Area MCQ Questions & Answers

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

Question 1

Square units 13 by 9 of an office area is

A. 97

B. 117

C. 107

D. 127

Question 2

The total surface area of a right circular cylinder with radius of the base 7 cm and height 20 cm, is :

A. 900 cm2

B. 140 cm2

C. 1000 cm2

D. 1188 cm2

Question 3

A path of uniform width runs round the inside of a rectangular field 38 m long 32 m wide. If the path occupies 600 m2, then the width of the path is :

A. 5 m

B. 10 m

C. 18.75 m

D. 30 m

Question 4

ΔABC is similar to ΔPQR. If ratio of perimeter of ΔABC : perimeter of ΔPQR is 5:9 and if PQ = 45 cm, then the length of AB (in cm) is?

A. 15

B. 20

C. 25

D. 16

Question 5

The number of sides of a regular polygon whose exterior angles are each 72 deg is

A. 7

B. 6

C. 5

D. 8

Question 6

The sum of the lengths of the edges of a cube is equal to the perimeter of a square. If the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the square is

A. 30 units

B. 9 units

C. 27 units

D. 12 units

Question 7

What are the co-ordinates of the centroid of a triangle, whose vertices are A(-2,5), B(3,-2) and C(5,3)?

A. (-2,-2)

B. (-2,2)

C. (2,2)

D. (2,-2)

Question 8

Three plots having areas 110, 130 and 190 square metres are to be subdivided into flower beds of equal size. If the breadth of a bed is 2 metres, the maximum length of a bed van be :

A. 5 m

B. 11 m

C. 13 m

D. 19 m

Question 9

The perimeter of a triangle is 30 cm and its area is 30 cm2. If the largest side measures 13 cm, then what is the length of the smallest side of the triangle ?

A. 3 cm

B. 4 cm

C. 5 cm

D. 6 cm

Question 10

The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ?

A. 14:9

B. 13:12

C. 16:5

D. 17:13

Question 11

The ratio between the length and the perimeter of a rectangular plot is 1 : 3. What is the ratio between the length and breadth of the of the plot ?

A. 1 : 2

B. 2 : 1

C. 3 : 2

D. Data inadequate

Question 12

If the radius of a circle is increased by 29% its area increases by

A. 58 percent

B. 29 percent

C. 33.205 percent

D. 66.41 percent

Question 13

ABCD is a quadrilateral inscribed in a circle (radius = ). The bisectors of the angles DAB and BCD intersect the circle at X and Y, respectively. What is the length of the straight line XY?

A. π (rxr)

B. 2r

C. (r + 2)

D. π (rxr)/2

Question 14

Find the area (in cm²) of a semi-circle of radius 35 cm.

A. 3850

B. 960

C. 1920

D. 1925

Question 15

If the radius of a circle is decreased by 50% , find the percentage decrease in its area.

A. 75%

B. 65%

C. 35%

D. 25%

Question 16

The area of a square is 72.25 cm². Find its perimeter (in cm).

A. 68

B. 44

C. 34

D. 88

Question 17

Three circles of radius 3.5cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is

A. 1.967

B. 1.867

C. 1.767

D. 1.567

Question 18

The area of a square is equal to its side, if the side is 1 unit.

A. Always

B. Sometimes

C. Often

D. Never

Question 19

What is the area of the shaded region ?

A. (32 - 4π) sq. units

B. (32 - 8π) sq. units

C. (16 - 4π) sq. units

D. (16 - 8π) sq. units

Question 20

The length of a rectangular plot is 20 meters more than its breadth. If the cost of fencing the plot @ 26.50 per meter is Rs. 5300. What is the length of the plot in meter?

A. 40m

B. 50m

C. 60m

D. 10m

Question 21

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A. 20%

B. 24%

C. 30%

D. 33%

Question 22

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle?

A. 10cm

B. 20cm

C. 30cm

D. 40cm

Question 23

What is the area (in sq cm) of a rectangle of perimeter 48 cm and breadth 10 cm?

A. 140

B. 480

C. 240

D. 440

Question 24

If length of each side of a rhombus PQRS is 8 cm and ∠PQR = 120°, then what is the length (in cm) of QS?

