – b4 – 1), then what is the value of a4 + b4?

A. 2
B. 16
C. 32
D. 64

Question 449

If ab = 21 and a+b2a-b2 = 254,then the value of a2+b2+3ab

A. 115
B. 121
C. 125
D. 127

Question 450

If a--b = 4 and ab = 45, find the value of a3 - b3

A. 604
B. 370
C. 253
D. 199

Question 451

If ab+c=bc+a=Cb+athen which one of the following statements is correct?

A. Each fraction is equal to 1 or -1
B. Each fraction is equal to 1/2 or 1
C. Each fraction is equal to 1/2 or -1
D. Each fraction is equal to 1.2 only

Question 452

If a-b=1 and a3-b3 = 61, then the value of ab will be

A. -20
B. 20
C. 30
D. 60

Question 453

If angles M and N measure 60 deg and 30 deg respectively, (sinM) x (cotN) = ?

A. 1/2
B. √3/2
C. 3/2
D. 0

Question 454

If angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is

A. 16°
B. 32°
C. 8°
D. 1°

Question 455

If ax + by = 1 and bx + ay  = 2aba2+b2 then x2+y2a2+b2 is equal to

A. 1
B. 2
C. 0.5
D. 0

Question 456

If cos ­-11π/6 = x, then the value of x is

A. -√3/2
B. 1/2
C. -2
D. √3/2

Question 457

If cos 135° = x, then the value of x is

A. -1/√2
B. -√3/2
C. -1/2
D. 2

Question 458

If cos 21° = x/y, then cosec 21° -­ cos 69° is equal to

A. x2yy2-x2
B. y2xy2-x2
C. y2xx2-y2
D. x2yx2-y2

Question 459

If cos -225° = x, then the value of x is

A. 1/2
B. √3/2
C. -2/√3
D. -1/√2

Question 460

If cos 240° = x, then value of x is

A. -1/√2
B. -√3/2
C. 1/2
D. -1/2

Question 461

If cos 27° = x, the value of tan 63° is

A. x1-x2
B. x1+x2
C. 1-x2x
D. 1+x2x

Question 462

If cos 2π/3c = x, then the value of x is

A. -1/2
B. 1/2
C. -√3/2
D. √3/2

Question 463

If cos -300° = x, then the value of x is

A. 1/2
B. -1/√2
C. -1/2
D. √3/2

Question 464

If cos 45° - ­ sec 30° = x, then value of x is

A. (1+√2)/2
B. (2√2­√3)/2
C. (√3­2√2)/√6
D. 4/√3

Question 465

If cos 45° - sec 60° = x, then the value of x is

A. (√3-4)/2√3
B. 1
C. (1-2√2)/√2
D. (√3+√2)/2

Question 466

If cos -4π/3 = x, then the value of x is

A. √3/2
B. 1/2
C. -√3/2
D. -1/2

Question 467

If Cos θ = 15/17 , then what is the value of Cosec θ?

A. 17/8
B. 8/17
C. 8/15
D. 17/15

Question 468

If Cos θ = 35/37 , then what is the value of Cot θ?

A. 12/35
B. 35/12
C. 37/12
D. 12/37

Question 469

If Cos θ = 35/37, then what is the value of Cosec θ?

A. 37/12
B. 33/12
C. 35/12
D. 12/35

Question 470

If Cos θ = 5/13, then Cosec θ = ?

A. 5/12
B. 12/5
C. 13/5
D. 13/12

Question 471

If cos3A = X, then value of X?

A. 4cos3A - 3cosA
B. 4cos3A + 3cosA
C. 3cosA - 4cos3A
D. cosA + 4cos3A

Question 472

If cosA = x, then x is

A. √(1 - cos2A)
B. √(1 + sin2A)
C. √(1 + cos2A)
D. √(1 - sin2A)

Question 473

If cosA/(1 - sinA) = x, then the value of x is

A. secA - tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA - tanA

Question 474

If cosAcotA/(1 -­ sinA) = x, then the value of x is

A. 1 -­ cosecA
B. 1 + cosecA
C. 1 + secA
D. 1 -­ secA

Question 475

If cosC + cosD = x, then value of x is

A. 2cos[(C+D)/2]cos[(C-D)/2]
B. 2sin[(C+D)/2]sin[(C-D)/2]
C. 2cos[(C+D)/2]sin[(C-D)/2]
D. 2sin[(C+D)/2]cos[(C-D)/2]

Question 476

If cosec 135° = x, then the value of x is

A. √2
B. 2
C. -√2
D. 1/√3

Question 477

If cosec 240° = x, then the value of x is

A. √2
B. 2
C. -2/√3
D. -√2

Question 478

If cosec 45° - sin 30° = x, then x is

A. 5/√3
B. (√6-1)/√2
C. √3+2
D. (2√2-1)/2

Question 479

If cosec ­4π/3 = x, then the value of x is

A. √2
B. 2/√3
C. √2
D. -1/√3

Question 480

If cosec θ + sinθ = 5/2 then the value of cosecθ - sinθ is

A. -3/2
B. 3/2
C. −√3/2
D. √3/2

Question 481

If Cosec θ = 17/8, then Cot θ = ?

A. 17/8
B. 15/8
C. 8/15
D. 17/15

Question 482

If Cosec θ = 17/8, then what is the value of Cos θ?

A. 15/8
B. 15/17
C. 8/15
D. 17/15

Question 483

If Cosec θ = 25/7 , then what is the value of Cot θ?

A. 24/25
B. 7/24
C. 7/25

Question 484

If cosec π/4 - ­ sin π/3 = x, then the value of x is

A. 4/√3
B. (2√2­-√3)/2
C. (1­-√3)/√3
D. √3+2

Question 485

If cosec θ + cot θ= 2, then cosec θ= ?

A. 1.5
B. 1.25
C. 1
D. 2

Question 486

If cosec2 θ = 625/576, then what is the value of [(sin θ – cos θ)/(sin θ + cos θ)]?

A. 1
B. 31/17
C. 17/31
D. 14/25

Question 487

If cosec4A -­ cosec2A = x, then value of x is?

A. tan4A + tan2A
B. cot4A + cot2A
C. cot4A -­ cot2A
D. tan4A -­ tan2A

Question 488

If cosecA + cotA = x, then value of x is

A. 1/(cosecA - cotA)
B. 1/(secA - tanA)
C. 1/(secA - cosA)
D. 1/(sinA - cosA)

Question 489

If cosx.cosy + sinx.siny = -1 then cosx + cosy is

A. -2
B. 1
C. 0
D. 2

Question 490

If cosθ + sinθ = m, secθ + cosecθ = n, what is m/n?

A. 1
B. sinθ cosθ
C. secθ cosecθ
D. cotθ tanθ

Question 491

If cosπ/4c - tanπ/4c = x, then x is

A. (√3+4)/2√3
B. (2√2-1)/2
C. (1-√2)/√2
D. 5/√3

Question 492

If cot 135° = x, then the value of x is

A. -1/√3
B. -√3
C. -1
D. -1/2

Question 493

If cot 240° = x, then the value of x is

A. -1
B. -1/√3
C. 1/√3
D. √3

Question 494

If cot ­-4π/3 = x, then the value of x is

A. -1
B. -1/√3
C. √3
D. 1

Question 495

If cot 60° + cosec 60° = x, then the value of x is

A. (1-2√2)/√2
B. (√3-4)/2√3
C. 1
D. √3

Question 496

If cot A = [sin B/(1 – cos B)], then what is the value of cot 2A?

A. cot(B/2)
B. cot 2B
C. cot B
D. tan B

Question 497

If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?

A. -1
B. 0
C. 1
D. 2

Question 498

If Cot θ = 21/20, then what is the value of Cosec θ?

A. 21/29
B. 29/21
C. 20/29
D. 29/20

Question 499

If Cot θ = 21/20, then what is the value of Sec θ?

A. 29/21
B. 21/29
C. 29/20
D. 20/29

Question 500

If Cot θ = 24/7, then Sin θ = ?

A. 24/25
B. 8/25
C. 7/25
D. 9/25

Question 501

If Cot θ = 24/7, then what is the value of Sec θ?

A. 7/25
B. 25/24
C. 8/25
D. 9/25

Question 502

If cot π/3c -­ tan π/4c = x, then the value of x is

A. √3+2
B. (1­-√3)/√3
C. (1-­√2)/√2
D. (√3+4)/2√3

Question 503

If cot(A/2) = x, then the value of x is

A. √[(1 + cosA)/(1 -­ cosA)]
B. cosecA -­ cotA
C. √[(1 -­ cosA)/2]
D. √[(1 + cosA)/2]

Question 504

If cot(A/2) = x, then the value of x is

A. cosecA -­ cotA
B. cosecA + cotA
C. secA + cotA
D. secA -­ cotA

Question 505

If cot(A/2) = x, then x is equal to

A. tanA/(1 + secA)
B. 1/(secA + cotA)
C. tanA/(1 + cosecA)
D. 1/(cosecA ­- cotA)

Question 506

If cot2A = x, then x is

A. 2cotA/(cot2A -­ 1)
B. (cot2A -­ 1)/2cotA
C. (cot2A + 1)/2cotA
D. 2cotA/(1 -­ cot2A)

Question 507

If cot2A -­ cos2A = x, then value of x is

A. tan2Asec2A
B. cotAcosA
C. cot2Acos2A
D. tanAsecA

Question 508

If cotA + cotB = x, then value of x is

A. (cotAcotB + 1)/(cotB - cotA)
B. (cotAcotB + 1)/(cotB + cotA)
C. (cotAcotB - 1)/(cotB + cotA)
D. (cotAcotB - 1)/(cotB - cotA)

Question 509

If cotA = x, then the value of x is

A. √(sec2A + 1)
B. √(cosec2A + 1)
C. √(sec2A - 1)
D. √(cosec2A - 1)

Question 510

If cotA/√(1 + cot2A) = x, then the value of x is

A. sinA
B. cosecA
C. secA
D. cosA

Question 511

If each median of an equilateral triangle has a length of 12cm. Then what will be the value of in-radius (in cm) of the equilateral triangle?

A. 3
B. 4
C. 5
D. 6

Question 512

If in a triangle ABC, Sin A = Cos B then the value of Cos C is

A. √3/2
B. 0
C. 1
D. 1/√2

Question 513

If l + m + n = 9 and l2+m2+n2 = 31, then the value of lm + mn + nl will be

A. 22
B. 50
C. 25
D. -25

Question 514

If m ­ n = 2 , mn = 15 , (m , n > 0) then the value of m2-n2m3-n3

A. 1856
B. 1658
C. 1586
D. 1568

Question 515

If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then what is the value of M/N?

A. 207/560
B. 339/1120
C. 113/350
D. 69/175

Question 516

If M = 0.1 + (0.1)2 + (0.01)2 and N = 0.3 + (0.03)2 + (0.003)2, then what is the value of M + N?

A. 0.411009
B. 0.413131
C. 0.313131
D. 0.131313

Question 517

If n + n2 + n4 + n8 = 45, then find the value of 'n' which will satisfy the equation.

A. 16
B. 24
C. 36
D. 48

Question 518

If one more cobbler is hired the output of a shoe making unit will increase from 50 pairs of shoes to 55 pairs per day, but then the shoe making unit will have to reduce the price of a pair of shoes from Rs 3200 to Rs 3000 per pair to sell the additional output, the marginal revenue product of the last cobbler is

A. Rs 1000
B. Rs 5000
C. Rs 4000
D. Rs 200

Question 519

If one root of the equation (1-m)x2 + 1 = 0 is double the other and 'I' is a real number, then which of the following is true?

A. m > 9/8
B. m> 8/9
C. m = 8/9
D. m <= 9/8

Question 520

If one root of the equation Ax2 +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?

A. 7B2 = 3 CA
B. 7B2 = 4 CA
C. 7B2 = 36 CA
D. 10B2 = 49 CA

Question 521

If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?

A. 148
B. 189
C. 194
D. 204

Question 522

If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?

A. 196
B. 194
C. 206
D. 182

Question 523

If P = 99, then the value of P(P2+ 3P + 3) is

A. 9999
B. 999999
C. 99999
D. 9999999

Question 524

If p = 99, then the value of p(p2+3p+3) will be

A. 999999
B. 1000000
C. 1000001
D. 999998

Question 525

If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

A. 55
B. 56
C. 60
D. 64

Question 526

If p/q = (x+3)/(x-3), then what is the value of p2+q2p2-q2 ?

A. x+9
B. x2+96x
C. x2+186x
D. 0

Question 527

If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)]?

A. 1/5
B. 5
C. 25
D. 60

Question 528

If P=9, Q=17 then the value of p2-q2-13

A. 4
B. 1/4
C. 3
D. 1/3

Question 529

If pq(p+q) = 1, then the value of 1p3q3-p3-q3 is equal to

A. 1
B. 2
C. 3
D. 4

Question 530

If price of oranges is increased by 30%, then a person can buy 12 oranges less for Rs 208. What is the original price (in Rs) of an orange?

A. 2
B. 4
C. 8
D. 3

Question 531

If 'Q ' means ' +', 'J ' means ' X',T ' ' means '- ' and 'K ' means '÷ ', then what is the value of18K3Q7J ?

A. 15
B. 10
C. 18
D. 12

Question 532

If sec (3x – 20°) = cosec (3y + 20°), then what is the value of tan (x + y)?

A. 1
B. √3
C. 1/√3
D. 2√3

Question 533

If sec (4x - 50°) = cosec(50° - x), Then the value of x is

A. 45°
B. 90°
C. 30°
D. 60°

Question 534

If sec 300° = x, then value of x is

A. ­√2
B. 1/√3
C. 2
D. ­1

Question 535

If sec -5π/4 = x, then the value of x is

A. -1/√3
B. -√2
C. -1
D. √3

Question 536

If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?

A. 3√2
B. 3/√2
C. 1/√2
D. √2

Question 537

If Sec θ = 13/12, then Cot θ = ?

A. 12/5
B. 13/5
C. 5/13
D. 5/12

Question 538

If Sec θ = 13/12, then what is the value of Sin θ?

A. 5/13
B. 12/5
C. 12/13
D. 5/12

Question 539

If Sec θ = 25/24 , then what is the value of Sin θ?

A. 24/25
B. 7/25
D. 25/7

Question 540

If Sec θ = 5/3, then what is the value of Cosec θ?

A. 0.8
B. 1.25
C. 4/3
D. 3/4

Question 541

If sec2A + cosec2A = X, then the value of X is

A. tan2A cot2A
B. sinA cosA
C. secA cosecA
D. sec2A cosec2A

Question 542

If sec2A cosec2A = x, then x is

A. sec2A + cosec2A + 2
B. tan2A + cot2A - 2
C. tan2A + cot2A + 2
D. sec2A + cosec2A - 2

Question 543

If secA - tanA = x, then the value of x is

A. 1/(sec2A - tan2A)
B. 1/(sec2A + tan2A)
C. 1/√[(sec2A - tan2A)]
D. 1/(secA + tanA)

Question 544

If secA -­ tanA = x, then the value of x is

A. √[(1 + sinA)/(1 ­- sinA)]
B. √[(1­-sinA)/(1+sinA)]
C. (1-­sinA)/(1+sinA)
D. (1 + sinA)/(1 -­ sinA)

Question 545

If secA + tanA = a, then the value of cosA is

A. a2+12a
B. 2aa2+1
C. a2-12a
D. 2aa2-1

Question 546

If secA + tanA = x, then find the value of x.

A. √[(1 - sinA)/(1 + sinA)]
B. (1 + sinA)/(1 - sinA)
C. (1 - sinA)/(1 + sinA)
D. √[(1 + sinA)/(1 - sinA)]

Question 547

If secA + tanA = x, then the value of x is

A. cosA/(1 + sinA)
B. √[cosA/(1 - sinA)]
C. √[cosA/(1 + sinA)]
D. cosA/(1 - sinA)

Question 548

If secA = x, then the value of x is

A. √(1 -­ cot2A)
B. √(1 -­ tan2A)
C. √(1 + cot2A)
D. √(1 + tan2A)

Question 549

If secA/(secA ­- 1) + secA/(secA + 1) = x, then x is

A. 2cosec2A
B. 2sec2A
C. 2cosecA
D. 2secA

Question 550

If secA/√(sec2A ­- 1) = x, then value of x is

A. tanA
B. cosecA
C. sinA
D. cosA

Question 551

If secθ = cosecq with 0° < θ , q < 90°, then the value of sin (θ + q) is

A. 1
B. 0
C. 2
D. 4

Question 552

If sin - 4π/3 = x, then the value of x is

A. -2
B. -2/√3
C. √3/2
D. √2

Question 553

If sin ­- 5π/3 = x, then the value of x is

A. -√3/2
B. √3/2
C. -2
D. -2/√3

Question 554

If sin (3x ­ 20°) = cos (3y + 20°), then find the value of (x + y).

A. 90°
B. 60°
C. 120°
D. 30°

Question 555

If sin = 2/3, find the value of secθ and cotθ

A. √5/2, 2/√5
B. 2/√5, 3/5
C. 3√5/5, √5/2
D. 3/5, 3√5/5

Question 556

If sin ­-240° = x, then the value of x is

A. ­2/√3
B. √2
C. 2
D. √3/2

Question 557

If sin ­-330° = x, then the value of x is

A. √3/2
B. 1/2
C. -2/√3
D. √2

Question 558

If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1]?

A. 0
B. 1
C. 2
D. 3

Question 559

If sin P + cosec P = 2, then the value of sin7P + cosec7P is

A. 1
B. 2
C. 3
D. 0

Question 560

If sin x + cos x = √2 sin x, then the value of tan x is

A. √2 - 1
B. √2 + 1
C. 1
D. √2

Question 561

If Sin x = 4/5, then Cosec x + Cot x =

A. 31/12
B. 35/12
C. 2
D. 1/2

Question 562

If sin θ + sin 5θ = sin 3θ and 0 < θ < (π/2), then what is the value of θ (in degrees)?

A. 30
B. 45
C. 60
D. 75

Question 563

If Sin θ = 12/13, then what is the value of Cot θ?

A. 13/12
B. 5/13
C. 5/12
D. 13/5

Question 564

If Sin θ = 20/29 , then what is the value of Sec Sin θ ?

A. 29/21
B. 29/20
C. 21/20
D. 21/29

Question 565

If Sin θ = 20/29, then what is the value of Cos θ?

A. 29/21
B. 21/29
C. 21/20
D. 20/29

Question 566

If sin π/6 + sec π/6 = x, then x is

A. (2√2-1)/2
B. 5/√3
C. (√6-1)/√2
D. (√3+4)/2√3

Question 567

If sin(A/2) = x, then the value of x is

A. √[(1 + cosA)/2]
B. √[(1 -­ cosA)/2]
C. √[(1 -­ sinA)/2]
D. √[(1 + sinA)/2]

Question 568

If sin3A = x, then value of x is

A. 3sinA + 4sin3A
B. 4sin3A -­ 3sinA
C. 4sin3A + sinA
D. 3sinA -­ 4sin3A

Question 569

If sinA = x, then x is equal to

A. √(1 - cos2A)
B. √(1 - sin2A)
C. √(1 + cos2A)
D. √(1 + sin2A)

Question 570

If sinA + sin2A = 1 then what is the value of cos2A + cos4A ?

A. 1
B. 2
C. 1/2
D. 1/4

Question 571

If sinA/(1 + cosA) = x, then x is

A. cosecA + cotA
B. secA - cotA
C. secA + cotA
D. cosecA - cotA

Question 572

If sinC - sinD = x, then value of x is

A. 2sin[(C+D)/2]cos[(C-D)/2]
B. 2cos[(C+D)/2]cos[(C-D)/2]
C. 2cos[(C+D)/2]sin[(C-D)/2]
D. 2sin[(C+D)/2]sin[(D-C)/2]

Question 573

If sinC + sinD =X, then the value of X is?

A. 2cos[(C+D)/2]sin[(C-D)/2]
B. 2sin[(C+D)/2]cos[(C-D)/2]
C. 2cos[(C+D)/2]cos[(C-D)/2]
D. 2sin[(C+D)/2]sin[(D-C)/2]

Question 574

If sinP = 2/3, find the value of secP and cotP.

A. √5/2, 2/√5
B. 2/√5, 3/5
C. 3√5/5, √5/2
D. 3/5, 3√5/5

Question 575

If Sinx = 4/5, then Secx/Sinx = ?

A. 23/12
B. 25/4
C. 4/5
D. 25/12

Question 576

If Sinx = 4/5, then Sec2x - 1 = ?

