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
D. 24/7
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 spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is
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
D. 24/7
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
C. 24/7
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
C. 24/7
D. 24/25
Question 591
If Tan θ = 7/24, then what is the value of Sec θ?
A. 24/25
B. 24/7
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
A. Π/12 radians
B. Π/15 radians
C. 2Π/5 radians
D. 3Π/13 radians
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
B. ad = bc
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. AB
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
C. 24/7
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
B. 24/7
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
C. 24/7
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
Question 1481
The least number that must be subtracted from 63522 to make the result a perfect square is = ?
A. 18
B. 20
C. 24
D. 30