A. 4√5

B. 6

C. 8

D. 12

Question 25

What is the slope of the line perpendicular to the line passing through the points (-5 , 1) and (-2 , 0)?

A. -3

B. 3

C. -1/3

D. 1/3

Question 26

A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?

A. 140

B. 150

C. 160

D. 170

Question 27

The length and breadth of a rectangle are 24 cm and 7 cm respectively. What must be the length of its diagonal (in cm)?

A. 50

B. 28

C. 25

D. 56

Question 28

A vertical rod of height 33 metres is bent to form a semi-circular shape so that the top touches the ground. The distance between the top head and the base on the ground is :

A. 10.5 m

B. 12 m

C. 21 m

D. 33 m

Question 29

Area of a square and a rectangle are equal. If side of the square is 40 cm and length of the rectangle is 64 cm, what is the perimeter of the rectangle ?

A. 187 cm

B. 178 cm

C. 149 cm

D. 194 cm

Question 30

Find the maximum area of a rectangle field which is surrounded by a rope of 400 m.

A. 5000 sq.m

B. 6250 sq.m

C. 4000 sq.m

D. 10000 sq.m

Question 31

The radius of a sphere is 6 cm. It is melted and drawn into a wire of radius 0.2 cm. The length of the wire is

A. 81 m

B. 80 m

C. 75 m

D. 72 m

Question 32

If the circumference of a circle is 100 units, then what will be the length of the arc described by an angle of 20 degrees ?

A. 5.55 units

B. 4.86 units

C. 5.85 units

D. None of these

Question 33

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in cm) is :

A. 44

B. 46

C. 48

D. 50

Question 34

The area of a square is equal to the area of a rectangle. The length of the rectangle is 5 cm more than a side of the square and its breadth is 3 cm less than the side of the square. What is the perimeter of the rectangle ?

A. 15 cm

B. 18 cm

C. 34 cm

D. 26 cm

Question 35

A carpenter is designing a table. The table will be in the form of a rectangle whose length is 4 feet more than its width. How long should the table be if the carpenter wants the area of the table to be 45 sq. ft ?

A. 6 ft

B. 9 ft

C. 11 ft

D. 13 ft

Question 36

If the length of a rectangle is increased by 50% and breadth is decreased by 25%, what is the percentage change in its area ?

A. 12.5% increase

B. 10% increase

C. 25% increase

D. 20% decrease

Question 37

What is the reflection of the point (2, -3.5) in the y-axis?

A. (-2, 3.5)

B. (-2, -3.5)

C. (-3.5,-2)

D. (3.5,-2)

Question 38

A rectangular swimming pool of length 20 m and breadth 10 m has a uniformly sloping floor. It is 1 m in depth on one end of its length and 3 m at the other. How much water is needed to completely fill this pool? (Take π = 22/7)

A. 800 cubic metres

B. 300 cubic metres

C. 480 cubic metres

D. 400 cubic metres

Question 39

If the radius of a circle is increased by 14% its area increases by

A. 28 percent

B. 29.96 percent

C. 14 percent

D. 14.98 percent

Question 40

A polygon has 9 sides. What is its interior angle?

A. 140 deg

B. 100 deg

C. 120 deg

D. 40 deg

Question 41

The ratio of the circumferences of two circles is 2 : 3. What is the ratio of their areas ?

A. 2 : 3

B. 4 : 9

C. 9 : 4

D. None of these

Question 42

Δ DEF is right angled at E. If m ∠D = 30°. What is the length (in cm) of DE, if EF = 2√3 cm?

A. 3

B. 4

C. 6

D. 2

Question 43

A sector of 120, cut out from a circle, has an area of 667cm2. Find the radius of the circle ?

A. 1

B. 2

C. 3

D. 4

Question 44

Calculate the area (in cm2) of a circle of radius 17.5 cm.