A. 16/25
B. 25/9
C. 9/16
D. 16/9

Question 577

If SinX-CosX=1, where 'X' is an acute angle, the value of SinX+CosX is

A. 0
B. 1
C. 1/2
D. 2

Question 578

If sinθ + cosθ = 1, then the sinθ cosθ is equal to

A. 0
B. 1
C. 1/2
D. -1/2

Question 579

If sinθ x cosθ = 1⁄2 . The value of sinθ ­- cosθ is where 0°< θ< 90°

A. 0
B. √2
C. 2
D. 1

Question 580

If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?

A. 125√3
B. 147√3
C. 156√3
D. 169√3

Question 581

If sum of the roots of a quadratic equation is ­-7 and product of the roots is 12. Find the quadratic equation.

A. x2 + 7x + 12 = 0
B. x2 -­ 7x + 12 = 0
C. x2 -­ 7x -­ 12 = 0
D. x2 + 7x -­ 12 = 0

Question 582

If tan 45° + cosec 30° = x, then find the value of x.

A. √3
B. (1-2√2)/√2
C. (√3-4)/2√3
D. 3

Question 583

If tan ­-5π/3 = x, then the value of x is

A. √3
B. 1
C. -1/2
D. √3/2

Question 584

If tan A = 1/2 and tan B = 1/3, then what is the value of tan (2A + B)?

A. 1
B. 3
C. 5
D. 9

Question 585

If Tan A = 15/8 and Tan B = 7/24, then Cos(A - B) = ?

A. 297/425
B. 304/425
C. 87/425
D. 416/425

Question 586

If Tan A = 15/8 and Tan B = 7/24, then Tan (A - B) = ?

A. 304/297
B. 304/425
C. 416/87
D. 87/416

Question 587

If tan θ + cot θ = x, then what is the value of tan4θ + cot4θ?

A. (x3 – 3)2 + 2
B. (x4 – 2x) + 4
C. x2 (x2 – 4) + 2
D. x

Question 588

If tan θ + sec θ = (x – 2)/(x + 2), then what is the value of cos θ?

A. (x2 – 1)/(x2 + 1)
B. (2x2 – 4)/(2x2 + 4)
C. (x2 – 4)/(x2 + 4)
D. (x2 – 2)/(x2 + 2)

Question 589

If Tan θ = 4/3, then what is the value of Sin θ?

A. 1.25
B. 0.8
C. 4/3
D. 3/4

Question 590

If Tan θ = 7/24, then what is the value of Cosec θ?

A. 25/24
B. 25/7
D. 24/25

Question 591

If Tan θ = 7/24, then what is the value of Sec θ?

A. 24/25
C. 25/7
D. 25/24

Question 592

If Tan θ = 9/40, then Sec θ = ?

A. 40/41
B. 9/41
C. 41/40
D. 41/9

Question 593

If tan π/3c + cosec π/6c = x, then x is

A. (1-√2)/√2
B. (√3+4)/2√3
C. √3+2
D. (2√2-1)/2

Question 594

If tan(A/2) = x, then the value of x is

A. sinA/(1 - cosA)
B. sinA/(1 + cosA)
C. √[sinA/(1 + cosA)]
D. √[sinA/(1 - cosA)]

Question 595

If tan(A/2) = x, then the value of x is

A. √[(1 + cosA)/(1 -­ cosA)]
B. (1 -­ cosA)/(1 + cosA)
C. (1 + cosA)/(1 -­ cosA)
D. √[(1 -­ cosA)/(1 + cosA)]

Question 596

If tan2A - sin2A = x, then value of x is

A. tan2A sin2A
B. cot2A cosec2A
C. tanA sinA
D. cotA cosecA

Question 597

If tan2A - tan2B = x, then the value of x is

A. (sin2A - sin2B)/(cos2A cos2B)
B. (sin2A sin2B)/(cos2A - cos2B)
C. (sin2A + sin2B)/(cos2A cos2B)
D. (sin2A sin2B)/(cos2A + cos2B)

Question 598

If tan2A + cot2A + 2 = x, then the value of x is

A. tan2Acosec2A
B. secAcosecA
C. sec2Acosec2A
D. tanAcosecA

Question 599

If tanA - cotA = x, then value of x is?

A. (1 + 2cos2A)/(sinA cosA)
B. (sinA cosA)/(1 - 2cos2A)
C. (sinA cosA)/(1 + 2cos2A)
D. (1 - 2cos2A)/(sinA cosA)

Question 600

If tanA -­ tanB = X, then the value of X is

A. (tanA + tanB)/(1 -­ tanAtanB)
B. (tanA + tanB)/(1 + tanAtanB)
C. (tanA -­ tanB)/(1-­ tanAtanB)
D. (tanA -­ tanB)/(1 + tanAtanB)

Question 601

If tanA + tanB = X, then the value of X is

A. (tanA - tanB)/(1 + tanAtanB)
B. (tanA + tanB)/(1 - tanAtanB)
C. (tanA + tanB)/(1 + tanAtanB)
D. (tanA - tanB)/(1 - tanAtanB)

Question 602

If tanA = x, then x is

A. √(cosec2A + 1)
B. √(sec2A + 1)
C. √(cosec2A - 1)
D. √(sec2A - 1)

Question 603

If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is

A. 60(√3+1) m
B. 30(√3-1) m
C. 30(√3+1) m
D. 60(√3-1) m

Question 604

If the difference between the roots of the equation Ax2 – Bx + C = 0 is 4, then which of the following is TRUE?

A. B2 – 16A2 = 4AC + 4B2
B. B2 – 10A2 = 4AC + 6A2
C. B2 – 8A2 = 4AC + 10A2
D. B2 – 16A2 = 4AC + 8B2

Question 605

If the equation 4x + 3y + 5 = 0 and 6x - ky - 7 = 0 have no solution, then the value of k is

A. -4.5
B. -8
C. 8
D. 4.5

Question 606

If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9), then what is the ratio between p and q respectively?

A. 1:9
B. 1:3
C. 3:1
D. 9:1

Question 607

If the expression px3 – qx2 – 7x – 6 is completely divisible by x2 – x – 6, then what is the value of p and q respectively?

A. 0, 1
B. 1, 0
C. 2, 1
D. 1, 2

Question 608

If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations?

A. 2m –m^2/n
B. 2m –m/n
C. 2m
D. 2m –m

Question 609

If the roots of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 are equal, then which of the following is true?

A. b = ( a + c)/ ac
B. 2/ b = (1/ a) + (1/ c)
C. 2 b = (1/ a) + (1/ c)
D. abc = ab + bc + ca

Question 610

If the selling price is Rs 1680 after getting a discount of 16%, what was the marked price?

A. Rs 2000
B. Rs 1948.8
C. Rs 1411.2
D. Rs 1448

Question 611

If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be

A. 10%
B. 8%
C. 12%
D. 6%

Question 612

If the sum of the digits of any integer between 100 and 1000 is subtracted from the same integer , the resulting number is always divisibleby

A. 2
B. 5
C. 6
D. 9

Question 613

If the two lines px + 6y+3=0 and 2x + qy+3=0 have infinite solutions then find the value of p and q respectively.

A. 2,6
B. 6,2
C. 2,2
D. 6,6

Question 614

If the value of √30  is approximately 5.477, then what is the approximate value of 56 ?

A. 0.853
B. 0.891
C. 0.913
D. 0.937

Question 615

If the value of √42 is approximately 6.480, then what is the approximate value of √(6/7)?

A. 0.925
B. 0.935
C. 0.945
D. 0.955

Question 616

If the value of 3-1.732, then calculate the value of 243-12108-147

A. 1.732
B. -1.464
C. 3.464
D. -1.732

Question 617

If the value 5 = 2.236,then calculate the value of 405 - 1280-125

A. 2.236
B. 4.472
C. 1.118
D. 8.994

Question 618

If the zeroes of the polynomial x2 - ax + b are 3 and 4, then 'a' and 'b' are respectively equal to

A. 4, 3
B. 12, 7
C. 3, 4
D. 7, 12

Question 619

If u : v = v : w, then what is the value of u4 : v4?

A. u2 : wv
B. u2 : w2
C. u2 v : w3
D. u : w

Question 620

If u+v = 10 and uv = 16, then find the value of u2-v2uv

A. 0
B. 15/8
C. 15/4
D. 15/2

Question 621

If x – (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 – 3x + 2) / (3x4 + 3)?

A. 1/3
B. 2/3
C. 4/3
D. 5/3

Question 622

If x - 1/x = 1 then what is the value of 1x1x-1-1x+1+1x2+1-1x2-1?

A. ±√5
B. 2/5
C. ±2/√5
D. ±√5/2

Question 623

If x - 2y = 2 and 3x + y = 20, then the value of (x,y) is

A. (6, 2)
B. (4, 1)
C. (3, 2)
D. (5, 5)

Question 624

If x – 3 + [1/(x – 3)] = 4, what is the value of [(x – 3)3+ [1/(x – 3)3]?

A. 14
B. 18
C. 52
D. 76

Question 625

If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?

A. 9/5
B. 11/5
C. 13/7
D. 9/7

Question 626

If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x2 – y2)?

A. 0
B. 1
C. 512√2
D. 612√2

Question 627

If x - y = -6 and x + y = 16, then x2- y2 is?

A. 96
B. -96
C. 22
D. -22

Question 628

If x - y = 6 and xy = 40, then find x2 + y2 ?

A. 116
B. 80
C. 89
D. 146

Question 629

If x -­ y = ­7 and x + y = 13, then x2 - y2 is

A. 91
B. -30
C. 30
D. -­91

Question 630

If x -­ y = 7 and xy = 32, then value of (x2 + y2) is

A. 49
B. 64
C. 113
D. 15

Question 631

If x - y = -8 and xy = 45, then (x2 + y2) is

A. 154
B. 64
C. 90
D. 26

Question 632

If x - y = -9 and xy = -20, then find x2 + y2 ?

A. 61
B. 41
C. 81
D. 51

Question 633

If x , y, and z are real numbers such that (x - 3)2 + (y - 4)2 + (z - 5)2 = 0 then (x+y+z) is equal to

A. -12
B. 0
C. 8
D. 12

Question 634

If x + (1/x) = 2, then what is the value of x21 + (1/x1331)?

A. 0
B. 1
C. 2
D. 3

Question 635

If x + [1/(4x)] = 5/2, then what is the value of (64x6+ 1)/8x3?

A. 110
B. 115
C. 125
D. 140

Question 636

If x + √5 = 5 + √y, and x, y are positive integers, then the value of x+yx + y

A. 1
B. 2
C. √5
D. 5

Question 637

If x + 1/x = √13, then 3x(x2-1) equal to

A. 3√13
B. √13/3
C. 1
D. 3

Question 638

If x + 1/x = 6, then value of x2 + 1/x2 is

A. 23
B. 16
C. 34
D. 32

Question 639

If X + 2Y = 27 and X - 2Y = -1, find the value of Y.

A. 13
B. 14
C. 7
D. 26

Question 640

If x + 3 ≤ 4x + 4 and 3(4 - x) - 4 ≥ 2x - 2, then x can take which of the following values?

A. 1
B. 3
C. -1
D. -3

Question 641

If x + y + z = 0, then what is the value of (3y2 + x2 + z2 )/(2y2 – xz)?

A. 2
B. 1
C. 3/2
D. 5/3

Question 642

If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2?

A. 793
B. 681
C. 758
D. 715

Question 643

If X + Y + Z = 9 then the value of (X -­ 4)3 + (Y -­ 2)3 + (Z -­ 3)3 - 3 (X -­ 4) (Y -­ Z) (Z ­- 3) is

A. 6
B. 9
C. 0
D. 1

Question 644

If x + y = 10 and x2 + y2 = 68, then find xy

A. 21
B. 24
C. 25
D. 16

Question 645

If x + y = 10 and xy = 4, then what is the value of x4 + y4?

A. 8464
B. 8432
C. 7478
D. 6218

Question 646

If x + y = 12 and x2 + y2 = 94, then xy is

A. 25
B. 50
C. 144
D. 238

Question 647

If x + y = 12 and xy = 32, then what is the value of  x2 + y2 ?

A. 24
B. 144
C. 128
D. 80

Question 648

If x + y = 13 and x2 + y2 = 89, then find xy is

A. 80
B. 169
C. 258
D. 40

Question 649

If X + Y = 19 and X - Y = 7, then XY = ?

A. 13
B. 48
C. 78
D. 72

Question 650

If x + y = 3, then what is the value of x3 + y3 + 9xy?

A. 15
B. 81
C. 27
D. 9

Question 651

If x + y = 5, x3 + y3 = 35, then what is the positive difference between x and y?

A. 0
B. 1
C. 5
D. 6

Question 652

If x +y = √3 and x - y = √2, then the value of 8xy (x2 + y2) is

A. 6
B. √6
C. 5
D. √5

Question 653

If x = (√2 + 1)/(√2 – 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?

A. 5
B. 2
C. 2√3
D. 2√2

Question 654

If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?

A. 31
B. 23√5
C. 27√5
D. 25

Question 655

If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?

A. – 4
B. 2
C. – 1
D. – 6

Question 656

If x = √2+1, then the value of x4-1/x4

A. 8√2
B. 18√2
C. 6√2
D. 24√2

Question 657

If x = 1 – y and x2 = 2 – y2, then what is the value of xy?

A. 1
B. 2
C. -1/2
D. -1

Question 658

If x = 1 + √2 + √3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is

A. 2√2
B. 3√3
C. 5√5
D. 6√6

Question 659

If x = 1.1, then what is the value of 4x2 -4x + 1 ?

A. 1.21
B. 1.331
C. 2.21
D. 1.2

Question 660

If x = 1/(√2+1) then the value of x2 + 2x - 1 is

A. 2√2
B. 4
C. 0
D. 2

Question 661

If x = 11, the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is

A. 11
B. 10
C. 12
D. -10

Question 662

If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?

A. 25
B. 22
C. 17
D. 43

Question 663

If x = 222, y = 223, z = 225 then the value of x3 + y3 + z3 - 3xyz is

A. 4590
B. 4690
C. 4950
D. 4960

Question 664

If x = 93 , y = 93 , z = 94 then the value of x2 - y2 + 10xz + 10yz is

A. 104784
B. 147840
C. 174840
D. 184740

Question 665

If x = 999, y = 1000, z = 1001, then the value of x3+y3+z3-3xyzx-y+z is

A. 1000
B. 9000
C. 1
D. 9

Question 666

If x = a cosθ+ b sinθ and y = b cosθ- a sinθ, then x2 + y2 is equal to

A. ab
B. a2+b2
C. a2-b2
D. 1

Question 667

If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is

A. x2+ y2+ 3 =1
B. x2y2 (x2+ y2+3)=1
C. x2 (x2+ y2 - 5)=1
D. y2 (x2+ y2 - 5)=1

Question 668

If x = y + 2 then x3 -  y3 -  z3 is

A. 0
B. 3xyz
C. -3xyz
D. 1

Question 669

If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x+ (– 1)y?

A. 2
B. – 2
C. 0
D. 1

Question 670

If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is

A. 6/7
B. 7/6
C. 5/6
D. 6/5

Question 671

If x varies as y and x = 8 when y = 15 then the value of x when y = 10 is:

A. 5
B. 15/8
C. 8/15
D. 16/3

Question 672

If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?

A. 45
B. 109
C. 117
D. 126

Question 673

If x, y, z are the three factors of a3 -7a - 6, then value of x+y+z will be

A. 3a
B. 3
C. 6
D. a

Question 674

If x/2 - [4(15/2 - x/3)]/3 = -x/18, then what is the value of x?

A. -10
B. 9/8
C. 10
D. -9/8

Question 675

If x/3 - [5(7x/5 - 4/3)]/2 = -x/6, then what is the value of x?

A. 10/9
B. -10/9
C. -9/10
D. 9/10

Question 676

If x/y = 4/9, then what is the value of (7x2 – 19xy + 11y2)/y2 ?

A. 59/81
B. 100/27
C. 319/81
D. 913/81

Question 677

If x+1/x = 2, then the value of x7+2/x6  is equal to?

A. 0
B. 1
C. 2
D. 3

Question 678

If x+y+z = 0, then what is the value of x23z+y33xz+z23x ?

A. 0
B. xz
C. y
D. 3y

Question 679

If x+y+z = 1, 1/x + 1/y + 1/z = 1 and xyz = -1, then x3+y3+z3 is equal to

A. -1
B. 1
C. -2
D. 2

Question 680

If x=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of x2+ y2 + z2 is

A. 2a2
B. 0
C. 4a2
D. a2

Question 681

If x1/4 + x-1/4 = 2, then what is the value of x81 + (1/x81)?

A. -2
B. 0
C. 1
D. 2

Question 682

If x2 – 12x + 33 = 0, then what is the value of (x – 4)2 + [1/(x – 4)2]?

A. 16
B. 14
C. 18
D. 20

Question 683

If x2 – 16x – 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]?

A. 14
B. 18
C. 16
D. 20

Question 684

If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?

A. 4
B. – 4
C. 1
D. – 1

Question 685

If x2 + (1/x2) = 1, then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1?

A. -9
B. 0
C. 1
D. 9

Question 686

If x2 + y2 + 6x + 5 = 4(x - y) then x - y is

A. 1
B. -1
C. 0
D. 4

Question 687

If x2+ x = 19, then what is the value of (x + 5)2+ [1/(x + 5)2]?

A. 77
B. 79
C. 81
D. 83

Question 688

If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

A. 0
B. 1
C. 5
D. 33/5

Question 689

If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + (1/x – 4)]?

A. 3
B. 5
C. 6
D. 8

Question 690

If x3 – y3 = 81 and x – y = 3, then what is the value of x2 + y2?

A. 18
B. 21
C. 27
D. 36

Question 691

If x3 = 62 - 32, then the value of x is

A. 9
B. 6
C. 3
D. 1

Question 692

If x3+ 2x2– 5x + k is divisible by x + 1, then what is the value of k?

A. -6
B. -1
C. 0
D. 6

Question 693

If xy (x + y) = m, then the value of x3 + y3 + 3m is:

A. m3xy
B. m3x+y3
C. m3x3y3
D. mx3y3

Question 694

If xy = -18 and x2+ y2= 85, then find the value of (x + y).

A. 8
B. 10
C. 9
D. 7

Question 695

If xy = 22 and x2+ y2= 100, then what will be the value of (x + y)?

A. 12
B. 144
C. 72
D. 6

Question 696

If xy = -30 and x2 + y2 = 61, then find the value of (x + y).

A. 2
B. 3
C. 1
D. 4

Question 697

If xy = 48 and x2 + y2 = 100, then (x + y) is

A. 12
B. 16
C. 18
D. 14

Question 698

If xy = 56 and x2+ y2= 113, then what will be the value of (x + y)?

A. 29
B. 21
C. 36
D. 15

Question 699

If XY = a+23 and YX = 13, then find the value of X2 + Y2X2 - Y2.

A. 1
B. 2
C. 3
D. 4

Question 700

If xy+yz+zx = 1, then the value of (1+y2)(x+y)(y+z) ?

A. 2
B. 3
C. 4
D. 1

Question 701

If y = √3 - √2, then find the value of 1y3 - y3.

A. 11
B. 11√2
C. 22
D. 22√2

Question 702

If y = 2x - 1x + 3, find x when y = 1

A. 4
B. -4
C. 3/2
D. 4/3

Question 703

If α + β = 90° and α:β = 2:1, then the ratio of cosα to cosβ is

A. 1:√3
B. 1:3
C. 1:√2
D. 1:2

Question 704

If α and β are roots of the equation 3x2 – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?

A. 65/28
B. 53/14
C. 9
D. 85/42

Question 705

If α and β are the roots of equation x2 – 2x + 4 = 0, then what is the equation whose roots are α3/β2 and β3/α2?

A. x2 – 4 x + 8 = 0
B. x2 – 32 x + 4 = 0
C. x2 – 2 x + 4 = 0
D. x2 – 16 x + 4 = 0

Question 706

If α and β are the roots of the equation x2+ x – 1 = 0, then what is the equation whose roots are α5 and β5?

A. x2 + 7x – 1 = 0
B. x2 – 7x – 1 = 0
C. x2 – 11x – 1 = 0
D. x2 + 11x – 1 = 0

Question 707

If α and βare the zeros of the polynomial 5x2 - 7x + 2 then the sum of their reciprocals is

A. 5/2
B. 7/5
C. 2/5
D. 7/2

Question 708

If θ is acute angle and sin(θ+18°)= 1/2, then the value of θ in circular measure is

Question 709

If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ?

A. -2
B. 0
C. 1
D. 2

Question 710

If θ is positive acute angle and 4sin2θ = 3, then the value of tan θ - cot θ/2 is

A. 1
B. 0
C. √3
D. 1/√3

Question 711

If  a+1/a = 3, then a3+1a3?

A. 12
B. 18
C. 9
D. 6

Question 712

If  x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y ?

A. 0
B. 1
C. -1
D. -2

Question 713

If  x = a + 1/a, y = a - 1/a, then the value of x4+y4-2x2y2

A. 4
B. 8
C. 16
D. 64

Question 714

If  2x+14x = 1, then the value of  x2+164x2 is

A. 0
B. 1
C. 1/4
D. 2

Question 715

If  C+1C = 3, then what is the value of C3+1C3 = ?

A. 0
B. 3√3
C. 1/√3
D. 6√3

Question 716

If  P2+1P2 = 47, then the value of P + 1P is

A. 5
B. 6
C. 7
D. 8

Question 717

If  tan2A / (secA -­ 1)2 = x, then the value of x is

A. (1+cosecA) / (1­-cosecA)
B. (1+cosA)(1-­cosA)
C. (1+cosA) / (1­-cosA)
D. (1+cosecA)(1­-cosecA)

Question 718

If  tan2θ + cot2θ = 2, then what is the value of 2sec θ cosec θ?

A. 0
B. 1
C. 2
D. 4

Question 719

If (4a-3)2=0, then the value of 64a3+12a+13 is

A. 0
B. 11
C. 22
D. 33

Question 720

If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?

A. 5
B. 9
C. 15
D. 20

Question 721

If (x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y?

A. 1
B. 0
C. -1
D. 2

Question 722

If [√(a2 + b2  + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?

A. 1/4
B. 4/7
C. 5/4
D. 3/4

Question 723

If √(1 - cos2A)/cosA = x, then the value of x is

A. cotA
B. cosecA
C. tanA
D. secA

Question 724

If √(sec2A - 1)/secA = x, then the value of x is

A. cosecA
B. cosA
C. sinA
D. tanA

Question 725

Coefficient of x in (x + 11)(3 -­ 5x) is _____.

A. 33
B. -5
C. 3
D. -52

Question 726

Coefficient of x in (x + 8)(6 -­ 3x) is

A. 18
B. 30
C. -18
D. -30

Question 727

Coefficient of x in (x + 9)(8 - 5x) is

A. 37
B. -53
C. -37
D. 53

Question 728

Coefficient of x2 in 4x3 - 2x2 + 2x -­ 3 are

A. 6
B. -2
C. 3
D. -3

Question 729

Coefficient of x2 in 6x3 + 4x2 + 2x + 3 is

A. 4
B. 6
C. 3
D. 2

Question 730

Coefficient of x2  in (x + 7)(5 - 3x)(3x - 6) is

A. 96
B. -30
C. 42
D. -18

Question 731

Coefficient of x2 in (x + 9)(6 -­ 4x) is

A. 54
B. -4
C. ­30
D. 4

Question 732

Coefficient of x2 in (x + 9)(6 - 4x)(4x - 7) is

A. 216
B. -4
C. -92
D. 108

Question 733

Common factor of 12a4b6, 18a6c2, 36a2b2 is

A. 36a2
B. 108b2
C. 6a2b2
D. 6a2

Question 734

Common factor of 24b6c8d2, 18a6c2d4, 12a4b4 is

A. 72a2b2c2d2
B. 72a6b6c8d4
C. 6a2b2
D. 6

Question 735

Compute : (50 + 0.5 x 20) / 0.7

A. 8.571
B. 85.1
C. 85.71
D. 72.85

Question 736

Compute : 1112 / 139 - 5

A. 557/67
B. -3
C. 556/67
D. 3

Question 737

Compute : 28854 / 458 / 9

A. 70
B. 567
C. 7
D. 576

Question 738

Compute : 4082 / 157 - 23

A. -3
B. 3
C. 2041/67
D. 2014/67

Question 739

Compute 33800/520/5

A. 31
B. 325
C. 13
D. 352

Question 740

Compute 4923 / 547 - 10

A. 1
B. -1
C. 1641/179
D. 1614/179

Question 741

Compute of 69696 x 9999 =

A. 696980304
B. 666890304
C. 696809304
D. 696890304

Question 742

Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?

A. 1:√3
B. 1:3
C. 1:2
D. 1:2√3

Question 743

cos3A is equal to

A. cos3A - 3sin2cosA
B. cos3A + 4sin2cosA
C. cos3A + 3sin2cosA
D. cos3A - 4sin2cosA

Question 744

cosA/(1 -­ sin A) is equal to

A. (secA -­ tanA)
B. (secA + tanA)
C. √[(secA + tanA)]
D. √[(secA -­ tanA)]

Question 745

Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

A. 415
B. 465
C. 440
D. Cannot be determined

Question 746

cot2A + cos2A is equal to

A. (cosecA -­ sinA)2(cosecA + sinA)
B. (cosecA + sinA)(cosecA -­ sinA)
C. (secA + sinA)(secA -­ sinA)
D. (secA -­ sinA)2(secA + sinA)

Question 747

cot3A is equal to

A. 3cotA -­ cot3A(1 -­ 3cot2A)
B. 3cotA + cot3A(1 -­ 3cot2A)
C. 3cotA -­ cot3A(1 + 3cot2A)
D. 3cotA + cot3A(1 + 3cot2A)

Question 748

If sinθ+cosecθ=2, the value of sinnθ+cosecnθ is

A. 2
B. 0
C. 1
D. 1/n

Question 749

If sinθ+cosθsinθ-cosθ=3, then the value of sin4θ-cos4θ is

A. 4/3
B. 3/4
C. 5/3
D. 3/5

Question 750

If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is

A. 2
B. 0
C. 1
D. -1

Question 751

If tanα = 2 - 1, then the value of  tanα - cotα = ?

A. -2
B. √2 + 1
C. 1
D. 2√2

Question 752

If tanθ = 43, then the value of 3sinθ+2cosθ3sinθ-2cosθ ?

A. 1/2
B. 3/2
C. 3
D. -3

Question 753

If tanθ = 724 then find the value of p such that tanθ - secθsinθ = -p28

A. 25
B. 75
C. 50
D. 100

Question 754

If tanθ = 815, then 1-sinθ1+sinθ is

A. 1/5
B. 2/5
C. 3/5
D. 0

Question 755

If x + 1x = -2, then the value of x631 + 1x632?

A. -2
B. -1
C. 0
D. 2

Question 756

If x + 1x = 3, then x18 + x12 + x6 + 1 value is

A. 0
B. 1
C. 2
D. 3

Question 757

If x + 1x = c + 1c, then the value of x =

A. C, 1/C
B. C, C2
C. C, 2C
D. 0,1

Question 758

If x + 3y - 2z4 = 6, x + 232y + 3z = 33 and 17x + y +z + 2z =9,  then what is the value of 46x+ 131y ?

A. 414
B. 364
C. 384
D. 464

Question 759

If x = 1 + √2 + √3, then the value of x2-2x-4=0

A. √6
B. 2√3
C. 3√2
D. 2√6

Question 760

If x = 2+32-3, then what is the value of x2+x-9 ?

A. 0
B. 3√2
C. 3√3
D. 5√3

Question 761

If x = 3+13, then the value of x-12642x-1x-233 is

A. √3/6
B. 2√3/6
C. 5/6
D. 2/3

Question 762

If x = 313- 3-13, then 3x2 + 9x is equal to

A. 5
B. 6
C. 7
D. 8

Question 763

If x = 313- 3-13, then 3x3 + 9x value is

A. 8
B. 9
C. 27
D. 16

Question 764

If X = 423 + 32 then find the value of  ( X + 1X ).

A. 103 + 15212
B. (103 - 52)12
C. -103 - 33212
D. (103+332)12

Question 765

If x = 4aba+b, then what is the value of x+2ax-2a+x+2bx-2b ?

A. 0
B. 2
C. 4
D. 1

Question 766

If x = 5 + 15 - 1 & y = 5 - 15 + 1 , then find the value of x2 - y2.

A. √5
B. 2√5
C. 3√5
D. 4√5

Question 767

If x = 6+26, then what is the value of x-1 + 1x-1 ?

A. 2√3
B. 3√2
C. 2√2
D. 3√3

Question 768

If x = a + 1a, y = a - 1a ,(a>0), then the value of x4+y4-2x2y2 is

A. 16
B. 20
C. 10
D. 5

Question 769

If x = at2 and y = 2at then

A. x2 = 4ay
B. y2 = 4ax
C. x2 + y 2 = a2
D. x 2 -­ y2 = a 2

Question 770

If x = x2+11 2 - 2, then x3 + 5x2 + 12x is

A. 0
B. 3
C. 7
D. 11

Question 771

If x+19x=4, then 9x2+19x2 is

A. 140
B. 142
C. 144
D. 146

Question 772

If x+1x ≠0 and x3+1x3 = 0, then the value of x+1x4 is :

A. 9
B. 12
C. 15
D. 16

Question 773

If x+1x:x-1x=5:3 then the value of x is

A. +- 1
B. +-2
C. +-3
D. +-4

Question 774

If x+1x=5, then the value of x1+x+x2 is

A. 1/5
B. 1/6
C. 5
D. 6

Question 775

If x+1x=5, then 6xx2+x+1 value is

A. 3
B. 2
C. 1
D. 0

Question 776

If x=2+3, then the value of x2-x+1x2+x+1 is

A. 2/3
B. 3/4
C. 4/5
D. 3/5

Question 777

If x=8+215, then what is the value of x+1x?

A. 2√15
B. 3√5
C. (3√5+√3)/2
D. 3√2+3

Question 778

If x-1x = 10, then find the value of x4+1x2

A. 98
B. 100
C. 102
D. 106

Question 779

If x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1  )] + [1/(2 + x2 )] + [1/(2 + x3 )]?

A. 1
B. 1/2
C. 2
D. 1/3

Question 780

If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3)?

A. 70/9
B. 154/27
C. 349/27
D. 349/7

Question 781

If x2+1x2 = 2, then the value of x - 1x is

A. -2
B. 0
C. 1
D. -1

Question 782

If x2+1x2 = 98, then x3+1x3 = ?

A. 970
B. 1030
C. -970
D. -1030

Question 783

If x2+5x+6 = 0, then the value of 2xx2-7x+6 is

A. 1/6
B. 1/3
C. -1/6
D. -1/3

Question 784

If x2+y2+z2-8x+6y-4z+29 = 0, then find the value of z(x+y).

A. 1
B. 2
C. 3
D. 4

Question 785

If x2-2x+1=0, then the value of x4+1x4 is

A. 0
B. 1
C. 2
D. 3

Question 786

If x2-3x+1=0, then x+1x is (x≠0)

A. 1
B. 0
C. 3
D. 2

Question 787

If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR?

A. 9
B. 8
C. 12
D. 6

Question 788

If x3-2x=3x, then the value of x2+1x2 will be

A. 3 1/9
B. 3 2/9
C. 2 1/9
D. 2 4/9

Question 789

If x4 + (1/x4) = 34, then what is the value of x3 – (1/x3)?

A. 0
B. 6
C. 8
D. 14

Question 790

If xa+b+1=xa-b+a-ba+b, then x is equal to

A. 2a-b
B. a+b
C. a-b
D. 2a+b

Question 791

If α and β are the roots of equation x2  – x + 1 = 0, then which equation will have roots α3 and β3?

A. x2 + 2x + 1 = 0
B. x2 – 2x – 1 = 0
C. x2 + 3x – 1 = 0
D. x2 – 3x + 1 = 0

Question 792

If θ is positive acute angle and 7cos2Ɵ + 3sin2Ɵ = 4, then the value of θ is

A. 60°
B. 30°
C. 45°
D. 90°

Question 793

If θ>0, be an acute angle, then the value of it in degrees satisfying cos2θ-3cosθ+2sin2θ=1 is

A. 90°
B. 30°
C. 45°
D. 60°

Question 794

If πsinθ= 1, πcosθ= 1, then (3tan 23θ+1) is

A. 1
B. √3
C. 2
D. 1/√3

Question 795

Ifab=45andbc=1516, then c2-a2c2+a2 is :

A. 7/5
B. 7/25
C. 7/125
D. 7

Question 796

In ∆DEF measure of angle E is 90°. If secD = 25/7, and DE = 1.4cm, then what is the length (in cm) of side DF?

A. 5
B. 4.8
C. 4
D. 5.6

Question 797

In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is

A. 30°
B. 45°
C. 60°
D. 90°

Question 798

In a circle, two arcs of unequal length subtend angles in the ratio 5:3. If the smaller angle is 45° then the measure of other angle in degrees.

A. 75°
B. 72°
C. 60°
D. 78°

Question 799

In a farm, in addition to 48 hens there are 42 sheep and 11 oxen with some shepherds. If the total number of feet be 224 more than the number of heads, find the number of shepherd.

A. 11
B. 13
C. 15
D. 17

Question 800

In a farm, there are goats and peacocks. If the number of heads are 60 and the number of feet are 170, then the number of goats = ?

A. 18
B. 20
C. 23
D. 25

Question 801

In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

A. 6
B. 10
C. 8
D. 12

Question 802

In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ?

A. 175
B. 145
C. 165
D. 135

Question 803

In a rectangle _____.

A. Consecutive angles are congruent as well as supplementary
B. Diagonals are perpendicular to each other
C. Diagonals bisect opposite angles
D. Diagonals are not equal

Question 804

In a Rhombus ABCD, measure of angle CAB is 35°, what is the measure of angle ABC?

A. 70°
B. 40°
C. 50°
D. 110°

Question 805

In a school there are 1500 students, 44% of them are girls. Monthly fee of each boy is 540 and fee of each girl is 25% less than that of a boy. The sum of fees of boys & girl is

A. Rs. 720600
B. Rs. 720800
C. Rs. 720900
D. Rs. 721000

Question 806

In a slip test, K got the 15th rank and he was 44th from the bottom of the list of passed students. 4 students did not take up the slip test and 3 students were failed. What is the total strenght of the class ?

A. 63
B. 62
C. 64
D. 65

Question 807

In a triangle PQR, ∠Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circum circle of the triangle?

A. 5
B. 6
C. 6.5
D. 6√2

Question 808

In an acute-angled triangle ABC is Sin(B+A+C)=32 and tan(C+A-B)=1, then C is equal to

A. 37.5°
B. 67.5°
C. 52.5°
D. 72.5°

Question 809

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :

A. 35
B. 38
C. 40
D. 42

Question 810

In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:

A. 35
B. 38
C. 40
D. 42

Question 811

In an isosceles trapezium _____.

A. Diagonals are congruent
B. Opposite sides are parallel
C. Diagonals are bisectors of each other
D. Diagonals bisect opposite angles

Question 812

In each of the following questions two equations I and II are given. Solve both the equations and give answer: I. x2+2x-195=0II. y2+30y+225=0

A. x = y or relation can’t be established between x and y
B. x > y
C. x < y
D. x ≥ y

Question 813

In the first 10 overs of a cricket game, the run rate was only 3.2. The run rate in the remaining 40 overs to reach the target of 282 runs is

A. 6.4
B. 6.3
C. 6.25
D. 6.5

Question 814

In the given figure, AB is a diameter of the circle with center O and XY is the tangent at a point C. If ACX = 35 deg, then what is the value (in deg) of CAB?

A. 45
B. 35
C. 55
D. 65

Question 815

In ΔABC measure of angle B is 90 deg. If cosA = 5/13, and AB = 10 cm, then what is the length (in cm) of side BC?

A. 26
B. 24
C. 25
D. 5

Question 816

In ΔABC measure of angle B is 90 deg. If cotA = 7/24, and AB = 1.4cm, then what is the length (in cm) of side AC?

A. 5
B. 4.8
C. 4
D. 5.6

Question 817

In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 8 cm, 6 cm and 7.2 cm respectively, find length of BC?

A. 12.6 cm
B. 9.3 cm
C. 8.1 cm
D. 5.4 cm

Question 818

In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 9 cm, 6 cm and 5.4 cm respectively find length of BC?

A. 3.6 cm
B. 4.8 cm
C. 11.2 cm
D. 9 cm

Question 819

In ΔDEF measure of angle E is 90 deg. If sinD = 15/17, and DE = 4cm, then what is the length (in cm) of side EF?

A. 8.5
B. 7.5
C. 5
D. 6

Question 820

In ΔPQR measure of angle Q is 90°. If cosP = 5/13, and PQ = 2.5cm, then what is the length (in cm) of side PR?

A. 6
B. 6.5
C. 4
D. 5.6

Question 821

In ΔPQR measure of angle Q is 90°. If tanP = 4/3, and PQ = 1.5cm, then what is the length (in cm) of side PR?

A. 2
B. 2.5
C. 3
D. 4.8

Question 822

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:1 and length of QR is 15 cm,what is the length of ST?

A. 3 cm
B. 5 cm
C. 12 cm
D. 10 cm

Question 823

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:3 and length of QR is 4.9 cm, find ST?

A. 5.6 cm
B. 7.2 cm
C. 2.8 cm
D. 3.6 cm

Question 824

In ΔUVW measure of angle V is 90 deg. If cosecU = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW?

A. 6.5
B. 6
C. 4
D. 5.6

Question 825

In ΔUVW measure of angle V is 90 deg. If sinU = 24/25, and UV = 0.7cm, then what is the length (in cm) of side VW?

A. 2.5
B. 3
C. 2.4
D. 4

Question 826

In ΔXYZ measure of angle Y is 90 deg. If cot X = 5/12, and XY = 2.5 cm, then what is the length (in cm) of side XZ?

A. 6
B. 4
C. 5.6
D. 6.5

Question 827

In ∆ABC if the median AD=1/2 BC, then ∠BAC is

A. 90°
B. 45°
C. 60°
D. 75°

Question 828

In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is

A. 40°
B. 75°
C. 90°
D. 105°

Question 829

In ∆UVW measure of angle V is 900. If cosecU = 13/12, and UV = 2.5 cm, then what is the length (in cm) of side VW?

A. 6.5
B. 6
C. 4
D. 5.6

Question 830

In ∆XYZ measure of angle Y is 90 deg. If cosecX = 13/12, and XY = 1cm, then what is the length ( in cm ) of side YZ?

A. 2.6
B. 1.5
C. 2.4
D. 2

Question 831

If 5x + 6(3-2x) = 4, then what is the value of x?

A. 1
B. 2
C. 3
D. 4

Question 832

If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?

A. 0
B. 1
C. 2
D. 3

Question 833

If 5x/2 - [7(6x - 3/2)]/4 = 5/8, then what is the value of x?

A. 1/4
B. -1/4
C. 4
D. -4

Question 834

If 60/75 is equivalent to 4/x, then the value of x is

A. 5
B. 4
C. 15
D. 18

Question 835

If 7x - (3/2) * (4x - 9) = 6.5, then the value of x is?

A. 7
B. 20
C. -7
D. -20

Question 836

If 7x - [3(2x - 3)]/2 = 1/2, then what is the value of x?

A. -1
B. 1
C. 3
D. -3

Question 837

If 7x ­- 5y = 13 and 2x -­ y = 5, then (x -­ y) is

A. 3
B. 4
C. 5
D. 1

Question 838

If 7x + 6y = 5xy and 10x ­- 4y = 4xy, then value of x and y is

A. 3, 2
B. 2, 3
C. 4, 2
D. 5, 6

Question 839

If 8x/3 + [7(5 - 2x/3)]/2 = 1/2 , then what is the value of x?

A. -17
B. 51
C. -51
D. 17

Question 840

If 9 * 6 = 45, 7 * 4 = 33, and 6 * 4 = 20, then what is the value of 5 * 3?

A. 24
B. 16
C. 13
D. 10

Question 841

If 9x - [5(2x + 1)/2] = 9/2, then the value of x is?

A. 7/4
B. -7/4
C. 4/7
D. -4/7

Question 842

If 9x - 6(3 - x) = 12, then the value of x is

A. 2
B. 4
C. 6
D. 9

Question 843

If 9x+2 = 240 + 9x, the value of (8x)x is

A. 1
B. -1
C. 0
D. 2

Question 844

If a – (1/a) = b, b – (1/b) = c and c – (1/c) = a, then what is the value of (1/ab) + (1/bc) + (1/ca)?

A. – 3
B. – 6
C. – 1
D. – 9

Question 845

If a - b = 1 and ab = 6, then what is the value of a3- b3?

A. 21
B. 23
C. 19
D. 25

Question 846

If a - b = -1 and ab = 6, then what is the value of a3- b3?

A. 33
B. -19
C. 18
D. 35

Question 847

If a - b = 10 and ab =-21, then what is the value of a3-b3 ?