A. 1925

B. 962.5

C. 809.5

D. 1619

Question 45

Find the area (in sq.cm) of a semi-circle of radius 7 cm

A. 154

B. 21

C. 42

D. 77

Question 46

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A. 153600

B. 143600

C. 13600

D. 16300

Question 47

If the sides of a square be double find the increase of percentage in area :

A. 100%

B. 200%

C. 300%

D. 400%

Question 48

The area of a rectangle in 60 sq.cm and its perimeter is 34 cm, then the length of the diagonal is

A. 17 cm

B. 11 cm

C. 15 cm

D. 13 cm

Question 49

Triangle PQR is such that PQ = 9 cm, QR = 6 cm, PR = 7.5 cm and triangle PQR is similar to triangle XYZ. If XY = 18 cm, find the value of YZ.

A. 15 cm

B. 18 cm

C. 12 cm

D. 9 cm

Question 50

The area of a square field is 69696sq.cm..its diagonal will be equal to

A. 373

B. 573

C. 473

D. 673

Question 51

Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed of the smaller wheel is

A. 22m/s

B. 33m/s

C. 44m/s

D. 55m/s

Question 52

The line passing through (3,4) and (0,3) is perpendicular to the line passing through (5,7) and (4,x). What is the value of x?

A. 4

B. -2

C. 2

D. -4

Question 53

The base of a triangle is half the base of a parallelogram having the same area as that of the triangle. The ratio of the corresponding heights of the triangle to the parallelogram will be

A. 1 : 4

B. 4 : 1

C. 2 : 1

D. 1 : 2

Question 54

What is the area (in sq cm) of a rectangle if its diagonal is 26 cm and one of its sides is 10 cm?

A. 120

B. 240

C. 360

D. 480

Question 55

Find the perimeter and area of a square that has a side of length 14 feet.

A. 176

B. 186

C. 196

D. 206

Question 56

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:

A. 1:1

B. 1:2

C. 1:3

D. 1:4

Question 57

The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is

A. Rs.174

B. Rs.274

C. Rs.374

D. Rs.474

Question 58

A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is :

A. 15 m × 6.67 m

B. 20 m × 5 m

C. 30 m × 3.33 m

D. 40 m × 2.5 m

Question 59

If the total surface area of a cube is 864 square cm, find the volume of the cube ?

A. 1728 cm3

B. 1624 cm3

C. 144 cm3

D. 1684 cm3

Question 60

The area of a circle is 346.5 cm2. Find its circumference (in cm).

A. 132

B. 38

C. 66

D. 76

Question 61

The area of playground is 1600 m2. What is the perimeter? I. It is a perfect square playground. II. It costs Rs. 3200 to put a fence around the playground at the rate of Rs. 20 per metre.

A. I alone sufficient while II alone not sufficient to answer

B. Either I or II alone sufficient to answer

C. Both I and II are not sufficient to answer

D. Both I and II are necessary to answer

Question 62

What is the measure (in degree) of an exterior angle of a regular polygon of 9 sides?

A. 36

B. 40

C. 30

D. 24

Question 63

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A. 2.91 m

B. 3 m

C. 5.82 m

D. None of these

Question 64

What would be the area of a rectangle whose area is equal to the area of a circle of radius 7 cm ?

A. 77 cm2

B. 154 cm2

C. 184 cm2

D. 180 cm2

Question 65

What is the cost painting the two adjacent walls of a hall at Rs. 5 per m2 which has no windows or doors? I. The area of the hall is 24 sq. m. II. The breadth, length and height of the hall are in the ratio of 4 : 6 : 5 respectively. III. Area of one wall is 30 sq. m.

A. I only

B. II only

C. III only

D. II and either I or III

Question 66

What will be the area of a semi-circle whose perimeter is 36 cm ?

A. 154 cm2

B. 168 cm2

C. 308 cm2

D. None of the above

Question 67

The circumference of a circle is 88 cm, find its area?

A. 616 sq cm

B. 308 sq cm

C. 154 sq cm

D. 77 sq cm

Question 68

Which of the following figures has the longest perimeter ?

A. A square of side 10 cm

B. A rectangular of sides 12 cm and 9 cm

C. A circle of radius 7 cm

D. A rhombus of side 9 cm

Question 69

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A. 40

B. 50

C. 120

D. None of these

Question 70

If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is :

A. 25%

B. 50%

C. 60%

D. 75%

Question 71

A typist uses a paper 30 cm by 15 cm. He leaves a margin of 2.5 cm at the top and bottom and 1.25 cm on either side. What percentage of paper area is approximately available for typing ?

A. 60%

B. 65%

C. 70%

D. 80%

Question 72

Find the area of the rectangle or square with the given dimensions s=10 feet

A. 500

B. 100

C. 200

D. 300

Question 73

Find the length of one side of a rhombus whose area is 24 sq.cm and the sum of the lengths of its diagonals is 14 cm.

A. 3 cm

B. 6 cm

C. 4 cm

D. 5 cm

Question 74

PQR is a right angled triangle in which PQ = QR. If the hypotenuse of the triangle is 20 cm, then what is the area (in cm2) of the triangle PQR?

A. 100√2

B. 100

C. 50√2

D. 50

Question 75

The area of a circle is 616 sq.m. Find its diameter.

A. 7 m

B. 14 m

C. 28 m

D. 56 m

Question 76

What is the length of diagonal, if area of a rectangle is 168 sq.cm and breadth is 7 cm?

A. 24 cm

B. 15 cm

C. 17 cm

D. 25 cm

Question 77

The crosssection of a canal is in the shape of an isosceles trapezium which is 3 m wide at the bottom and 5 m wide at the top. If the depth of the canal is 2 m and it is 110 m long, what is the maximum capacity of this canal? (Take π = 22/7)

A. 1760 cubic metres

B. 1650 cubic metres

C. 1056 cubic metres

D. 880 cubic metres

Question 78

The area of the largest triangle that can be inscribed in a semicircle of radius 6m is

A. 36 sq.m

B. 72 sq.m

C. 18 sq.m

D. 12 sq.m

Question 79

The circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel ?

A. 850 ft

B. 950 ft

C. 1200 ft

D. 1450 ft

Question 80

Two equal circles intersect so that their centres, and the points at which they intersect form a square of side 1 cm. The area (in sq.cm) of the portion that is common to the circles is

A. π4

B. π2-1

C. π5

D. √2 - 1

Question 81

In a wheelchair slalom event, athletes weave around cones and race to the finish line. A diagram of the rectangular course is shown. Find the perimeter of the course

A. 32

B. 42

C. 62

D. 92

Question 82

The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 6√3 sq cm, what is the area of the equilateral triangle?

A. 9√3 sq cm

B. 9 sq cm

C. 9√2 sq cm

D. 12 sq cm

Question 83

What is the area (in sq cm) of an equilateral triangle of side 6 cm?

A. 36√3

B. 9

C. 36

D. 9√3

Question 84

Length and breadth of a rectangle are increased by 40% and 70% respectively. What will be the percentage increase in the area of rectangle?

A. 118

B. 110

C. 138

D. 128

Question 85

If a 36 cm thread is used to wrap a book, lengthwise twice and breadth wise once, what is the size of the book ?

A. 288 sq.cm

B. 188 sq.cm

C. 144 sq.cm

D. 244 sq.cm

Question 86

The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle :

A. 71.5 cm

B. 71.7 cm

C. 72.3 cm

D. 72.7 cm

Question 87

The area of the largest sphere ( in cm2) that can be drawn inside a square of side 18 cm is

A. 972Π

B. 11664Π

C. 36Π

D. 288Π

Question 88

The length of one side and the diagonal of a rectangle are 5 cm and 13 cm respectively. Find its area (in cm2).

A. 60

B. 120

C. 35

D. 70

Question 89

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, the n the area of the park (in square metre) is :

A. 15360 square metre

B. 153600 square metre

C. 30720 square metre

D. 307200 square metre

Question 90

In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and AE are 8 cm, 4 cm and 12 cm respectively, what is the length of AC?

A. 6 cm

B. 18 cm

C. 9 cm

D. 15 cm

Question 91

In triangle ABC, AB = 8 cm, angle A is bisected internally to intersect BC at D. BD = 6 cm and DC = 7.5 cm. What is the length of CA?

A. 12 cm

B. 10 cm

C. 12.5 cm

D. 10.5 cm

Question 92

The circumference of a circle, whose area is 24.64 m2 , is :

A. 14.64 m

B. 16.36 m

C. 17.60 m

D. 18.40 m

Question 93

Line segment AB is parallel to line segment CD. AD intersects BC in E. If lengths of AE, BC and ED are 12 cm, 12 cm and 18 cm respectively, what is the length of EC?