A. 316
B. 370
C. 185
D. 158

Question 848

If a – b = 11 and ab = 24, then value of a2 + b2 is

A. 169
B. 37
C. 73
D. 48

Question 849

If a - b = 2 and ab = 15, then what is the value of a3- b3?

A. 152
B. 112
C. 108
D. 98

Question 850

If a - b = 2 and ab = 24, then what is the value of a3- b3?

A. 280
B. 124
C. 140
D. 152

Question 851

If a - b = 2 and ab = 8, then what is the value of a3 - b3?

A. 65
B. 34
C. 43
D. 56

Question 852

If a -­ b = 3 and ab =28, then a3 - b3 is

A. 279
B. 387
C. 513
D. 91

Question 853

If a - b = 3,  a2+b2=29, find the value of ab.

A. 10
B. 12
C. 15
D. 18

Question 854

If a - b = 4 and ab = -3, then what is the value of a3- b3?

A. 21
B. 28
C. 23
D. -20

Question 855

If a - b = 5 and a2 + b2 = 97, ab = ?

A. 48
B. 32
C. 36
D. 72

Question 856

If a - b = -6 and a2 + b2 = 44, then ab is

A. -4
B. 8
C. 4
D. -8

Question 857

If a - b = -7 and a2+ b2= 85, then find ab.

A. 18
B. -30
C. -44
D. 60

Question 858

M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?

A. 2
B. 1
C. 3
D. 6

Question 859

Mayur can complete a work in 27 hours. If he is joined by Jayantika who is 100% more efficient, in what time will they together finish the work?

A. 6 hours
B. 3 hours
C. 9 hours
D. 10 hours

Question 860

Mr. Ankit is on tour to Siachin and he has Rs. 360 for his expenditure. If he exceeds his tour by 4 days, he must trim down his daily expenditure by Rs.3. Forhow many days is Mr. Ankit is on tour?

A. 20
B. 22
C. 24
D. 26

Question 861

N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?

A. 8
B. 9
C. 7
D. 10

Question 862

On dividing 111a2b2c2 by 37a2, we get ______.

A. 2c2
B. 2b2
C. 3
D. 3b2c2

Question 863

On dividing 221a2b2 by 13b2, we get _____.

A. 17a2
B. 17b2
C. 13a2b2
D. 13

Question 864

On dividing 24a2b2 by 6b2, we will get

A. 4b
B. 4ab
C. 4
D. 4a2

Question 865

On dividing 256a2b2c2 by 64a2, we get

A. 2cxc
B. 2bxb
C. 4 bxb.cxc
D. 4

Question 866

On dividing 8a2b2c2 by 4a2, we get

A. 2b2
B. 2c2
C. 2b2c2
D. 2

Question 867

On dividing a number by 38, we get 70 as quotient and 12 as remainder. What is the number?

A. 2648
B. 2636
C. 2684
D. 2672

Question 868

One of the roots of the equation x2 - 4x + k = 0 is x = 3. The other root is

A. x = -1
B. x = -4
C. x = 1
D. x = 4

Question 869

Out of the 60 students of a class, 29 took Mathematics, 32 took Biology and 8 took none of the two subjects. How many students took both Mathematics and Biology?

A. 8
B. 9
C. 7
D. 6

Question 870

P + Q = 2(P-Q). If Q = 10, what is the value of P?

A. 10
B. 40
C. 20
D. 30

Question 871

P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?

A. 1.5
B. 2
C. 2.5
D. 3

Question 872

P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?

A. 5x - 2y = 16
B. 5x - 2y = -16
C. 5x + 2y = -16
D. 5x + 2y = 16

Question 873

P(4,2) and R(-2,0) are vertices of a rhombus PQRS. What is the equation of diagonal QS.

A. x - 3y = -2
B. 3x + y = 4
C. 3x + y = -4
D. x - 3y = 2

Question 874

p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?

A. 4
B. 8
C. 2
D. 12

Question 875

Point A (4 , 2) divides segment BC in the ratio 2:5. Co-ordinates of B are (2 , 6) and C are (7 , y). What is the value of y?

A. 8
B. -8
C. 6
D. -6

Question 876

Point A divides segment BC in the ratio 4:1. Co-ordinates of B are (6 , 1) and C are (7/2 , 6). What are the co-ordinates of point A?

A. (4 , 3)
B. (4 , 5)
C. (2 , 5)
D. (3 , 5)

Question 877

Point P (-2, 5) is the midpoint of segment AB. Co-ordinates of A are (-5, y) and B are (x, 3). What is the value of x?

A. 1
B. -1
C. 2
D. -2

Question 878

Point P is the midpoint of seg AB. Co­-ordinates of P are (­-1,1) and A are (4,3). What are the co-­ordinates of point B?

A. (6, 1)
B. (-­6, ­1)
C. (6, ­-1)
D. (­-6, -1)

Question 879

Point P is the midpoint of segment AB. Co-ordinates of P are (5, -1) and A are (2, -4). What are the co-ordinates of point B?

A. (6, 4)
B. (8, 2)
C. (1,-2)
D. (-6, -2)

Question 880

Point P is the midpoint of segment AB. Co-ordinates of P are (5,-4) and A are (7,0). What will be the co-ordinates of point B?

A. (3, -8)
B. (-3, -8)
C. (3, 8)
D. (-3, 8)

Question 881

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS =

A. 65°
B. 130°
C. 115°
D. 55°

Question 882

PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?

A. 5/√3
B. 10√3
C. 10/√3
D. 5√2

Question 883

Product of 6ab, 3b and 4a is

A. 72a2b2
B. 144ab
C. 72ab
D. 144a2b2

Question 884

Product of 9b2, 3a2 and 4ab is

A. 108a2b2
B. 108a3b3
C. 108a3b2
D. 108a4b4

Question 885

Profit of Rs 144000 has to be divided among three partners Akram, Bipin and Chintan in the ratio 3:2:7. How much Rs. Chintan get?

A. 84000
B. 24000
C. 36000
D. 42000

Question 886

Reciprocal of 235?

A. 235
B. 532
C. 513
D. 335

Question 887

Reduce 2530/1430 to lowest terms.

A. 47/17
B. 23/13
C. 47/19
D. 29/17

Question 888

Reduce 3596 / 4292 to lowest terms.

A. 29/37
B. 17/43
C. 31/37
D. 19/23

Question 889

Reflection of the point (­1,4) in the x­axis is

A. (1,4)
B. (1,­-4)
C. (­-1,4)
D. (-­1,-­4)

Question 890

Reflection of the point (­2,5) in the x­ axis is

A. (2,5)
B. (-2,­5)
C. (­2,-5)
D. (­-2,­-5)

Question 891

Reflection of the point (2,­7) in the y­axis is

A. (2,7)
B. (­-2,-­7)
C. (­-7,2)
D. (7,­2)

Question 892

Reflection of the point (-3,6) in the x-axis is

A. (3,6)
B. (6,-3)
C. (-3,-6)
D. (-6,3)

Question 893

Reflection of the point (3,-6) in the y-axis is

A. (3,6)
B. (3,-6)
C. (-3,-6)
D. (-3,6)

Question 894

Reflection of the point (4,-5) in the y-axis is

A. (4,5)
B. (-4,-5)
C. (4,-5)
D. (-4,5)

Question 895

Reflection of the point (4,­6) in the origin is

A. (4,6)
B. (­-4,­-6)
C. (­-4,6)
D. (4,­-6)

Question 896

Rehman walks at 8 km/hr and Roma cycles at 13 km/hr towards each other. What was the distance between them when they started if they meet after 36 minutes?

A. 12.6 kms
B. 18.9 kms
C. 15.8 kms
D. 9.5 kms

Question 897

Rs.7750 is divided among X, Y and Z such that 3 times of X's share is equal to 5 times of Y's share which is equal to 2 times of Z's share. What is the share (in Rs) of Z?

A. 4250
B. 3750
C. 3875
D. 4475

Question 898

Sec 45% + Tan 30% =

A. (√6 + 1)/√3
B. (1 + √3)/2
C. (√3 + 2)/√3
D. 5/√3

Question 899

sec2Acosec2A is equal to

A. sec2A -­ cosec2A
B. √[sec2A + cosec2A]
C. sec2A + cosec2A
D. √[sec2A -­ cosec2A]

Question 900

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 cm sq, what is the area (in sq cm) of quadrilateral BDEC?

A. 98
B. 94
C. 90
D. 86

Question 901

D and E are the points on the sides AB and AC respectively of a ΔABC and AD = 8 cm, DB = 12 cm, AE= 6 cm and EC = 9 cm, then BC is equal to:

A. 2/5 DE
B. 5/2 DE
C. 3/2 DE
D. 2/3 DE

Question 902

Derivative of sinx by first principle?

A. -sinx
B. -cosx
C. cosx
D. sinx

Question 903

Determine the value of ‘r’ for which the equation 13x + 5 = rx + 18 has no solution.

A. 0
B. 5
C. 13
D. 18

Question 904

Determine the value of “s” for which the equation 5x + 35 = 60x + s has infinite number of solutions.

A. 420
B. 440
C. 460
D. 480

Question 905

Determine the value of a/b + b/a when a + b = 8 and ab = 4.

A. 4
B. 8
C. 12
D. 14

Question 906

Determine the value of 'x' in x = 11+2+12+3+13+2

A. -1
B. 0
C. 1
D. 2

Question 907

Determine the value of z in the equation: z = 20+20+20+20+...∞

A. 4
B. 5
C. 20
D. 25

Question 908

Determine the value of  'a' which satisfies the equation 9a + 40a = 41a

A. 1
B. 2
C. 3
D. 4

Question 909

Determine the value of a+1b-1 when ab = 343.

A. 9
B. 64
C. 125
D. 216

Question 910

Determine the value of a2+b2a3+b3 when a = 2+√3 and b = 2-√3.

A. 0.27
B. 0.42
C. 0.58
D. 0.93

Question 911

Determine the value of y-1y2 when y4+1y4=34

A. 1
B. 2
C. 3
D. 4

Question 912

Shaan got a total of Rs. 912 in the denomination of equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins do Shaan posses?

A. 16
B. 57
C. 171
D. 323

Question 913

Simplify (2/7 + 3/5) / (2/5 + 2/7)

A. 31/24
B. 24/31
C. 26/25
D. 12/13

Question 914

Simplify : (-4.6)x(-4.6)/(-4.6+0.6)

A. -5.29
B. -0.529
C. -4.06
D. 5.01

Question 915

Simplify : 132 - 142 + 172 - 250 = ?

A. 196
B. 169
C. 121
D. 144

Question 916

Simplify : 213 - 112 of 35 + 125 ÷ 213

A. 1/10
B. 3/10
C. 11/10
D. 1

Question 917

Simplify : -21973 × -1253 ÷ 275123

A. 492/7
B. 520/3
C. 554/7
D. 571/5

Question 918

Simplify : 69 X 69 X 69 -65 X 65 X 669 X 69 + 69 X 65 + 65 X 65

A. 1
B. 4
C. 0.216
D. 0.164

Question 919

Simplify 4(x-1) -3x

A. 7x - 4
B. 7x + 4
C. x + 4
D. x - 4

Question 920

Simplify 437bxaz / 23ab.

A. 17xzb
B. 9xz
C. 19xz
D. 19ab

Question 921

Simplify the equation 0.733+0.2730.732+0.272-0.73×0.27

A. 1
B. 0.4087
C. 0.73
D. 0.27

Question 922

Simplify  413 + 215 + 414 = ?

A. 10 47/60
B. 11 45/73
C. 11 47/36
D. 10 35/48

Question 923

Simplify (533bxaz)/(41ab)

A. 17xzb
B. 19xz
C. 13xz
D. 31ab

Question 924

Simplify (b2x 3a2z4 ) × (b2x 4a4z3 )/(a3b2z4 )

A. b2x7a3z3
B. b3x7a3 z3
C. b2x5a3 z3
D. b2x7a3z2

Question 925

Simplify (b5x2a3z4)*(b3x2a4z5) / (a2b3z2)

A. b5x4a5z5
B. b5x4a5z7
C. b5x4a4z7
D. b4x4a5z7

Question 926

Simplify 0.1x0.1x0.1 + 0.3x0.3x0.30.3x0.3 - 0.3x0.1 + 0.1x0.1

A. 0.09
B. 0.03
C. 0.05
D. 0.04

Question 927

Simplify 11.9983 = ?

A. 1727.136
B. 1331.136
C. 1685.136
D. 1700.136

Question 928

Simplify 486b3x2a4z3/27a3b2z

A. 18bx2az2
B. 18bx2a2z
C. 36ba2z
D. 36bxaz

Question 929

Simplify 50 + 18 - 8

A. 8√2
B. 7√2
C. 6√2
D. 5√2

Question 930

Simplify 576b3x2a4z3/36a3b2z

A. 16bx2az2
B. 8bx2az2
C. 32ba2 z
D. 32bxa2

Question 931

Simplify 81x2 - 49y29x + 7y

A. 9x++7y
B. 9x-7y
C. 9x
D. 7y

Question 932

Simplify x5 ÷ x43 ÷ x

A. x3
B. x2
C. X
D. 1/X

Question 933

Simplify: (213 x 213 + 187 x 187)

A. 80338
B. 80438
C. 60338
D. 60438

Question 934

Simplify: b-[b-(a+b)-{b-(b-a-b)}+2a]

A. 2b
B. 1
C. 0
D. 3b

Question 935

Simplyfiy : 314÷114-12212-14+16

A. 78
B. 88
C. 98
D. 108

Question 936

sin(A+B) -­ sin(A-­B) is equal to

A. 2sinAcosB
B. 2cosAcosB
C. 2cosAsinB
D. 2sinAsinB

Question 937

Sin6A + Cos6A - 1 is equal to

A. -3Sin2ACos2A
B. 1 - 3 SinACosA
C. 1 + 3Sin2ACos2A
D. 0

Question 938

sinA/(1 + cos A) is equal to

A. (cosecA -­ cotA)
B. (cosecA + cotA)
C. √[(cosecA ­- cotA)]
D. √[(cosecA + cotA)]

Question 939

Slope of the line AB is -2/3. Co-ordinates of points A and B are (x , -3) and (5 , 2) respectively. What is the value of x?

A. 4
B. -14
C. 12.5
D. -4

Question 940

Slope of the line AB is -4/3. Co-ordinates of points A and B are (x, -5) and (-5, 3) respectively. What is the value of x?

A. -1
B. 2
C. -2
D. 1

Question 941

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

A. 6
B. 9√3
C. 12
D. 12√3

Question 942

Solve : (x + 2y) (2x - y)

A. 2x2 + 5xy + 2y2
B. 2x2 + 3xy - 2y2
C. x2 + 4xy + y2
D. x2+ 4xy - y2

Question 943

Solve : 1000x - 5 = -6

A. 1/1000
B. -1/1000
C. -11/1000
D. 11/1000

Question 944

Solve : 12 - [26 - {2 + 5 x (6 - 3)}]

A. 2
B. 3
C. 7
D. 8

Question 945

Solve the following : -1/4 { -45 - (-96) / (-32)} = ?

A. 12
B. 10.5
C. -12
D. -10.5

Question 946

Solve the following : 27 - [38 - {46 - (15 - 13 - 2)}]

A. 31
B. 35
C. 30
D. 29

Question 947

Solve the following : 3/4+{3/4 + 3/4 ÷ (3/4 + 3/4)} = ?

A. 0
B. 3/4
C. 1
D. 2

Question 948

Solve the following 7 x {4 + (-2) x (-3)} = ?

A. 14
B. -42
C. -14
D. 70

Question 949

Solve the following equation to find x: (x − 2)2 − 36 = 0 : xεN

A. 4
B. 8
C. -4
D. -8

Question 950

Solve the following : 80÷[48−56−(60−36÷12×4)]=?

A. 5
B. 8
C. 4
D. 2

Question 951

Solve the following: (−18)[36÷7−(−2)]÷{}(−4)19−(−3)×(−5)={}?

A. -4.5
B. 4.5
C. -2.5
D. 2.5

Question 952

Solve this inequality 3b - 7 < 32?

A. b = 13
B. b < 13
C. b > = 13
D. b < = 13

Question 953

Solve this inequality 3p - 16 < 20?

A. p >= 12
B. p <= 11/3
C. p < 12
D. p > 11/3

Question 954

Square of (3x – 5xy) is

A. 9x2 - 30x2y + 25x2y2
B. 9x2 - 15x2y + 25x2y2
C. 25x2 - 15x2y + 9x2y2
D. 25x2 - 30x2y + 9x2y2

Question 955

Square of (7 ­- 4x) is

A. 16x2 - 28x + 49
B. 49 -­ 28x ­- 16x2
C. 49 - ­ 56x -­ 16x2
D. 16x2 - 56x + 49

Question 956

Square root of 0.9 is equal to

A. 0.03
B. 0.3
C. 0.9487
D. 0.9463

Question 957

Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?

A. 4/5
B. 9/4
C. 4/9
D. 5/4

Question 958

Sum of twice a fraction and its reciprocal is 17/6. What is the fraction?

A. 4/3
B. 5/4
C. 3/4
D. 4/5

Question 959

Sumit and Amit undertook a work for Rs 7200. Sumit alone can do the work in 5 days and Amit alone can do the work in 4 days. If they work together,then what will be the difference (in Rs.) in the amount they receive?

A. 800
B. 1600
C. 1200
D. 1400

Question 960

Tan 45° + Cosec 60° =

A. (1 + 2√2)/2
B. (√3 + 2)/√6
C. 5/√3
D. (3 + 2√3)/3

Question 961

tan(A/2) is equal to

A. tanA/(1 + secA)
B. 1/(cosecA + cotA)
C. tanA/(1 + cosecA)
D. 1/(secA + cotA)

Question 962

tan(A/2) is equal to

A. cosecA + cotA
B. secA - cotA
C. cosecA - cotA
D. secA + cotA

Question 963

tan2Asin2A is equal to

A. tan2A - sin2A
B. tan2A + sin2A
C. cot2A - sin2A
D. cot2A + sin2A

Question 964

tan3A is equal to

A. 3tanA -­ tan3A(1 -­ 3tan2A)
B. 3tanA + tan3A(1 -­ 3tan2A)
C. 3tanA -­ tan3A(1 + 3tan2A)
D. 3tanA + tan3A(1 + 3tan2A)

Question 965

tanAcosec2A is equal to

A. (1 + tan2A)cotA
B. (1 -­ tan2A)cotA
C. √[(1 + tan2A)cotA]
D. √[(1 -­ tan2A)cotA]

Question 966

The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?

A. 23
B. 17
C. 20
D. 26

Question 967

The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower in meters is

A. √3
B. 5√3
C. 10√3
D. 20√3

Question 968

The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 meter and 64 meter from the base of tower are x and 90° - x respectively . The height of the tower will be

A. 39 m
B. 89 m
C. 1.6 m
D. 40 m

Question 969

The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is

A. h(cotβ-cotα)cos(α+β)
B. h(cotα - cotβ)
C. h(tanβ - tanα)tanα tanβ
D. h(cotα+cotβ)

Question 970

The areas of two similar triangles ΔABC and ΔPQR are 121 sq cms and 64 sq cms respectively. If PQ = 12 cm, what is the length (in cm) of AB?

A. 7.25
B. 6.25
C. 16.5
D. 5.25

Question 971

The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 8 : 9. Then what is the number of visitors on the 5th day of the library ?

A. 54
B. 64
C. 68
D. 72

Question 972

The average of 100 observations was calculated as 35.It was found later, that one of the observation was misread as 83 instead of 53. The correct average is :

A. 32.7
B. 34.7
C. 35.7
D. 36.7

Question 973

The average revenues of 13 consecutive years of a company is Rs 70 lakhs. If the average of first 7 years is Rs 65 lakhs and that of last 7 years is Rs 77 lakhs, find the revenue for the 7th year.

A. Rs 86 lakhs
B. Rs 84 lakhs
C. Rs 82 lakhs
D. Rs 80 lakhs

Question 974

The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?

A. 35 c
B. 36 c
C. 34 c
D. 32 c

Question 975

The average weight of Sudesh, Jyothi and Ritu is 89 kg. If the average weight of Sudesh and Jyothi be 98 kg and that of Jyothi and Ritu be 83 kg, then the weight of Jyothi is

A. 58
B. 56
C. 95
D. 66

Question 976

The co-ordinates of the centroid of a triangle ABC are (3,-2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,-2) respectively?

A. (-5,-9)
B. (5,-9)
C. (5,9)
D. (-5,9)

Question 977

The coordinates of the point that divides the line segment joining the points (-5, 5) and (7,-3) internally in the ratio 3 : 1 are given by

A. (-2, 3)
B. (4, -1)
C. (5/2, 0)
D. (1, 1)

Question 978

The cost of 15 kg of groundnuts and 4 kg of cashews is Rs.7,000. The cost of 10 kg of cashews is equal to 25 kg of groundnuts. Find the cost of groundnut per kg.

A. Rs.320
B. Rs.700
C. Rs.540
D. Rs.280

Question 979

The cost of one dozen bananas is Rs.5. The cost of one dozen oranges is Rs.75. What will the cost of one and a quarter dozen bananas and three-fourth dozen oranges?

A. Rs. 109.25
B. Rs. 87.25
C. Rs. 71.75
D. Rs. 62.50

Question 980

The costs of daily ticket of local train is Rs. 50 and Monthly Pass costs is Rs. 1125. If I buy the Monthly Pass and travel for 30 days in a month then I save?

A. 10 percent
B. 25 percent
C. 14 percent
D. 15 percent

Question 981

The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 12 sq cm, what is the area of the equilateral triangle?

A. 12√3 sq cm
B. 6√3 sq cm
C. 12√2 sq cm
D. 24 sq cm

Question 982

The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number

A. 1526
B. 1431
C. 1485
D. 1234

Question 983

The difference of 18 and its reciprocal is equal to :

A. 1/8
B. 4/3
C. 15/16
D. 105/304

Question 984

The distance between the points (11,­5) and (k,0) is 13. Find k.

A. k = 1 or 23
B. k = ­-1 or 23
C. k = ­1 or ­-23
D. k = -1 or ­-23

Question 985

The distance between the points (2, 7) and (k, -5) is 13. What is the value of k?

A. -7
B. 7
C. 6
D. -6

Question 986

The distance between the points (7,7) and (k,-5) is 13. Find k?

A. -2
B. 4
C. -4
D. 2

Question 987

The expenses of a person increase by Rs. 50000 for every month in February and March. If his expenses in January was Rs. 50000, calculate his average expenditure (in Rs.) from January to March.

A. 100000
B. 150000
C. 75000
D. 50000

Question 988

The factors of x2 + 8x + 12 are

A. (x+6)(x+2)
B. (x-6)(x+2)
C. (x-4)(x-4)
D. (x+6)(x-2)

Question 989

The first and last terms of an arithmetic progression are 25 and ­52. What is the sum of the series if it has 12 terms?

A. -162
B. -110
C. 162
D. 110

Question 990

The first and last terms of an arithmetic progression are 37 and ­18. If the sum of the series is 114, then it has how many terms?

A. 13
B. 12
C. 14
D. 15

Question 991

The highest score in an inning was  3/11 of the total and the next highest was 3/11 of the reminder . If the score  differ by 9, the total score was :

A. 110
B. 121
C. 132
D. 143

Question 992

The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?

A. 5
B. 10√3
C. 20
D. 20√3

Question 993

The least value of tan2x + cot2x is

A. 3
B. 2
C. 0
D. 1

Question 994

The length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is

A. 10 cm
B. 5 cm
C. 6 cm
D. 12 cm

Question 995

The length of a median of an equilateral triangle is 12√3 cms. Then the area of the triangle is

A. 144 sq. cms
B. 288√3 sq. cms
C. 144√3 sq. cms
D. 288sq.cms

Question 996

The line passing through (-2,5) and (6,b) is perpendicular to the line 20x + 5y = 3. Find b?

A. -7
B. 4
C. 7
D. -4

Question 997

The line passing through the point (5,a) and point (4,3) is perpendicular to the line x - 6y = 8. What is the value of 'a'?

A. -3
B. -2
C. 4
D. 5

Question 998

The measures of the three angles of a triangle are in the ratio 1:2:3. What is the measure of the biggest angle?

A. 30°
B. 60°
C. 90°
D. 120°

Question 999

The number of solutions of the pair of linear equations x + 2y - 8 = 0 and 2x + 4y = 16 is

A. 0
B. 1
C. Infinitely many
D. 2

Question 1000

The number whose square is equal to the difference of the squares of 37 and 23 is:-

A. 45.09
B. 28.98
C. 47.09
D. 28

Question 1001

The orthocentre of an obtuse­angled triangle lies

A. inside the triangle
B. outside the triangle
C. on one side of a triangle
D. none of these

Question 1002

The pair of linear equations 3x + y = 1 and px + 2y = 5 has no finite solution if

A. p>=6
B. p = 6
C. 0 < p < 6
D. p = 0

Question 1003

The perimeter of two similar triangles is 36 units and 48 units. Find the ratio of their corresponding areas.

A. 1 : 3
B. 3 : 4
C. 4 : 9
D. 9 : 16

Question 1004

The point P (a,b) is first reflected in origin to P1 and P1 is reflected in Y­axis to (4,­3). The co­-ordinates of point P are

A. (4,3)
B. (-­4,3)
C. (­-3,4)
D. (3,­-4)

Question 1005

The point P(a,b) is first reflected in origin to P1 and P1 is reflected in y-­axis to (6,­-5). The co-­ordinates of point P are

A. (­-6,­-5)
B. (6,5)
C. (­6,-5)
D. (-6,­5)

Question 1006

The point Q(a,b) is first reflected in y­-axis to Q1 and Q1 is reflected in x­axis to (­-5,3). The co­ordinates of point Q are

A. (­-5,­3)
B. (5,-3)
C. (­-5,-3)
D. (5,­3)

Question 1007

The point Q(a,b) is first reflected in y­axis to Q1 and Q1 is reflected in x­axis to (­6,2). The co­ordinates of point Q are

A. (-­6,­2)
B. (2,­-6)
C. (6,­-2)
D. (­-2,6)

Question 1008

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in x-axis to (-3,4). The co-ordinates of point R are

A. (3,4)
B. (-3,-4)
C. (-3,4)
D. (3,-4)

Question 1009

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in x­axis to (­-4,2). The co-­ordinates of point R are

A. (­4,­-2)
B. (­-4,2)
C. (4,2)
D. (-4,­-2)

Question 1010

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in X-axis to (-5,1). The co-ordinates of point R are?

A. (5,-1)
B. (-1,5)
C. (1,-5)
D. (5,1)

Question 1011

The points A(3,­-2), B(1,4) and C(­-2,x) are collinear. What is the value of x?

A. 13
B. -2
C. 5
D. 3

Question 1012

The points A(x,2), B(­2,1) and C(6,­3) are collinear. Find x?

A. 4
B. -2
C. -4
D. 2

Question 1013

The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples  ?

A. Rs. 10
B. Rs. 15
C. Rs. 20
D. Rs. 25

Question 1014

The price of 4.5 m of cloth is Rs.60.75. Find the cost per meter.

A. 15.5
B. 13.5
C. 14.75
D. 13.75

Question 1015

The quadratic equation 1+a2x2+2abx+b2-c2=0 has only one root. What is the value of c21+a2 ?

A. a2
B. b2
C. c2
D. ab

Question 1016

The rate of discount on an article whose marked price is Rs. 170 and selling price is Rs. 130?

A. 24.26%
B. 22.45%
C. 23.53%
D. 23.60%

Question 1017

The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?

A. 4312√6
B. 3822√6
C. 4522√6
D. 4642√6

Question 1018

If 1+121+141+161+181-131-151-17 = 1+ 1x, then what is the value of x?

A. 6
B. 8
C. 5
D. 7

Question 1019

If 11+11+11+1x = 58, then what is the value of x?

A. 2
B. 3
C. 1
D. 4

Question 1020

If 11-13xx + 11-13yy + 11-13zz = 5 then what is the value of 1x + 1y + 1z = ?

A. 1
B. 13/11
C. 13/5
D. 4

Question 1021

If 1aa2+1 = 3, then the value of a6+1a3 is

A. 9
B. 18
C. 27
D. 1

Question 1022

If 1p+1q = 1p+q, then the value of p3-q3

A. p-q
B. pq
C. 1
D. 0

Question 1023

If 2+aa + 2+bb + 2+cc = 4, then the value of ab+bc+caabc is

A. 2
B. 1
C. 0
D. 1/2

Question 1024

If 2sec2x - tan2x = 5 and 0° ≤ x ≤ 90° , then x = ?

A. 60°
B. 90°
C. 30°
D. 45°

Question 1025

If 2x+13x = 5, the value of 5x6x2+20x+1 is

A. 1/4
B. 1/6
C. 1/5
D. 1/7

Question 1026

If 2x+29x = 4, then the value of 27x3+127x3

A. 180
B. 198
C. 234
D. 252

Question 1027

If 2x+2x=3, then the value of x3+1x3+2 is

A. 3/4
B. 4/5
C. 5/8
D. 7/8

Question 1028

If 2x+4-2x+2=3, then the value of x?

A. 0
B. 2
C. -1
D. -2

Question 1029

If 2x-12x = 5, then what is the value x2 + 116x2 - 2

A. 19/4
B. 23/4
C. 27/4
D. 31/4

Question 1030

If 2x-y2+(3y-2z)2=0, then the ratio of x:y:z is

A. 1 : 3 : 2
B. 1 : 2 : 3
C. 3 : 1 : 2
D. 3 : 2 : 1

Question 1031

If 3+12=x+3y, then the x+y is

A. 2
B. 4
C. 6
D. 8

Question 1032

If 310 × 272 = 92 × 3n then the value of n is

A. 10
B. 12
C. 15
D. 20

Question 1033

If 3a+4b3c+4d = 3a-4b3c-4d, then

A. ab = cd
C. ac = bd
D. a = b = c ≠ d

Question 1034

If 3n = 2187, then the value of n is:

A. 13
B. 14
C. 15
D. 16

Question 1035

If 3sinθ+4cosθ=5 (0<θ<90°) then the value of sinθ is

A. 1/5
B. 2/5
C. 3/5
D. 4/5

Question 1036

If 3x+22x+1 = a2x+1+bx+2 be an identity, then the value of b

A. 0
B. -1
C. 2
D. 3

Question 1037

If 3x+7=x2+p=7x+5, what is the value of P ?

A. 17/2
B. 25/3
C. 33/4
D. 41/5

Question 1038

If 3x-y=27, 3x+y=243 then find the x value

A. 2
B. 8
C. 4
D. 1

Question 1039

If 4x + 1x = 5, (x≠0), then the value of 5x4x2+10x+1 is

A. 1/2
B. 1/3
C. 2/3
D. 3

Question 1040

If 5+x+5-x5+x-5-x = 3,then what is the value of x ?

A. 5/2
B. 25/3
C. 4
D. 3

Question 1041

If -5x3+2 = x-6, then find the value of x?

A. 1
B. 2
C. 3
D. 4

Question 1042

If 9x = 24311, then what is the value of x?

A. 5/11
B. 5/22
C. 5/7
D. 5/33

Question 1043

If 9x2 + 16y2 = 60 and 3x + 4y = 6, then the value of xy is

A. -1
B. 1
C. -2
D. 2

Question 1044

If a -­ b = 6 and ab =16, then a3 -­ b3 is

A. 504
B. 702
C. 728
D. 511

Question 1045

If a + b = 8 and ab =15, then a3 + b3 is

A. 224
B. 244
C. 152
D. 128

Question 1046

If A = 0.216 + 0.0080.36+0.04-0.12 & B = 0.729-0.0270.81+0.09+0.27, then what is the value of A2+B22 ?

A. 0.8
B. 1
C. 1.4
D. 2.2

Question 1047

If a = 3+23-2, b = 3-23+2 then a2+b2-ab ?

A. 97
B. (2√3) + 2
C. (4√6) + 1
D. 98

Question 1048

If a+1a2 = 3, then the value of  a3+1a3 is

A. 0
B. a
C. 1/a
D. 1

Question 1049

If a+1b = 1 and b+1c = 1 then c+1a = ?

A. 0
B. 2
C. 1
D. 3

Question 1050

If a+1b= b+1c = c+1a (a , b, c are not equal) then the value of abc =

A. + 1
B. - 1
C. +1 & -1
D. None of the options

Question 1051

If a+1b=1 and b+1c=1 , then the value of c+1a is

A. 0
B. 1
C. -1
D. 2

Question 1052

If a+bab=21 ,  then the value of (a-b) is

A. 1
B. 0
C. -1
D. 2

Question 1053

If a1-2a+b1-2b+c1-2c = 12, then 11-2a+11-2b+11-2c value is

A. 1
B. 2
C. 3
D. 4

Question 1054

If a-1a=1, then a2 + 1a2 ?

A. 1
B. 3
C. 2
D. 4

Question 1055

If a2+1a2 = 38, then find the value of a-1a?

A. 2
B. 4
C. 6
D. 8

Question 1056

If a2+b2+c2=14 and a+b+c=6, then the value of ab+bc+ca is,

A. 11
B. 12
C. 13
D. 14

Question 1057

If a2+b2+c2=83 and a+b+c=15 then the value of ab+bc+ca is

A. 69
B. 70
C. 71
D. 72

Question 1058

If a2+b2=80 and ab = 32, then calculate the value of a-b/a+b.

A. 0.337
B. 0.339
C. 0.333
D. 0.335

Question 1059

If a2+b2c2 = b2+c2a2 = c2+a2b2 = 1k k≠0 then k =

A. 2
B. 1
C. 0
D. 1/2

Question 1060

If a2b+c=b2C+a=a2a+b=1 then 11+a+11+b+11+c is

A. 1
B. 2
C. 3
D. 4

Question 1061

If a2b+c=b2c+a=c2a+b=1 then the value of 21+a+21+b+21+c

A. 0
B. 1
C. 2
D. 3

Question 1062

If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?

A. 31
B. 26
C. 28
D. 24

Question 1063

If a3 + b 3 = 35 and ab = 6, then what is the value of a + b?

A. 5
B. 8
C. 2
D. -8

Question 1064

If a3+1a3 = 2, then the value of a2+1a?

A. 1
B. 2
C. 3
D. 4

Question 1065

If ab+ba = -1, then the value of a2b-b2a is

A. 1
B. -1
C. 0
D. 2

Question 1066

If ab+ba=1, then the value of a3+b3 is

A. 1
B. 0
C. -1
D. 2

Question 1067

If ab-1b=cb-1c=ac-1a, then ac+ba+cb

A. 1
B. 2
C. 3
D. 4

Question 1068

If aq-r+br-p-cp-q, then find the value of (pa + qp + rc) is

A. 0
B. 1
C. 2
D. -1

Question 1069

If ax= by= cz and b2= ac, then what is 1x+1z equal to ?

A. 1/y
B. -1/y
C. 2/y
D. -2/y

Question 1070

If C + 1C = 3, then what is the value of C-37+1C7?

A. 2
B. 0
C. 3
D. 1

Question 1071

If cos2x + cos4x = 1, then tan2x + tan4x =

A. 0
B. 1
C. 2tanx
D. tanx

Question 1072

If Cosecθ + Cotθ = 2, then Cotθ = ?

A. 0
B. 0.5
C. 1
D. 0.75

Question 1073

If cosαcosβ=m and cosαsinβ=n, then the value of m2+n2 cos2β is

A. n2
B. m2
C. mn
D. 1

Question 1074

If cosθ = x2-y2x2+y2, then the value of cotθ is

A. 2xyx2-y2
B. 2xyx2+y2
C. x2+y22xy
D. x2-y22xy

Question 1075

If cosθ1-sinθ+cosθ1+sinθ = 4, then the value of θ (0°<θ<90°)?

A. 60°
B. 45°
C. 30°
D. 35°

Question 1076

If cotθ = 4, then the value of 5sinθ+3cosθ5sinθ-3cosθ is

A. 1/9
B. 1/3
C. 3
D. 9

Question 1077

If P + 1P+2 = 1, then the value of P+23+1P+23-3 ?

A. 12
B. 16
C. 18
D. 15

Question 1078

If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812, then what is the value of P – Q?

A. 24645
B. 26075
C. 29317
D. 31515

Question 1079

If sec2θ+tan2θ=3, then sec4θ-tan4θ =

A. 1/√3
B. 1
C. √3
D. 0

Question 1080

If secθ + tanθ = 4, then secθ - tanθ = ?

A. 1
B. 0.25
C. 0.5
D. 0.75

Question 1081

If Sin 31° = xy, then the value of Sec 31° - Sin 59° is

A. x2yy2-x2
B. -x2yy2-x2
C. -y2y2-x2
D. x

Question 1082

If sinA + sin2A =1 then what is the value of cos2A + cos4A

A. 1/2
B. 1
C. 2
D. 3

Question 1083

The simplest form of 3565/1495 is

A. 31/13
B. 43/19
C. 23/13
D. 31/23

Question 1084

The simplest form of 3774/2958 is

A. 43/19
B. 37/29
C. 31/13
D. 31/23

Question 1085

The simplest value of 38-212+20318-227+45 is

A. 3/2
B. 2/3
C. 1/3
D. 2

Question 1086

The Simplified form of (b3x2a4z3)*(b4x3a3z2)/(a2b4z3) is

A. b2x4a6z
B. b3x2a4z3
C. b3x5a5z2
D. bazx

Question 1087

The simplified form of (x + 3)2 + (x - 1)2 is

A. (x2 + 2x + 5)
B. 2(x2 + 2x + 5)
C. (x2 - 2x + 5)
D. 2(x2 - 2x + 5)

Question 1088

The slope of the line passing through the points (2,-1) and (x,5) is -1. Find x?

A. 4
B. -4
C. 8
D. -8

Question 1089

The slope of the line passing through the points (7,-2) and (x,1) is -3/10. Find x.

A. 4
B. 2
C. -4
D. -3

Question 1090

The slopes of two lines are 1 and √3. What is the angle between these two lines?

A. 15°
B. 30°
C. 45°
D. 60°

Question 1091

The solution set of 4x -­ 3y = 10 and 3x + y = 14 is

A. {(5, 3)}
B. {(4, 2)}
C. {(11, ­1)}
D. {(2, 3)}

Question 1092

The solution set of 4x - 3y = 47 and 3x + y = 32 is

A. {(15, 3)}
B. {(4, 12)}
C. {(11, -1)}
D. {(12, 3)}

Question 1093

The square root of 4096 is

A. 56
B. 68
C. 74
D. 64

Question 1094

The square root of 6084 is

A. 82
B. 78
C. 74
D. 76

Question 1095

The standard deviation of the set {10, 11, 9, 11, 9} is

A. 1/√5
B. 2/√5
C. 3/√5
D. 0

Question 1096

The sum of 2xy(3x + 4y - 5z) and 5yz(2x - 3y) is

A. 6x2y - 8xy2 + 15y2z
B. 6x2y + 8xy2 - 15y2z
C. 6x2y + 8xy2 - 15y2z - 20xyz
D. 6x2y - 8xy2 + 15y2z + 20xyz

Question 1097

The sum of 4x + 3y ­ 7z, x ­ y ­ z and ­2x ­ 3y + 4z is

A. 3x -­ y -­ 4z
B. 3x -­ y + 4z
C. 3x + y -­ 4z
D. 3x + y + 4z

Question 1098

The sum of 6xy(2x - 4z) , 3yz(2x - 3z) and 4xz(3y - 2y2) is

A. 12x2y - 6xyz - 9yz2 + 8xy2z
B. 12x2y - 6xyz + 9yz2 - 8xy2z
C. 12x2y - 6xyz - 9yz2 - 8xy2z
D. 12x2y + 6xyz - 9yz2 - 8xy2z

Question 1099

The sum of a fraction and 3 times its reciprocal is 37/10. What is the fraction?

A. 5/2
B. 2/5
C. 5/4
D. 4/5

Question 1100

The sum of a fraction and 4 times its reciprocal is 13/3. What is the fraction?

A. 4/3
B. 3/4
C. 5/4
D. 4/5

Question 1101

The sum of a number and 4 times its reciprocal is 5. What is the number?

A. 4
B. 5
C. 6
D. 7

Question 1102

The sum of the parallel sides of a trapezium is 12.4 cm. If the distance between the parallel sides is 3.5 cm, what is the area of this trapezium?

A. 43.4 sq cm
B. 86.8 sq cm
C. 130.2 sq cm
D. 21.7 sq cm

Question 1103

The sum of two numbers is 7 and the sum their squares is 23, their product is equal to:

A. 10
B. 11
C. 12
D. 13

Question 1104

The sum of two positive integers is 80 & difference between them is 20. Then what is difference of squares of those numbers ?

A. 1400
B. 1600
C. 1800
D. 2000

Question 1105

The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is :

A. 50
B. 100
C. 150
D. 200

Question 1106

The two lines 4x+3y=0 and 7x+5y=0 will ______ in their graphical representation.