A. 4.8 cm

B. 9.3 cm

C. 8.1 cm

D. 7.2 cm

Question 94

The ratio of the radii of two circle is 3 : 2. What is the ratio of their circumferences ?

A. 2 : 3

B. 3 : 2

C. 4 : 9

D. None of these

Question 95

If the perimeter of a semicircle is 36 cm, then find its area (in cm2).

A. 154

B. 35

C. 77

D. 70

Question 96

The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:

A. 75

B. 85

C. 95

D. 105

Question 97

An error of 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is

A. 4.04%

B. 5.04%

C. 6.04%

D. 7.04%

Question 98

The base of triangle is 15 cm and height is 12 cm the height of another triangle of double the area having base 20 cm is :

A. 22 cm

B. 20 cm

C. 18 cm

D. 10 cm

Question 99

The area of the square field is 196 sq.m. Its each side is

A. 16 m

B. 17 m

C. 14 m

D. 13 m

Question 100

If the radius of a circle is increased by 200%, then its area will increase by :

A. 200%

B. 400%

C. 800%

D. 900%

Question 101

Find the area (in cm²) of a semi-circle of radius 21 cm.

A. 1386

B. 960

C. 693

D. 1920

Question 102

The area of a triangle is 456 sq.cm and its height is 24 cm. The length of its base is

A. 32

B. 36

C. 34

D. 38

Question 103

If 4 circles of equal radius are drawn with vertices of a square as the centre , the side of the square being 7 cm, find the area of the circles outside the square ?

A. 119.21 sq cm

B. 115.395 sq cm

C. 104.214 sq cm

D. 111.241 sq cm

Question 104

An angle is 60 deg more than one fifth of its complement. Find the smaller angle in degrees.

A. 65 deg

B. 35 deg

C. 25 deg

D. 45 deg

Question 105

The area of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is :

A. 0.525 cm

B. 4.2 cm

C. 4.41 cm

D. 8.4 cm

Question 106

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

A. 2%

B. 2.02%

C. 4%

D. 4.04%

Question 107

The area of a rhombus with side 13 cm and one diagonal 10 cm will be :

A. 140 cm2

B. 130 cm2

C. 120 cm2

D. 110 cm2

Question 108

The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is

A. 240

B. 140

C. 40

D. 340

Question 109

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A. Rs. 456

B. Rs. 458

C. Rs. 558

D. Rs. 568

Question 110

The measures of the four angles of a quadilateral are in the ratio 3:4:5:6. What is the measure of the biggest angle?

A. 120°

B. 100°

C. 80°

D. 60°

Question 111

In a rhombus _____.

A. opposite angles are supplementary

B. diagonals form two congruent triangles

C. diagonals are congruent

D. diagonals do not bisect opposite angles

Question 112

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?

A. (0 , 13)

B. (0, 5)

C. (0, -5)

D. (0 , -13)

Question 113

ABCD is a square. E is the mid-point of BC and F is the mid-point of CD. The ratio of the area of triangle AEF to the area of the square ABCD is :

A. 1 : 2

B. 1 : 3

C. 1 : 4

D. 3 : 8

Question 114

The four sides of a quadrilateral are in the ratio of 2:3:4:5 and its perimeter is 280m. The length of the longest side is

A. 100m

B. 150m

C. 175m

D. 180m

Question 115

In a triangle the length of the side opposite the angle which measures 30 degree is 12 cm, what is the length of the side opposite to the angle which measures 60 degree?

A. 9 cm

B. 12√3 cm

C. (15√3)/2 cm

D. (9√3)/2 cm

Question 116

A pentagonal prism has 15 edges. How many vertices does it have?

A. 12

B. 10

C. 15

D. 20

Question 117

What is the area of an obtuse angled triangle given below with two sides are 8 and 12 and the angle included between two sides is 150 deg?

A. 48 sq units

B. 24 sq units

C. 12 sq units

D. 6 sq units

Question 118

The area of a square is 40.5 cm². Find the length of its diagonal (in cm).