A. be parallel to each other
B. intersect each other at one point only
C. intersect each other at three points only
D. coincide each other

Question 1107

The two roots of a quadratic equation are given as x = 1/7 and x = -1/8 . The equation can be written as:

A. (7x − 1)(8x − 1) = 0
B. (7x − 1)(8x + 1) = 0
C. (7x + 1)(8x − 1) = 0
D. (7x + 1)(8x + 1) = 0

Question 1108

The two roots of an quadratic equation are given as x = 1/2 and x = -1/3. The equation can be written as

A. (2x - 1)(3x - 1) = 0
B. (2x + 1)(3x - 1) = 0
C. (2x - 1)(3x + 1) = 0
D. (2x + 1)(3x + 1) = 0

Question 1109

The two roots of an quadratic equation are given as x = 2/3 and x = -1/2. The equation can be written as

A. (2x - 1) (3x + 2) = 0
B. (2x + 1) (3x + 2) = 0
C. (2x + 1) (3x - 2) = 0
D. (2x - 1) (3x - 2) = 0

Question 1110

The value of (0.00000729/0.00000027) is

A. 0.27
B. 0.027
C. 2.7
D. 27

Question 1111

The value of (1 - √2) + (√2 - √3) + (√3 - √4) + ..... + (√15 - √16) is

A. 0
B. 1
C. -3
D. 4

Question 1112

The value of (sec245 - cot245) - (sin230 + sin260) is

A. 1
B. 2√3
C. 0
D. 1/√2

Question 1113

The value of 1/64 is equal to square of

A. 0.125
B. 0.135
C. 0.145
D. 0.225

Question 1114

The value of 122 + 345 - 3 / 1116 x 372 is

A. 466
B. 469
C. 446
D. 460

Question 1115

The value of 16 - [5 - 2{14 of 2 - (8 ÷ 4 x 2 - 1 + 3}] is

A. -12
B. -9
C. -10
D. -14

Question 1116

The value of 2.31 x 0.34 = ?

A. 1.7854
B. 0.7854
C. 0.7845
D. 0.7584

Question 1117

The value of -261+(-380)-(-521)+821-(-121)

A. 833
B. 825
C. 822
D. 800

Question 1118

The value of cos (1110°) is

A. √3/2
B. 1/2
C. 1/√2
D. 1

Question 1119

The value of cos(1110) is

A. √3/2
B. 1/2
C. 1/√2
D. 1

Question 1120

The value of cos0 deg is

A. 0
B. infinite
C. not defined
D. 1

Question 1121

The value of Sin 60 is

A. √1/2
B. √3/2
C. 1/√2
D. 1/2

Question 1122

The value of tan 315° cot (­ -405° ) is equal to

A. -1
B. 1
C. 0
D. 2

Question 1123

The value of the expression 2(sin6θ+cos6θ) - 3(sin4θ+cos4θ) + 1 is

A. -1
B. 0
C. 1
D. 2

Question 1124

The value of x for which the expressions 15 ­ 7x and 15x + 7 become equal is _____.

A. -4/11
B. 11/4
C. -11/4
D. 4/11

Question 1125

The value of x for which the expressions 15x + 4 and 13x - 2 become equal is ______

A. -1
B. 1
C. -3
D. 3

Question 1126

The value of x for which the expressions 5x + 17 and 17x - 5 become equal is _____.

A. 11/6
B. -11/6
C. 6/11
D. -6/11

Question 1127

The value of x for which the expressions 7x + 13 and 13x - 7 become equal is _____

A. -10/3
B. 3/10
C. -3/10
D. 10/3

Question 1128

The value of  (0.3)2/100=?

A. 0.09
B. 0.0009
C. 0.009
D. 0.9

Question 1129

The value of 14 ÷ 5 of 2 - 3 x 47 - 2 is

A. 44
B. 40
C. 1/10
D. 14/19

Question 1130

The value of 2 Tan53°Cot37°-Cot80°Tan10° ?

A. 3
B. 2
C. 1
D. 0

Question 1131

The value of 2.33+0.0272.33-0.69+0.09

A. 2
B. 2.27
C. 2.33
D. 2.6

Question 1132

The value of 3x9n+1+9x32n-19x32n-6x9n-1 is equal to

A. 335
B. 325
C. 315
D. 3

Question 1133

The value of 8(sin6θ + cos6θ) - 12(sin4θ + cos4θ) is equal to

A. 20
B. -20
C. 4
D. -4

Question 1134

The value of aa-b+bb-a is

A. a+b/a-b
B. -1
C. 2ab
D. 1

Question 1135

The value of cos220°+cos270° is

A. 0
B. 1
C. 1/2
D. 13

Question 1136

The value of cosec260 + sec260  cot260 + tan230 will be

A. 5
B. 5 1/2
C. 5 1/3
D. 5 2/3

Question 1137

The value of Cot17°Cot73°Cos222° + 1Cot17°Sec268° is

A. 0
B. 1
C. 2
D. √3

Question 1138

The value of ds+t÷ds÷dt

A. 0
B. d
C. 1
D. ds+t

Question 1139

The value of sec217°-1tan273°-sin17°sec73°

A. 1
B. 0
C. -1
D. 2

Question 1140

The value of sec2θ + 2tanθcotθ - tan2θ is

A. 0
B. 1
C. 2
D. 3

Question 1141

The value of sinθ+sin∅cosθ+cos∅ + cosθ-cos∅sinθ-sin∅ is

A. 1
B. 2
C. 1/2
D. 0

Question 1142

The value of sinθ1+cosθ + sinθ1-cosθ

A. 2sinθ
B. 2cosθ
C. 2secθ
D. 2cosecθ

Question 1143

The value of tan(-405°)

A. 1
B. -1
C. 2
D. 0

Question 1144

The value of x13+x-13x23-1+x-23

A. x-1+x23
B. x+x-13
C. x13+x-1
D. x+x-1

Question 1145

The value of(1(p-n)(n-q)+1(n-q)(q-p)+1(q-p)(p-n)) is

A. 1
B. 0
C. p+q+n
D. 2np+q

Question 1146

The zeros of the cubic polynomial 2x3-x2-2x+1 are a, b and c respectively. Find a+b+c :

A. -1
B. 2
C. 1
D. none

Question 1147

There are 10 dozen apples, 15 dozen mangoes and 20 dozen oranges for selling. If 1/2, 1/3 and 1/4 of them are sold respectively. How many of the total fruits are remaining?

A. 420
B. 380
C. 180
D. 360

Question 1148

There are 90 coins, comprising of 5 and 10 paisa coins. The value of all the coins is Rs. 7. How many 5 paisa coins are there?

A. 50
B. 45
C. 40
D. 35

Question 1149

To fill a tank, 25 buckets of water is required.  How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?

A. 52.5
B. 62.5
C. 72.5
D. 82.5

Question 1150

Triangle DEF is right angled at E. If cot D = 5/12, then what is the value of sin F?

A. 5/12
B. 13/5
C. 5/13
D. 13/12

Question 1151

Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?

A. 40
B. 45
C. 50
D. 55

Question 1152

Twenty times a positive integer is less than its square by 96. What is the integer ?

A. 42
B. 36
C. 48
D. 24

Question 1153

Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10√3 cm, then what is the diameter of the circle?

A. 10 cm
B. 15 cm
C. 20 cm
D. 30 cm

Question 1154

Two fractions are such that their product is ­2/5 and sum is 1/15. What are the two fractions.

A. 4/3, ­-3/10
B. 2/7, -­7/5
C. 4/7, ­-7/10
D. 2/3, ­-3/5

Question 1155

Two labourers A and B are paid a total of Rs. 1120 per day. If A is paid 180 percent of what is paid to B, how much (in Rs) is B paid?

A. 400
B. 720
C. 500
D. 620

Question 1156

Two numbers are such that the sum of twice the first number and thrice the second number is 36 and the sum of thrice the first number and twice the second number is 39. Find the difference between the numbers?

A. 15
B. 3
C. 9
D. 6

Question 1157

Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle?

A. 14.69 cm
B. 15.69 cm
C. 18.65 cm
D. 16.42 cm

Question 1158

Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?

A. xy
B. √( y/ x)
C. √( x/ y)
D. √( xy)

Question 1159

Value of (4a2+ 12ab + 9b2)/(2a + 3b) is

A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b

Question 1160

Value of (cos 53° - sin 37°) is

A. 2 sin 37 ̊
B. 2 cos 53 ̊
C. 0
D. 1

Question 1161

Vishnu spends Rs. 5000 in buying 12 tables and some chairs. The cost of one table is Rs. 50 and that of one chair is Rs. 40. What is the ratio of the numbers of tables purchased?

A. 5 :2
B. 55 : 6
C. 5 : 1
D. 55 : 4

Question 1162

Water boils at 212°F or 100°C and melts at 32°F or 0°C .  If the temparature of the particular day  is 35°C , it is equal  to :

A. 85°F
B. 95°F
C. 96°F
D. 97°F

Question 1163

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? √580×∛510+ 49.999 x 3.999=?

A. 384
B. 392
C. 410
D. 372

Question 1164

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? 499.99 + 1999 ÷ 39.99 × 50.01=?

A. 3200
B. 2700
C. 3000
D. 2500

Question 1165

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)?(55.01+16.0003)×22.01÷10.998 =?

A. 190
B. 130
C. 110
D. 142

Question 1166

What are the components of X6 - X4 - X5 - X4 + X2 - 4?

A. (X - 1)
B. (X + 2)
C. Both 1 and 2
D. Neither 1 nor 2

Question 1167

What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(4, 0) and C(-2, 2)?

A. (1 , -1)
B. (-1 , 1)
C. (2 , -2)
D. (-2 , 2)

Question 1168

What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?

A. ( 0, 3)
B. ( 0, -3)
C. ( 0, -5)
D. ( 0, 5)

Question 1169

What are the co­ordinates of the centroid of a triangle, whose vertices are A(­2,­5), B(4,­4) and C(7,3)?

A. (4,­-3)
B. (-­1,0)
C. (-­3,­-3)
D. (3,­-2)

Question 1170

What are the co­-ordinates of the mid point of the segment joining points C(0,­-3) and D(8,5)?

A. (4, 1)
B. (­-4, ­1)
C. (­4, -1)
D. (-4, ­-1)

Question 1171

What are the co­ordinates of the mid point of the segment joining points C(5,­-2) and D(­-1,8).

A. (­-2, ­3)
B. (2, 3)
C. (­2, -3)
D. (-2, -­3)

Question 1172

What are the roots of the quadratic equation: x2 + 3x ­- 154 = 0

A. 11, 14
B. 11, ­-14
C. 14, -­11
D. 14, -­22

Question 1173

What is the area (in sq cm) of a regular hexagon of side 9 cm?

A. 50√3
B. 300√3
C. 243√3/2
D. 200√3

Question 1174

What is the area (in square units) of the figure enclosed by the x-axis, the y-axis and the line x + 2y = 6 ?

A. 3
B. 6
C. 9
D. 12

Question 1175

What is the area of the sector whose central angle is 90° and radius of the circle is 14 cm?

A. 308 sq cm
B. 77 sq cm
C. 154 sq cm
D. 231 sq cm

Question 1176

What is the difference between the total sale of English newspapers and the total sale of Hindi newspapers in all the localities together.

A. 7500
B. 5600
C. 6500
D. 5700

Question 1177

What is the distance between the points (4,­-8) and (­-2,0)?

A. 100 units
B. 5 units
C. 25 units
D. 10 units

Question 1178

What is the equation of a line having a slope -1/3 and y-intercept equal to 6?

A. x + 3y = 18
B. x - 3y = 6
C. x + 3y = -18
D. x - 3y = -6

Question 1179

What is the equation of a line of slope 1/3 and y-intercept 5?

A. x - 3y = -15
B. x - 3y = 15
C. x + 3y = -15
D. x + 3y = 15

Question 1180

What is the equation of a line which has 3 as x-intercept and -5 as y-intercept?

A. 3x - 5y = 15
B. 5x - 3y = 15
C. 5x + 3y = 15
D. 3x + 5y = 15

Question 1181

What is the equation of line whose slope is -1/2 and passes through the intersection of the lines x - y = -1 and 3x - 2y = 0?

A. x + 2y = 8
B. 3x + y = 7
C. x + 2y = -8
D. 3x + y = -7

Question 1182

What is the equation of the line if its slope is 1/4 and y-­intercept is ­-3?

A. x ­- 4y = 12
B. x + 4y = 12
C. x -­ 4y = ­-12
D. x + 4y = -­12

Question 1183

What is the equation of the line if its slope is ­2/5 and y-­intercept is 6?

A. 2x + 5y = 6
B. 2x + 5y = 30
C. 2x - 5y = 6
D. 2x + 5y = ­-30

Question 1184

What is the equation of the line if its slope is 4/3 and it passes through the point (-7 , 2)?

A. 4x - 3y = -22
B. 4x + 3y = -34
C. 4x + 3y = -22
D. 4x - 3y = -34

Question 1185

What is the equation of the line passing through the point (0,­4) and making an angle of ­45° with the positive x­axis?

A. x + y = 4
B. x -­ y = - ­4
C. x + y = -­4
D. x ­- y = 4

Question 1186

What is the equation of the line passing through the point (-1,3) and having x-intercept of 4 units?

A. 3x - 5y = 12
B. 3x + 5y = 12
C. 3x + 5y = -12
D. 3x - 5y = -12

Question 1187

What is the equation of the line passing through the point (1,3) and making an angle of -45° with the positive x-axis?

A. x + y = 4
B. x + y = 2
C. x - y = 4
D. x - y = 2

Question 1188

What is the equation of the line passing through the point (2,-3) and making an angle of -45°with the positive X-axis?

A. x - y = -5
B. x - y = -1
C. x + y = -5
D. x + y = -1

Question 1189

What is the equation of the line perpendicular to the line 5x + 3y = 6 and having Y-intercept -3?

A. 3x - 5y = 15
B. 3x + 5y = 15
C. 3x - 5y = -15
D. 3x + 5y = -15

Question 1190

What is the equation of the line which has 3/2 and -­4/7 as x and y intercept respectively?

A. 8x ­- 21y = ­-12
B. 8x + 21y = 14
C. 8x -­ 21y = 12
D. 8x + 21y = ­-14

Question 1191

What is the equation of the line which intercepts x­axis and y­axis at 3/4 and ­2/3 respectively?

A. 8x + 9y = 6
B. 9x + 8y = 12
C. 8x ­- 9y = 6
D. 9x + 8y = ­-12

Question 1192

What is the equation of the line which passes through the points (3,­2) and (5,3)?

A. 5x ­- 2y = ­-19
B. 5x ­- 2y = 19
C. 5x + 2y = ­31
D. 5x + 2y = -31

Question 1193

What is the equation of the line whose y­-intercept is ­3/4 and making an angle of 45° with the positive x-­axis?

A. 4x -­ 4y = 3
B. 4x - 4y = -­3
C. 3x -­ 3y = 4
D. 3x ­- 3y = -­4

Question 1194

What is the equation of the line whose y­-intercept is 4 and making an angle of 45° with the positive x-­axis?

A. x + y = -­4
B. x -­ y = 4
C. x + y = 4
D. x -­ y = ­-4

Question 1195

What is the perimeter of the sector whose central angle is 60° and radius of the circle is 21 cm?

A. 128 cm
B. 96 cm
C. 64 cm
D. 32 cm

Question 1196

What is the reflection of the point (-1 , 3) in the line x = -4?

A. (-7 ,-3)
B. (-7 ,3)
C. (7 ,-3)
D. (7 ,3)

Question 1197

What is the reflection of the point (-1 , 5) in the line x = 1?

A. (3 , -5)
B. (-3 , -5)
C. (3 , 5)
D. (-3 , 5)

Question 1198

What is the reflection of the point (2, 3) in the line y = 4?

A. (2, 5)
B. (2, -5)
C. (-2, -5)
D. (-2, 5)

Question 1199

What is the reflection of the point (3,-5) in the origin?

A. (-3, -5)
B. (5,-3)
C. (-5,-3)
D. (-3, 5)

Question 1200

What is the reflection of the point (4 , -3) in the line y = 1?

A. (4, -5)
B. (4, 5)
C. (-4, -5)
D. (-4, 5)

Question 1201

What is the reflection of the point (4, 7) in the line y = -1?

A. (-6 , 7)
B. (-4 , -9)
C. (4 , -9)
D. (-6 , -7)

Question 1202

What is the reflection of the point (5, -2) in the line x = -1?

A. (-7 , -2)
B. (5 , 0)
C. (7 , -2)
D. (5 , 2)

Question 1203

What is the reflection of the point (5, 2) in the line x = -3?

A. (-11 ,2)
B. (-11 ,-2)
C. (11 ,-2)
D. (11 ,2)

Question 1204

What is the reflection of the point (5, -2) in the line y = -1?

A. (-7 , -2)
B. (-5 , 0)
C. (5 , 0)
D. (-7 , 2)

Question 1205

What is the reflection of the point (6, -1) in the line y = 2?

A. (-2 , -1)
B. (-6 , 5)
C. (-2 , 1)
D. (6 , 5)

Question 1206

What is the simplest form of (1 + cosA)(cosecA ­ cotA)?

A. cosA
B. tanA
C. cotA
D. sinA

Question 1207

What is the simplified value of (1– sin A cos A)(sin A + cos A)?

A. sin2A – cos2A
B. sin3A + cos3A
C. 0
D. 1

Question 1208

What is the simplified value of (cos4 A – sin4 A)?

A. 0
B. 2 cos2 A
C. cos2A
D. 1

Question 1209

What is the simplified value of (cosec A – sin A)(sec A – cos A)(tan A + cot A)?

A. -1
B. 0
C. 1
D. 2

Question 1210

What is the simplified value of (sec A + cos A)(sec A – cos A)?

A. 2 tan2A
B. 2 sin2 A
C. sin2 A tan2 A
D. sin2A + tan2 A

Question 1211

What is the simplified value of (sec4 A – tan2 A) – (tan4 A + sec2 A)?

A. -1
B. 1/2
C. 1
D. 0

Question 1212

What is the simplified value of (sin A – cosec A)(sec A – cos A) (tan A + cot A)?

A. 1
B. -1
C. 0
D. 2

Question 1213

What is the simplified value of [2/(cot A – tan A)]?

A. sin A cos A
B. tan 2A
C. sin2 A
D. cos2 A

Question 1214

What is the simplified value of cosec 2A + cot 2A?

A. sec A
B. sec (A/2)
C. cot A
D. cot2 A

Question 1215

What is the simplified value of cosec6A – cot6A – 3 cosec2A cot2A?

A. -2
B. -1
C. 0
D. 1

Question 1216

What is the simplified value of sec4θ – sec2θ tan2θ?

A. cosec2θ
B. Cot2θ
C. sec2 θ
D. secθ tan θ

Question 1217

What is the simplified value of sec6 A – tan6 A – 3 sec2 A tan2 A?

A. -1
B. 0
C. 1
D. sec A tan A

Question 1218

What is the simplified value of sin2(90–θ)–[sin(90–θ)sinθ/tanθ]?

A. 1
B. cosec θ
C. 0
D. cos θ

Question 1219

What is the simplified value of 0.042+0.212-0.00840.043+0.213

A. 0.5
B. 2
C. 10.25
D. 10.3

Question 1220

What is the simplified value of 0.072+0.292-0.02030.073+0.293

A. 0.6
B. 0.06
C. 1/0.6
D. 1/0.06

Question 1221

What is the simplified value of 12-13 ?

A. 5√3
B. 5/√3
C. 3√5
D. 3/√5

Question 1222

What is the simplified value of 18 - 12 ?

A. 5/√2
B. 5√2
C. 2√5
D. 2/√5

Question 1223

What is the simplified value of 1-sin A1+sin A ?

A. tan A
B. sec A
C. sec A + tan A
D. sec A – tan A

Question 1224

What is the simplified value of 22433+393-11253?

A. 593
B. 493
C. 793
D. 1193

Question 1225

What is the simplified value of 31253 + 4253 + 36753

A. 18253
B. 5253
C. 9√125
D. 1253

Question 1226

What is the simplified value of cosec Acot A + tan A2 ?

A. 2cos 2A
B. 1 – sin2 A
C. sec2A
D. secA tanA

Question 1227

What is the simplified value of Sec ACot A + Tan A2 ?

A. 1 – cos2A
B. 2sin2A
C. sec2A
D. 0

Question 1228

What is the slope of the line 2x - 5y = 12?

A. 2/5
B. 5/2
C. -2/5
D. -5/2

Question 1229

What is the slope of the line 4x - 8y = 3?