A. 9

B. 4.5

C. 18

D. 13.5

Question 119

The circumference of a circle is equal to the side of a square whose area measures 407044 sq.cm. What is the area of the circle ?

A. 22583.2 sq.cm

B. 32378.5 sq.cm

C. 39483.4 sq.cm

D. 41263.5 sq.cm

Question 120

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

A. 14

B. 13

C. 12

D. 11

Question 121

If a cylinder of radius 4 cm and height 8 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A. 48 cm

B. 24 cm

C. 36 cm

D. 12 cm

Question 122

Find the area (in sq.cm) of a semi-circle of radius 14cm.

A. 308

B. 616

C. 160

D. 320

Question 123

The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of direct common tangent to the length of the transverse common tangent?

A. √51 : √68

B. √33 : √17

C. √66 : √51

D. √28 : √17

Question 124

A circular piece of thin wire is converted into a rhombus of side 11 cm. Find the diameter of the circular piece?

A. 28 cm

B. 3.5 cm

C. 7 cm

D. 14 cm

Question 125

The number of diagonals in a hendecagon is

A. 44

B. 39

C. 40

D. 33

Question 126

A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in cm2) of the remaining part?

A. 3842

B. 4312

C. 3296

D. 4436

Question 127

In Δ ABC, the median AD is 6 cm and CB is 12 cm, measure of angle CAB is

A. 90°

B. 30°

C. 60°

D. 120°

Question 128

Triangle ABC is similar to triangle PQR and AB : PQ = 2 : 3. AD is the median to the side BC in triangle ABC and PS is the median to the side QR in triangle PQR. What is the value of (BD/QS)2?

A. 3/5

B. 4/9

C. 2/3

D. 4/7

Question 129

The ratio of the radii of two circles is 1 : 3. Then the ratio of their areas is :

A. 1 : 3

B. 1 : 6

C. 1 : 9

D. None of these

Question 130

The cost of levelling a circular field at 50 Paise per square metre is Rs 7700. The cost (in Rs) of putting up a fence all round it at Rs 1.20 per meter is ( Use π = 22/7)

A. Rs 132

B. Rs 264

C. Rs 528

D. Rs 1056

Question 131

The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circum circle and the incircle of the triangle is (use: π = 22/7)

A. 50 1/7 sq.cm

B. 50 2/7 sq.cm

C. 75 1/7 sq.cm

D. 75 2/7 sq.cm

Question 132

A wire is in the shape of a rectangle. Its length is 42.7m and breadth is 21.8m. If the same wire is re-bent in the shape of a square, what will be the measure of the side of the square?

A. 16.125

B. 32.25

C. 11.35

D. 22.7

Question 133

What will be the length of the diagonal of that square plot whose area is equal to the area of a rectangular plot of length 45 metres and breadth 40 metres ?

A. 45.5 metres

B. 60 metres

C. 75 metres

D. Data inadequate

Question 134

In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

A. 13:9

B. 16:9

C. 15:9

D. 14:9

Question 135

The area of a trapezium is 18 sq. cm. Its height and 3 cm and 5 cm respectively. Find the length of the side parallel to the base.

A. 4 cm

B. 6 cm

C. 8 cm

D. 7 cm

Question 136

At what point does the line 4x - 3y = -6 intercept the y-axis?

A. (0,2)

B. (0,3/2)

C. (2,0)

D. (3/2,0)

Question 137

What is the length of the arc whose central angle is 30° and radius of the circle is 21 cm?

A. 22 cm

B. 16.5 cm

C. 11 cm

D. 28 cm

Question 138

The area of a rectangular field is 2100 sq. meters. If the field is 60 metres long, what is its perimeter ?

A. 180 m

B. 210 m

C. 240 m

D. None of the above

Question 139

Calculate the area (in cm2 ) of a circle of radius 10.5 cm.

A. 693

B. 157.5

C. 315

D. 346.5

Question 140

A rectangular grassy plot 120 m. by 60 m has a gravel path 1.5 m wide all round it on the inside. Find the cost of gravelling the path at 65 paise per sq. metre ?

A. Rs. 345.15

B. Rs. 245.1

C. Rs. 234.18

D. Rs. 456.65

Question 141

There is a square field of area ‘X’ square meters. A cylindrical ditch of radius 7 meters and depth 2 meters is dug, and the earth is taken out and spread over the remaining part of the square field, the height of square field which goes up by 0.77 meters. What is the value of ‘X’ ?

A. 548 sq. m

B. 524 sq. m

C. 518 sq. m

D. 554 sq. m

Question 142

A skating champion moves along the circumference of a circle of radius 28 m in 44 sec. How many seconds will it take her to move along the perimeter of a hexagon of side 48 m ?

A. 48 sec

B. 68 sec

C. 72 sec

D. 84 sec

Question 143

If the circumference of a circle is increased by 20%, what will be the effect on the circle ?

A. 40% increase

B. 44% increase

C. 48% increase

D. Cannot be determined

Question 144

Find the greatest length which can be used to measure exactly three pieces of lengths 1.26 m, 1.98 m and 12.62 m respectively.

A. 12 cm

B. 14 cm

C. 16 cm

D. 18 cm

Question 145

∆XYZ is right angled at Y. If m∠Z = 60°, then find the value of (cotX - 1/3).

A. (3√3-1)/3

B. (2√3-√6)/2√2

C. -5/3

D. (2-√3)/2√3

Question 146

In a rectangle _____.

A. Diagonals are perpendicular to each other

B. Diagonals are not equal

C. Diagonals bisect each other

D. Diagonals bisect opposite angles

Question 147

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A. 20

B. 24

C. 30

D. 33

Question 148

The length and breadth of a rectangle are 24 cm and 7 cm respectively. Calculate its perimeter (in cm).

A. 124

B. 48

C. 62

D. 96

Question 149

Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

A. 3(√11) – 7

B. 5(√13) – 8

C. 4(√7) – 11

D. 6(√11) – 9

Question 150

A parallelogram PQRS, the length of whose sides are 8 cm and 12 cm, has one diagonal 10 cm long Ile length of the other diagonal is approximately:

A. 17.8 cm

B. 17.5 cm

C. 17 cm

D. 18 cm

Question 151

A man runs round a circular field of radius 50m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?

A. 220/7 min

B. 110/7 min

C. 90/7 min

D. 230/7 min

Question 152

The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ?

A. 5 : 18

B. 16 : 7

C. 14 : 5

D. None of the above

Question 153

The perimeter of a rectangle whose length is 6 metre more than its breadth is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?

A. 360sq metre

B. 380 sq metre

C. 360 metre

D. 400 sq metre

Question 154

A line DE parallel to the side BC intersects the other two sides of triangle at point D and E such that AD = 1/6 AB and AE = 1/6 AC. If the value of BC is 18 cm then calculate the value of DE (in cm).

A. 2

B. 3

C. 6

D. 8

Question 155

The diagonal of a rhombus is 8m and 6m respectively. Find its area.

A. 48 sq.m

B. 24 sq.m

C. 12 sq.m

D. 96 sq.m

Question 156

A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?

A. 1033

B. 1433

C. 733

D. 2133

Question 157

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A. 20

B. 200

C. 300

D. 400

Question 158

The area of circle is 616 sq.m. Find its diameter. (pi = 22/7)

A. 7 m

B. 14 m

C. 28 m

D. 56 m

Question 159

A hall 50 m long and 45 m broad is to be paved with square tiles. Find the largest tile as well as its number in the given options so that the tiles exactly fit in the hall :

A. 36 sq. m and 80 tiles

B. 16 sq. m and 80 tiles

C. 25 sq. m and 90 tiles

D. 36 sq. m and 90 tiles

Question 160

The cost of papering the four walls of a room is Rs. 475. Each one of the length, breadth and height of another room is double that of this room. The cost of papering the walls of this new room is :

A. Rs. 712.50

B. Rs. 950

C. Rs. 1425

D. Rs. 1900

Question 161

If an equilateral triangle of area X and a square of area Y have the same perimeter, then X is :

A. equal to Y

B. greater than Y

C. less than Y

D. less than or equal to Y

Question 162

A man walked diagonally across a square plot. Approximately what was the percent saved by not walking along the edges?