A. -1/2
B. 2
C. 1/2
D. -2

Question 1230

What is the slope of the line parallel to the line passing through the points (-­4,­-6) and (2,­-3)?

A. -1/2
B. -2
C. 2
D. 1/2

Question 1231

What is the slope of the line perpendicular to the line passing through the points (-2, 3) and (2, 0)?

A. 4/3
B. 3/4
C. -3/4
D. -4/3

Question 1232

What is the slope of the line perpendicular to the line passing through the points (8,­2) and (3,­1)?

A. 5
B. 3/5
C. 5/3
D. 1/5

Question 1233

What is the slope of the line, parallel to the line 3x -­ 6y = 4?

A. -1/2
B. 1/2
C. 2
D. -­2

Question 1234

What is the slope of the line, perpendicular to the line 3x - 6y = 4?

A. -2
B. 2
C. 2/3
D. -2/3

Question 1235

What is the smplified value of Sin2A/1+Cos2A ?

A. tan A
B. cot A
C. sin A
D. cos A

Question 1236

What is the square root of 5041?

A. 79
B. 81
C. 71
D. 69

Question 1237

What is the square root of 9409?

A. 83
B. 87
C. 89
D. 97

Question 1238

What is the sum of a3+b3+c3-3abc, when the value of a=4, b=2 and c=-6?

A. 0
B. 2
C. 4
D. 6

Question 1239

What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?

A. 67
B. 45
C. -30
D. -48

Question 1240

What is the total number of points in the plane of triangle ABC which is equidistant from the vertices of the triangle?

A. 0
B. 1
C. 2
D. 3

Question 1241

What is the unit digit of 15+25+35+...+205 ?

A. 0
B. 5
C. 2
D. 4

Question 1242

What is the value of ( 1/√3 + cot60) ?

A. 3√3/2
B. 7/2√3
C. (4+√3)/2√3
D. 2/√3

Question 1243

What is the value of ( 1/2 - cot45) ?

A. (2√2-√3)/2
B. 3/2
C. (3√3-1)/3
D. -1/2

Question 1244

What is the value of ( 1/3 - cosec30°) ?

A. (√6-1)/√3
B. -1/2
C. -5/3
D. 3/2

Question 1245

What is the value of ( 1/3 + cosec30)?

A. (√6+1)/√3
B. 7/3
C. (4+√3)/2
D. (√3+1)/2

Question 1246

What is the value of (√3 - sec60) ?

A. √3-2
B. (1-√6)/√2
C. (2√3-√6)/2√2
D. (1-3√2)/3

Question 1247

What is the value of (1/√2) Cot 45° + (1/√3) Cosec 60°?

A. (√6 + 1)/√3
B. √3
C. (1 + 3√2)/√3
D. (3 + 2√2)/3√2

Question 1248

What is the value of (1/√3 + sin45 ) ?

A. √3+2
B. (√2+√3)/√6
C. (1+√6)/√3
D. (4+√3)/2

Question 1249

What is the value of (1/2) Sec 30° + √2 Tan 60°?

A. (1 + 3√2)/√3
B. (√3 + 2)/√3
C. √3 + 2
D. (√3 + 2)/2

Question 1250

What is the value of (1+cosA)/(1-­cosA)?

A. (cosecA ­- cotA)2
B. (cosecA + cotA)2
C. (secA + cotA)2
D. (secA -­ cotA)2

Question 1251

What is the value of (3/5 + 7/9)?

A. 62/45
B. 31/28
C. 5/7
D. 1/7

Question 1252

What is the value of (32 cos6x – 48 cos4x + 18 cos2x – 1)/[4 sin x cos x sin (60 – x) cos (60 – x) sin (60 + x) cos (60 + x)]?

A. 4 tan 6x
B. 4 cot 6x
C. 8 cot 6x
D. 8 tan 6x

Question 1253

What is the value of (4a2 + 8b + 14c + 2)/2 ?

A. 2a2 + 4b + 7c + 1
B. a2 + 4b + 7c + 1
C. 2a2 + 4b + 7c + 2
D. a2 + 4b + 7c + 2

Question 1254

What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?

A. 2√3
B. 2/√3
C. 1/√3
D. √3

Question 1255

What is the value of (cos 45 - 1/3) ?

A. 2-√3
B. 2/√3
C. (3-√2)/3√2
D. 1/2√3

Question 1256

What is the value of (cos30° + 1/2) ?

A. (√3+1)/√3
B. (√2+1)/√2
C. (√3+1)/2
D. (2√3+1)/√3

Question 1257

What is the value of (cos45° + 1/3) ?

A. 2+√3
B. (2√2+1)/√2
C. (3+√2)/3√2
D. 5/√3

Question 1258

What is the value of (cosec30 - 1/√3)?

A. (2√3-1)/√3
B. (√3-4)/2√3
C. -1/√3
D. 2/√3

Question 1259

What is the value of (cosec45 + √3/2) ?

A. 5/6
B. (4+√3)/2√3
C. (2√2+√3)/2
D. 3√3/2

Question 1260

What is the value of (cosecA - cotA) / (secA + tanA)?

A. (secA + tanA)/(cosecA - cotA)
B. √[(secA - tanA)/(cosecA + cotA)]
C. (secA - tanA)/(cosecA + cotA)
D. √[(secA + tanA)/(cosecA - cotA)]

Question 1261

What is the value of (cot30°+ 2/√3) ?

A. 5/√3
B. (1+2√3)/2
C. 5/6
D. 2/√3

Question 1262

What is the value of (cot45 - √2) ?

A. (√3-1)/2√3
B. (√3-1)/2
C. 1-√2
D. 1-√3

Question 1263

What is the value of (cot60 + 1/√3) ?

A. 4/√3
B. (2√2+√3)/2
C. 2/√3
D. (2√2+1)/√2

Question 1264

What is the value of (sin60° - 2/√3) ?

A. -1/2√3
B. -1/2
C. 1/√3
D. (1-2√3)/2

Question 1265

What is the value of (sin60° + 2/√3) ?

A. (2√3+1)/√3
B. 7/2√3
C. 3
D. 2+√3

Question 1266

What is the value of (tan60 - 1/3) ?

A. 3-√2
B. (2√2-√3)/2
C. -1/2√3
D. (3√3-1)/3

Question 1267

What is the value of (tan60 + 1/3) ?

A. (2√2+1)/2
B. (√3+1)/√3
C. (3√3+1)/3
D. (3+√2)/3√2

Question 1268

What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?

A. cos 2θ
B. sin 2θ
C. tan 2θ
D. cot θ sin 2θ

Question 1269

What is the value of [(cos 7A + cos 5A)÷(sin 7A – sin 5A)]?

A. tan A
B. tan 4 A
C. cot 4 A
D. cot A

Question 1270

What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?

A. 0
B. 1
C. 2
D. 4

Question 1271

What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

A. 1
B. 2 tan x
C. tan 2 x
D. tan (3 x/2)

Question 1272

What is the value of [(sin x + sin y) (sin x – sin y)]/[(cosx + cosy) (cosy – cosx)]?

A. 0
B. 1
C. – 1
D. 2

Question 1273

What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

A. sin 2θ
B. cos 2θ
C. tan 4θ
D. cot 2θ

Question 1274

What is the value of [1 – sin (90 – 2A)] / [1 + sin (90 + 2A)]?

A. sinA cosA
B. cot2A
C. tan2A
D. sin2A cosA

Question 1275

What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?

A. cot (θ/2)
B. tan (θ/2)
C. sin θ
D. cos θ

Question 1276

What is the value of [12/(√5 + √3)] + [18/(√5 – √3)]?

A. 15(√5 – √3)
B. 3(5√5 + √3)
C. 15(√5 + √3)
D. 3(3√5 + √3

Question 1277

What is the value of [2 sin (45 + θ) sin (45 – θ)]/cos 2θ?

A. 0
B. tan 2θ
C. cot 2θ
D. 1

Question 1278

What is the value of [2 cot × (p – A)/2]/[1 + tan2× (2p – A)/2]?

A. 2 sin2 A/2
B. cos A
C. sin A
D. 2 cos2 A/2

Question 1279

What is the value of [cos (90 + A)÷sec (270 – A)] + [sin (270 + A)÷cosec (630 – A)]?

A. 3 sec A
B. tan A sec A
C. 0
D. 1

Question 1280

What is the value of [sin (90 – A) + cos (180 – 2A)]/[cos (90 – 2A) + sin (180 – A)]?

A. sin (A/2) cos A
B. cot (A/2)
C. tan (A/2)
D. sin A cos (A/2)

Question 1281

What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?

A. tan 2θ
B. cot 2θ
C. cot θ
D. cot 3θ

Question 1282

What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]?

A. cos x sin y
B. (sin y)/(sin x)
C. sin z
D. sin x tan y

Question 1283

What is the value of [tan (90 – A) + cot (90 – A)]2/[2 sec2(90 – 2A)]?

A. 0
B. 1
C. 2
D. – 1

Question 1284

What is the value of {(sin 4x + sin 4y) [(tan 2x – 2y)]}/(sin 4x – sin 4y)?

A. tan 2 (2x + 2y)
B. tan2
C. cot (x – y)
D. tan (2x + 2y)

Question 1285

What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?

A. 0
B. tan2x
C. 1
D. 2 tan x

Question 1286

What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}?

A. -cos y
B. -sin y
C. cos x
D. tan y

Question 1287

What is the value of |3(1) - 6|?

A. 3
B. 0
C. -3
D. 4

Question 1288

What is the value of √[(1 ­- cosA)/(1 + cosA)]?

A. cosecA ­- cotA
B. cosecA + cotA
C. secA -­ cotA
D. secA + cotA

Question 1289

What is the value of √[(1 - sinA)/(1 + sinA)]?

A. cosA/(1 - sinA)
B. cosecA/(1 + sinA)
C. cosA/(1 + sinA)
D. cosecA/(1 - sinA)

Question 1290

What is the value of √[(1 + sinA)/(1 -­ sinA)]?

A. secA -­ tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA -­ tanA

Question 1291

What is the value of √2 Sec 45 - Tan 30?

A. (2√3 - 1)/3
B. (√3 - 1)/√3
C. (2√3 - 1)/√3
D. (√3 - 1)/3

Question 1292

What is the value of √2 Sec 45° + (1/√3)Tan 30°?

A. (1 + √3)/2
B. (1 + 3√2)/√3
C. 7/3
D. (3 + 2√2)/3√2

Question 1293

What is the value of 0.55 x 4.5/0.81 ?

A. 3.555
B. 55/18
C. 3.05
D. 55/81

Question 1294

What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?

A. (3√3 + 2√2)/3√2
B. (3√3 - 2√2)/3√2
C. (3√3 + 2√2)/√2
D. (3√3 - 2√2)/√2

Question 1295

What is the value of 12 + 3(-2 x 3) - (18 / 6) ?

A. -5
B. 9
C. -9
D. 5

Question 1296

What is the value of 299996 x 300004?

A. 89999999984
B. 89999699984
C. 89999999884
D. 89999999974

Question 1297

What is the value of 2sec2A?

A. secA/(cosecA - ­1) + secA/(cosecA +1)
B. cosecA/(secA -­1) + cosecA/(secA +1)
C. cosecA/(cosecA - ­1) + cosecA/(cosecA +1)
D. secA/(secA - ­1) + secA/(secA +1)

Question 1298

What is the value of 99992 x 100008?

A. 9999999936
B. 9999899936
C. 9999999836
D. 9999999926

Question 1299

What is the value of a-b when a2+b2-6a-6b+18 = 0 ?

A. 0
B. 3
C. 6
D. 9

Question 1300

What is the value of cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) – sin (90 – C) cos (A + B)?

A. 1
B. sin ( A + B – C)
C. cos ( B + C – A)
D. 0

Question 1301

What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?

A. sin 2θ sin 4θ
B. cos 2θ cos 6θ
C. sin 2θ sin 6θ
D. cos 2θ cos 4θ

Question 1302

What is the value of cos 11π/6?

A. -1/√2
B. -√3/2
C. 2/√3
D. √3/2

Question 1303

What is the value of cos 4π/3?

A. -1/2
B. √3/2
C. - 1/√2
D. √3/2

Question 1304

What is the value of cosec 11π/6?

A. -2/√3
B. √2
C. -2
D. -√2

Question 1305

What is the value of cosec 120°

A. 2/√3
B. 2
C. -2/√3
D. -2

Question 1306

What is the value of cosec -150°?

A. -2
B. 2/√3
C. 2
D. -2/√3

Question 1307

What is the value of cosec 3π/4?

A. -√2
B. √2
C. 2/√3
D. -2/√3

Question 1308

What is the value of cosec 5π/3?

A. √2
B. -2/√3
C. -√2
D. 1/√3

Question 1309

What is the value of cosec -7π/6?

A. -2
B. 2
C. 2/√3
D. -2/√3

Question 1310

What is the value of cosecA/√(cosec2A ­- 1)?

A. sinA
B. secA
C. tanA
D. cosA

Question 1311

What is the value of cot 11π/6?

A. -√3
B. -1
C. √3
D. -1/2

Question 1312

What is the value of Cot 45° - (1/√3)Cosec 60°?

A. 1/√3
B. 1/2
C. 1/√2
D. 1/3

Question 1313

What is the value of Cot 45° + Cosec 60°?

A. (√6 + 1)/√3
B. (1 + √3)/2
C. 5/√3
D. (√3 + 2)/√3

Question 1314

What is the value of cot 5π/3?

A. 1/√3
B. -1/√3
C. √3
D. -√3

Question 1315

What is the value of Cot 60 - Sec 30?

A. -1/3
B. -1/√3
C. 1/√3
D. 1/3

Question 1316

What is the value of Cot 45°+ 1/3 Cosec 60°?

A. √3 + 2
B. (9 + 2√3)/9
C. √3
D. (2√2 + 3)/√6

Question 1317

What is the value of Cot 60°- Sec 45°?

A. (√2 - √3)/√6
B. (√3 - 3√2)/3
C. (1 - 2√2)/2
D. (1 - √3)/2

Question 1318

What is the value of cot210°?

A. 1/√3
B. -1/√3
C. √3
D. -√3

Question 1319

What is the value of equation a3+b3+c3-3abc if a2+b2+c2=ab+bc+ca+4 and a+b+c = 4.

A. 0
B. 1
C. 16
D. 256

Question 1320

What is the value of sec -2π/3 ?

A. -2
B. 2
C. 2/√3
D. -2/√3

Question 1321

What is the value of sec 30° + cot 30°?

A. (√6­-1)/√2
B. √3+2
C. 5/√3
D. (√3­-2√2)/√6

Question 1322

What is the value of Sec 30° + Tan 60°?

A. 5/√3
B. (√6 + 1)/√3
C. (√3 + 2)/√3
D. (1 + √3)/2

Question 1323

What is the value of sec 330°?

A. 2
B. -2/√3
C. -2
D. ­2/√3

Question 1324

What is the value of sec 4π/3?

A. 2
B. -2
C. 2/√3
D. -2/√3

Question 1325

What is the value of sec 5π/4?

A. 1/√3
B. -√2
C. √3
D. 1

Question 1326

What is the value of sin (630 + A) + cos A?

A. √3/2
B. 1/2
C. 0
D. 2/√3

Question 1327

What is the value of sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D)?

A. 3/2
B. – 3
C. 1
D. 0

Question 1328

What is the value of sin (–π/3) + cos(–π/6)?

A. 0
B. 1
C. 2
D. 3

Question 1329

What is the value of Sin 30- √2 Cos 30

A. (1 - √6)/√2
B. (1 - √6)/2
C. (3 - √6)/2
D. (3 - √6)/√2

Question 1330

What is the value of Sin 30° - Cosec 45°?

A. (2√6 - 1)/√3
B. (1 - 2√3)/2
C. (√2 - √3)/√6
D. (1 - 2√2)/2

Question 1331

What is the value of Sin 30° + Cos 30°?

A. (√6 + 1)/√3
B. (√3 + 2)/√3
C. (1 + √3)/2
D. 5/√3

Question 1332

What is the value of sin 300°?

A. -1/2
B. 2
C. 2/√3
D. -√3/2

Question 1333

What is the value of sin ­-300°?

A. 1
B. √3/2
C. ­1/2
D. √3/2

Question 1334

What is the value of sin 330°?

A. 2
B. 2/√3
C. √2
D. -1/2

Question 1335

What is the value of sin 46 cos 44+ cos 46 sin 44?

A. 2
B. sin 2
C. 1
D. 0

Question 1336

What is the value of sin 5π/3?

A. √3/2
B. 2/√3
C. 1/√3
D. -2/√3

Question 1337

What is the value of Sin 60° + (1/2)Cosec 45°?

A. (√3 + 2)/2
B. (√3 + √2)/√2
C. (√3 + 2)/√2
D. (√3 + √2)/2

Question 1338

What is the value of sin 75°+ sin 15°?

A. √3
B. 2√3
C. √(3/2)
D. 3/√2

Question 1339

What is the value of sin(11π/6)?

A. 2/√3
B. -2/√3
C. -1/2
D. 1/2

Question 1340

What is the value of sin225°+ sin265°?

A. 0
B. 1
C. 2
D. 4

Question 1341

What is the value of sin6θ + cos6θ + 3 sin2θ cos2θ –1?

A. 0
B. 1
C. 2
D. 4

Question 1342

What is the value of sinAtanA/(1 - cosA)?

A. 1 - secA
B. 1 + secA
C. 1 + cotA
D. 1 - cotA

Question 1343

What is the value of tan­ -240°?

A. -√3
B. 1/√3
C. -1/√3
D. √3

Question 1344

What is the value of tan 300°?

A. -1/2
B. -1/√2
C. -√3
D. -√3/2

Question 1345

What is the value of Tan 45° - 1/√3 Sec 60°?

A. (1 - 2√3)/2
B. (√2 - √3)/√6
C. (3 - 2√3)/3
D. (1 - 2√2)/2

Question 1346

What is the value of Tan 45° + 4/√3 Sec 60°?

A. (√3 + 8)/√3
B. (√3 + 8)/3
C. (√3 - 8)/√3
D. (√3 - 8)/3

Question 1347

What is the value of tan 4π/3?

A. ­1/2
B. √3
C. √3/2
D. ­1/√2

Question 1348

What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?

A. 1/2
B. 1/√2
C. 1
D. 1/3

Question 1349

What is the value of Tan 60 + Cosec 60?

A. 5/3
B. 2/√3
C. 5/√3
D. 2/3

Question 1350

What is the value of tan 7π/4?

A. √3
B. -1/2
C. √3/2
D. -1

Question 1351

What is the value of tan 7π/6?

A. 1/√3
B. -1/√3
C. √3
D. -√3

Question 1352

What is the value of tan 1° tan 2° tan 3°....... tan 89°?

A. 0
B. 1
C. 2
D. infinity

Question 1353

What is the value of tan150°?

A. -√3
B. 1/√3
C. √3
D. -1/√3

Question 1354

What is the value of tan3A?

A. (3tanA -­ tan3A)/(1 -­ 3tan2A)
B. (3tanA + tan3A)/(1 + 3tan2A)
C. (3tanA -­ tan3A)/(1 + 3tan2A)
D. (3tanA + tan3A)/(1-­ 3tan2A)

Question 1355

What is the value of tan4A + tan2A?

A. sec4A - sec2A
B. sec4A + sec2A
C. cosec4A - sec2A
D. sec4A + cosec2A

Question 1356

What is the value of the expression a3 - 5 + 2816a, when a = 2?

A. 2
B. 5
C. 7
D. 8

Question 1357

What is the value of xy if x - y = 3 and x2+y2=15?

A. 1
B. 3
C. 5
D. 7

Question 1358

What is the value of  4cos90-A sin390+A - 4sin90+A cos390-Acos180+8A2 ?

A. 1
B. -1
C. 0
D. 2

Question 1359

What is the value of (4a2 - 9b2 )/(2a + 3b) is

A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b

Question 1360

What is the value of (-7776)25

A. 16
B. 36
C. 64
D. 21

Question 1361

What is the value of (sinA -­ 2sin3A)/(2cos3A -­ cosA)?

A. cotA
B. cosecA
C. secA
D. tanA

Question 1362

What is the value of [(sin 59° cos 31° + cos 59° sin 31° )÷(cos 20° cos 25° – sin 20° sin 25° )]?

A. 1/√2
B. 2√2
C. √3
D. √2

Question 1363

What is the value of 1.23+0.83+0.73-2.0161.351.22+0.82+0.72-0.96-0.84-0.56 =

A. 1/4
B. 1/2
C. 1
D. 2

Question 1364

What is the value of 1+aa1/2+a-1/2-a1/2+a-1/21+a+a-1/2 ?

A. √a
B. 1/√a
C. 0
D. √a+1

Question 1365

What is the value of 128 + 7232

A. 3.5
B. 7
C. 4.5
D. 9

Question 1366

What is the value of 13 x 4932?

A. 4369
B. 4459
C. 4549
D. 4639

Question 1367

What is the value of 13×7+17×11+111×15+...+1899×903 ?

A. 21/509
B. 18/403
C. 25/301
D. 29/31

Question 1368

What is the value of 13313 + 729 - 5123

A. 15
B. 20
C. 30
D. 23

Question 1369

What is the value of 143 + 163 + 183 + ... + 303?

A. 134576
B. 120212
C. 115624
D. 111672

Question 1370

What is the value of 1sin490-θ+1cos290-θ - 1 ?

A. tan2θ sec2θ
B. sec4θ
C. tan4θ
D. tan2θ sin2θ

Question 1371

What is the value of 1xp-q+1+1xq-p+1?

A. 0
B. 1
C. x
D. cant determine

Question 1372

What is the value of 2 - 2z + z22 + 2z - z2, when z+2z = 2 ?

A. 0
B. 2
C. 4
D. 8

Question 1373

What is the value of 2+2+2+2.......

A. 1
B. 2
C. 3
D. 4

Question 1374

What is the value of 23+5252-23 ?

A. 9
B. 49
C. 561
D. 571

Question 1375

What is the value of 26 + 152?

A. 17
B. 19
C. 15
D. 21

Question 1376

What is the value of 3.6×1.62+0.48×3.61.8×0.8+10.8×0.3-2.16 ?

A. 2.4
B. 2
C. 4
D. 3

Question 1377

What is the value of 34+122 ?

A. 13
B. 15
C. 17
D. 19

Question 1378

What is the value of 36+729381+643

A. 5/12
B. 5/9
C. 4/9
D. 4/15

Question 1379

What is the value of 4600+540+1280+250+36 ?

A. 69
B. 68
C. 70
D. 72

Question 1380

What is the value of 5.6x0.36+0.42x3.20.8 x 2.1 ?

A. 2
B. 1
C. 3
D. 3/2

Question 1381

What is the value of 643 × 121289 - 169 ?

A. 12
B. 11
C. 1/11
D. 1/12

Question 1382

What is the value of 7293 + 441 - 3433 ?

A. 48
B. 23
C. 7
D. 41

Question 1383

What is the value of 7293×16+676+169

A. 75
B. 64
C. 35
D. 60

Question 1384

What is the value of 96+21624?

A. 8
B. 4
C. 5
D. 10

Question 1385

What is the value of a2 + b2a3 - b3, when a + b = 8 and a - b = 2?

A. 0.313
B. 0.347
C. 0.368
D. 0.381

Question 1386

What is the value of cos2A/(1 + sinA)?

A. 1 + sinA
B. 1 ­- sinA
C. 1 -­ secA
D. 1 + secA

Question 1387

What is the value of S = 11x3x5 + 11x4 + 13x5x7 + 14x7 + 15x7x9 + 17x10 + ... upto 20 terms. Then what is the value of S?

A. 6179/15275
B. 6070/14973
C. 7191/15174
D. 5183/16423

Question 1388

What is the value of sec2θ + 1sec2θ - 1 x 12cotθ - tanθ ?

A. 0
B. 1
C. cosec θ
D. sec θ

Question 1389

What is the value of sin (90° + 2A)[4 – cos2(90° – 2A)]?

A. 2(cos3 A – sin3 A)
B. 2(cos3 A + sin3 A)
C. 4(cos6 A+ sin6 A)
D. 4(cos6 A – sin6 A)

Question 1390

What is the value of Sin 30° + 2 Cos 30° ?

A. (2√2 + 3)/√6
B. (9 + 2√3)/9
C. (1 + 2√3)/2
D. (2√6 + 1)/√3

Question 1391

What is the value of tanπ4+A×tan3π4+A ?

A. 1
B. 0
C. cot A/2
D. – 1

Question 1392

What is the value of x3-1x3+8 when 8x-8x-16=0 ?

A. 6
B. 8
C. 16
D. 22

Question 1393

What is the value of x4+y4 when the value of x3+y3=8 and x+y=2 ?

A. 2
B. 8
C. 16
D. 32

Question 1394

What is the value of z2+1z2 when z = 5+26 ?

A. 49
B. 50
C. 98
D. 100

Question 1395

What is the value 32cos 39sin 51-sin239 + sin251

A. 1/2
B. 5/2
C. 0
D. Both 1/2 and 5/2

Question 1396

What is the x – intercept of the linear equation 18x + 25y – 900 = 0?

A. 18
B. 25
C. 50
D. 450

Question 1397

What is the x-intercept of line joining (4, 2) and (6, 3)?

A. 0
B. 1
C. 2
D. 3

Question 1398

What is the y – intercept of the linear equation 59x + 14y – 112 = 0?

A. 8
B. 14
C. 28
D. 59

Question 1399

What is value of P+QP-Q  if PQ=7 ?

A. 1/3
B. 2/3
C. 4/3
D. 5/3

Question 1400

What is (x-y)3+y-23+z-x33x-yy-zz-x =?

A. 1
B. 0
C. 1/3
D. 3

Question 1401

What should be added to 3(x­ - 2y) to obtain 2(3x + y) -­ 5(2x + 3)?

A. 8y -­ 7x ­- 15
B. 8y -­ 7x + 15
C. 8y + 7x + 15
D. 8y + 7x -­ 15

Question 1402

What should be added to 5(2x-y) to obtain 4(2x - 3y) + 5(x + 4y)?

A. 3x - 13y
B. 3x + 13y
C. 13x - 3y
D. 13x + 3y

Question 1403

What should be added to 8(3x - ­4y) to obtain 18x ­- 18y?

A. 6x -­ 14y
B. 14y + 6x
C. 14y -­ 6x
D. 6xy

Question 1404

What value of 'p' will satisfy the equation p540 = 240p ?

A. 6
B. 10
C. 6√10
D. √10

Question 1405

What will be the roots of the quadratic equation x2 - 25x + 156 = 0?

A. 12, 13
B. 25, 1
C. 9, 16
D. 31, 6

Question 1406

What will be the value of r2+p2+s2-rp-ps-rs when r = 4, p = 2, s = 8?

A. 8
B. 18
C. 28
D. 38

Question 1407

What is the value of (1 + cotA)2 + (1 -­ cotA)2?

A. 2cosec2A
B. 2sec2A
C. 1 -­ 2cosec2A
D. 1 -­ 2sec2A

Question 1408

What is the value of (4/3) cot2 (p/6) + 3 cos2 (150) – 4 cosec2 45 + 8 sin (p/2)?

A. 25/4
B. 1
C. – 7/2
D. 13/2

Question 1409

What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?

A. 0
B. 1
C. -1
D. 2

Question 1410

When [x + (1/x)] = 5, then what is the value of [x – (1/x)]?

A. 11
B. ± √22
C. 21
D. ± √21

Question 1411

When a number is increased by 28, it becomes 107% of itself. What is the number?

A. 336
B. 420
C. 400
D. 252

Question 1412

When 2x + 2x = 3, then x3 + 1x + 2 value is

A. 2/7
B. 7/8
C. 7/2
D. 8/7

Question 1413

When 721+722+723+724 is divided by 25 the remainder is:

A. 5
B. 17
C. 7
D. 0

Question 1414

When x2+ax+b is divided by (x-1), the remainder is 15 and when x2+bx+a is divided by (x+1), the remainder is -1, then the value of a2+b2 is

A. 10
B. 20
C. 8
D. 16

Question 1415

Which of the following conditions is TRUE for the two line segments AB and CD to be congruent?

A. AB=CD
B. AB>CD
C. ABD. None of these

Question 1416

Which of the following equations has real and distinct roots?

A. 3x2 - 6x + 2 = 0
B. 3x2 - 6x + 3 = 0
C. x2 - 8x + 16 = 0
D. 4x2 - 8x + 4 = 0

Question 1417

Which of the following equations has the sum of its roots as 11?

A. x2 - 11x + 18 = 0
B. x2 - 7x + 10 = 0
C. x2 + 2x - 26 = 0
D. x2  + 5x - 6 = 0

Question 1418

Which of the following fractions is largest?

A. 3/4
B. 4/5
C. 5/6
D. 7/8

Question 1419

Which of the following is a Pythagorean triplet?

A. 8, 15, 17
B. 17, 21, 29
C. 7, 9, 11
D. 2, 3, 5

Question 1420

Which of the following is correct?

A. (4x - 5y)2 = 16x2 - 20xy + 25y2
B. (4x - 5y)2 = 16x2 + 40xy - 25y2
C. (4x - 5y)2 = 16x2  - 40xy + 25y2
D. (4x - 5y)2  = 16x2 - 20xy - 25y2

Question 1421

Which of the following is correct?

A. (3x -­ 2y)2 = 9x2 -­ 12xy + 4y2
B. (3x -­ 2y)2 = 9x2 -­ 6xy + 4y2
C. (3x + 2y)2 = 9x2 -­ 12xy + 4y2
D. (3x + 2y)2 = 9x2 -­ 6xy + 4y2

Question 1422

Which of the following is correct?

A. (4x + 5y)(5x - 4y) = 20x2 + 9xy - 20y2
B. (4x + 5y)(5x - 4y) = 20x2 + 41xy - 20y2
C. (4x + 5y)(5x - 4y) = 20x2 - 9xy + 20y2
D. (4x + 5y)(5x - 4y) = 20x2 - 41xy + 20y2

Question 1423

Which of the following is correct?

A. (3x + 4y)(4x -­ 3y) = 12x2 + 7xy ­- 12y2
B. (3x + 4y)(4x -­ 3y) = 12x2  + 251xy -­ 12y2
C. (3x + 4y)(4x -­ 3y) = 12x2 -­ 7xy + 12y2
D. (3x + 4y)(4x -­ 3y) = 12x2 - ­ 251xy + 12y2

Question 1424

Which of the following is not a quadratic equation?

A. 3x(x + 5) ­11 = 2x(x -­ 2) + 6
B. 4x(x + 3) + 7 = 4x(x -­ 11) + 9
C. x(x + 2) ­15 = x(2x -­ 5) + 11
D. 4x - 6x +­ 9 = 0

Question 1425

Which of the following is not a quadratic equation?

A. 2x(x + 4) -11 = x(x - 3) + 6
B. 4x(x + 4) -11 = 5x(x - 3) + 5
C. x(x + 2) -15 = x(x - 5) + 11
D. 2x2 + 8x - 11 = 0

Question 1426

Which of the following is TRUE?

A. 1123>1294>15
B. 1294>1123>15
C. 15>1123>1294
D. 15>1294>1123

Question 1427

Which of the following numbers is completely divisible by 99?

A. 57717
B. 57627
C. 55162
D. 56982

Question 1428

Which of the following pair of numbers is the solution of the equation 3x+2+ 3–x= 10 ?

A. 0, 2
B. 0, -2
C. 1, -1
D. 1, 2

Question 1429

Which of the following points lies on the line 3x -­ 4y = ­-13?

A. (­5,­7)
B. (­-5,­7)
C. (­5,­-7)
D. (­-5,­-7)

Question 1430

Which of the following quadratic equations has equal roots?

A. x2 -­ 14x -­ 49 = 0
B. x2 + 7x + 49 = 0
C. x2 -­ 7x -­ 49 = 0
D. x2 + 14x + 49 = 0

Question 1431

Which of the following quadratic equations has real roots?

A. 3x2 -­ 5x + 2 = 0
B. 3x2 -­ 4x + 2 = 0
C. 4x2 -­ 3x + 2 = 0
D. 5x2 -­ 2x + 2 = 0

Question 1432

Which of the following quadratic equations has real roots?

A. 4x2 -­ 9x + 6 = 0
B. 3x2 -­ 2x + 6 = 0
C. 2x2 -­ 7x + 6 = 0
D. x2 -­ 2x + 2 = 0

Question 1433

Which of the following quadratic equations has real roots?

A. 4x2 - 3x + 6 = 0
B. 2x2 + 7x + 6 = 0
C. x2 - 2x + 4 = 0
D. 3x2 - 4x + 3 = 0

Question 1434

Which of the following value of 'x' satisfies the equation 814x+4 = 2432x+8?

A. 3
B. 4
C. 5
D. 6

Question 1435

x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?

A. 19
B. 23
C. 31
D. 29

Question 1436

x, y and z are real numbers. If x3 + y3 + z3 = 13, x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?

A. -1
B. 1
C. 3
D. -3

Question 1437

XYZ is a right angled triangle and ∠Y = 90°. If XY = 2.5 cm and YZ = 6 cm then the circumradius of ∆XYZ is

A. 6.5 cm
B. 3.25 cm
C. 3 cm
D. 2.5 cm

Question 1438

You have 20 big and 16 small diaries and want to make gift packs containing both in each pack. What is the maximum number of gift packs you can make without any left over?

A. 5
B. 4
C. 3
D. 2

Question 1439

You purchased two pieces of cloth measring 1.2 m and 1.3 m each at Rs. 330 and Rs. 270 per meter respectively and gave Rs. 1000 at the payment counter. How much cash will you get back?

A. Rs. 253
B. Rs. 604
C. Rs. 649
D. Rs. 235

Question 1440

α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots α4 and β4?

A. x2 – 1522x + 14641 = 0
B. x2 + 1921x + 14641 = 0
C. x2– 1764x + 14641 = 0
D. x2+ 2520x + 14641 = 0

Question 1441

Δ ABC is right angled at B. If m∠A = 60°, then what is the value of 2 Sec C x 1/2 Sin A?

A. 1/2
B. 1/3
C. 1
D. 1/√2

Question 1442

Δ ABC is right angled at B. If m∠A = 60°, then what is the value of sec C.sin A?

A. 2/√3
B. √3/2
C. 2/3
D. 1

Question 1443

Δ DEF is right angled at E. If m∠D = 45%., then Cosec F =

A. 1/2
B. 1/√2
C. √2
D. 1/√3

Question 1444

Δ DEF is right angled at E. If m∠D = 45°, then what is the value of cosecF X cotD?

A. 1/√2
B. 2
C. 1/2
D. √2

Question 1445

Δ DEF is right angled at E. If m∠F = 45, then what is the value of Sin F x Tan F?

A. √2
B. 1/√3
C. 1/√2
D. 2/√3

Question 1446

Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?

A. √2
B. 2
C. 1/√2
D. 1/2

Question 1447

Δ LMN is right angled at M. If m∠N = 60 deg., then Tan L =______.

A. 1/2
B. 1/√3
C. 1/√2
D. 2

Question 1448

Δ LMN is right angled at M. If m∠N = 60°, then Tan L =______.

A. 1/2
B. 1/√3
C. 1/√2
D. 2

Question 1449

Δ PQR is right angled at Q. If m√R = 30°, then what is the value of Cot P?

A. 1/2
B. 1/√2
C. 1/√3
D. 2

Question 1450

Δ XYZ is right angled at Y. If m∠Z = 60°, then what is the value of (1/√2) Sec X?

A. 2/√3
B. 1/√6
C. 1/√3
D. 2/√6

Question 1451

Δ XYZ is right angled at Y. If m∠Z = 60°, what is the length of YZ (in cm), if ZX = 3√3 cm?

A. 3√3/2
B. 3√3
C. 9
D. 6

Question 1452

ΔABC and ΔDEF are two similar triangles and the perimeter of ΔABC and ΔDEF are 30 cm and 18 cm respectively. If length of DE = 36 cm, then length of AB is

A. 60 cm
B. 40 cm
C. 45 cm
D. 50 cm

Question 1453

ΔABC is right angled at B. If cotA = 7/24, then what is the value of cosecC ?

A. 7/25
B. 25/7
D. 7/24

Question 1454

ΔABC is right angled at B. If m ∠A = 60°, then what is the value of 1/√3 Cosec C?

A. 2/√3
B. 2/3
C. √2/√3
D. √2/3

Question 1455

ΔABC is right angled at B. If m∠A = 45 deg, then find the value of (tanC + √3/2).

A. 4/√3
B. (2+√3)/2
C. (√2+2)/2√2
D. (2+√3)/3

Question 1456

ΔABC is right angled at B. If m∠A = 45°, then find the value of (cosecC + 1/√3).

A. (3√2+1)/3
B. (2+√3)/2
C. 5/√3
D. (√6+1)/√3

Question 1457

ΔABC is right angled at B. If m∠C = 60°, then find the value of (cotA - 1/2).

A. -1/√3
B. (3-√2)/3√2
C. (2√3-1)/2
D. (√2-√3)/√6

Question 1458

ΔDEF is right angled at E. If cosD = 8/17, then what is the value of secF ?

A. 17/8
B. 8/17
C. 17/15
D. 15/17

Question 1459

ΔDEF is right angled at E. If cosecD = 5/4, then what is the value of cosecF?

A. 5/3
B. 3/4
C. 4/5
D. 4/3

Question 1460

ΔDEF is right angled at E. If m∠D = 45°, then find the value of (tanF + 1/3).

A. 4/3
B. 3√3/2
C. (√2+1)/√2
D. (3√2+1)/3

Question 1461

ΔDEF is right angled at E. If m∠F = 30 deg, then find the value of (sinD - 1/3).

A. -1/2√3
B. (3√3-2)/6
C. (√2-√3)/√6
D. (2√2-1)/√2

Question 1462

ΔDEF is right angled at E. If secD = 25/7, then what is the value of cosecF ?

A. 7/25
C. 25/7
D. 7/24

Question 1463

ΔPQR is right angled at Q. If cosP = 5/13, then what is the value of cosecR ?

A. 13/5
B. 5/12
C. 5/13
D. 13/12

Question 1464

ΔPQR is right angled at Q. If m∠P = 45°, then find the value of (cosecR + 1/3).

A. (√3+2)/2√3
B. (√3+2)/2
C. (3√2+1)/3
D. (2+2√3)/√3

Question 1465

ΔPQR is right angled at Q. If m∠R = 45°, then find the value of (tanP - 1/2).

A. (2-√3)/√3
B. (2√3-√6)/2√2
C. 1/2
D. (√6-6)/3√3

Question 1466

ΔPQR is right angled at Q. If secP = 13/5, then what is the value of sinR ?

A. 5/13
B. 5/12
C. 13/5
D. 13/12

Question 1467

ΔPQR is right angled at Q. If tanP = 24/7, then what is the value of cosR ?

A. 25/7
B. 24/25
D. 7/24

Question 1468

ΔUVW is right angled at V. If secU = 5/3, then what is the value of tanW ?

A. 3/4
B. 5/3
C. 4/5
D. 4/3

Question 1469

ΔXYZ is right angled at Y. If m∠X = 30 deg, then find the value of (sinZ + √3).

A. 4/√3
B. 5/√3
C. 4/3
D. 3√3/2

Question 1470

ΔXYZ is right angled at Y. If m∠Z = 45°, then find the value of (cosecX - 2/√3).

A. (2-√3)/2√3
B. (1-√6)/√2
C. (√6-2)/√3
D. -1/√3

Question 1471

ΔXYZ is right angled at Y. If m∠Z = 60°, then Cosec X =

A. 2
B. 1/2
C. 1/√2
D. 1/√3

Question 1472

θ is a positive acute angle and sinθ ­ cosθ = 0, then the value of secθ + cosecθ is

A. 2
B. √2
C. 2√2
D. 3√2

Question 1473

If a - b = 3 and a2 + b2 = 29, find the value of ab.

A. 10
B. 12
C. 15
D. 18

Question 1474

David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

A. 19th floor
B. 28th floor
C. 30th floor
D. 37th floor

Question 1475

5 - [4 - {3 - (3 - 3 - 6)}] is equal to:

A. 10
B. 6
C. 4
D. 0

Question 1476

1 - [5 - {2 + (- 5 + 6 - 2) 2}] is equal to:

A. -4
B. 2
C. 0
D. 2

Question 1477

(98764 + 89881 + 99763 + 66342) ÷ (1186 + ? + 1040 + 1870) = 55

A. 2254
B. 2354
C. 2368
D. 2404

Question 1478

Given that ( 12 + 22 + 32 + .......... + 102 ) = 385, then the value of ( 22 + 32 + 42 + .......... + 202 ) is equal to = ?

A. 770
B. 1155
C. 1540
D. (385)2

Question 1479

If the sum of two numbers is 22 and the sum of their squares is 404, then the product of two numbers is = ?

A. 40
B. 44
C. 80
D. 88

Question 1480

Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4), The maximum value among the above three is?

A. a
B. b
C. c
D. All equal