A. 10%

B. 20%

C. 30%

D. 40%

Question 163

Find the maximum area of a rectangular field which is surrounded by a rope of 100 meters?

A. 500 sq.m

B. 325 sq.m

C. 400 sq.m

D. 100 sq.m

Question 164

Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is :

A. 22 cm/sec

B. 44 cm/sec

C. 66 cm/sec

D. 132 cm/sec

Question 165

What is the area (in sq cm) of a circle whose circumference is 22 cm?

A. 77

B. 38.5

C. 44

D. 88

Question 166

The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is

A. 20

B. 25

C. 30

D. 35

Question 167

The area of a circle of radius 5 is numerically what percent its circumference?

A. 150%

B. 250%

C. 350%

D. 450%

Question 168

The area of a regular hexagon is equal to the area of the square. What is the ratio of the perimeter of the regular hexagon to the perimeter of square?

A. 63 : 36

B. 23 : 62

C. 63 : 2

D. 63 : 23

Question 169

A rectangle becomes a square when its length is reduced by 10 units and its breadth is increased by 5 units. but by this process the area of the rectangle is reduced by 210 sq.units. The area of the rectangle (A) in square units is :

A. 2950 > A < 2900

B. 2900 > A > 2875

C. 2925 < A > 2875

D. 2925 > A > 2900

Question 170

The side of an equilateral triangle is 14 cm. Find its area (in sq.cm).

A. 64√3

B. 49√2

C. 64√2

D. 49√3

Question 171

The distance between the centres of two circles is 61 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?

A. 60

B. 54

C. 48

D. 72

Question 172

Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.

A. 84

B. 64

C. 44

D. 22

Question 173

The length of the base of an isosceles triangle is 2x2y+4z, and its perimeter is 4x2y+6z. Then the length of each of the equal sides is

A. x+y

B. x+y+z

C. 2(x+y)

D. x+z

Question 174

The length of the diagonal and the breadth of a rectangle are 25 cm and 7 cm respectively. Find its perimeter (in cm).

A. 124

B. 41

C. 82

D. 62

Question 175

In a trapezium ABCD, AB || CD, AB < CD, CD = 6 cm and distance between the parallel sides is 4 cm. If the area of ABCD is 16 sq.cm, then AB is

A. 1 cm

B. 3 cm

C. 2 cm

D. 8 cm

Question 176

Find the area (in sq units) enclosed by y = 0, x+6=0 and 2x-3y=6.

A. 9

B. 16

C. 20

D. 27

Question 177

If the diagonal and the area of a rectangle are 25 m2 and 168 m2, what is the length of the rectangle ?

A. 12 m

B. 17 m

C. 24 m

D. 31 m

Question 178

An angle is (2/3)rd of its supplementary angle. What is the measure of the angle?

A. 108°

B. 72°

C. 54°

D. 36°

Question 179

The area of a rhombus having one side 10 cm and one diagonal 12 cm is

A. 48 cm2

B. 96 cm2

C. 144 cm2

D. 192 cm2

Question 180

The area of a circle of radius 5 is numerically what percent of its circumference ?

A. 200%

B. 225%

C. 240%

D. 250%

Question 181

Two concentric circles form a ring. The inner and outer circumferences of ring are 5187m and 3527 m respectively. Find the width of the ring.

A. 4

B. 5

C. 6

D. 7

Question 182

How many metres of carpet 63 cm wide will be required to cover the floor of a room 14 metres by 9 metres ?

A. 185 metres

B. 200 metres

C. 210 metres

D. 220 metres

Question 183

The perimeter of a square is 30 cm. Find its area (in cm²).

A. 56.25

B. 112.5

C. 60.25

D. 120.5

Question 184

A circular grassy plot of land, 42 cm is diameter, has a path 3.5 m wide running around it outside. The cost of gravelling the path at Rs. 4 per square metre is :

A. Rs. 1002

B. Rs. 1802

C. Rs. 2002

D. Rs. 3002

Question 185

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 2:5, and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

A. 49 sq cm

B. 45 sq cm

C. 25 sq cm

D. 21 sq cm

Question 186

In a triangle, the distance of the centroid from the three vertices is 4cm, 6cm and 8cm respectively. Then the length of the smallest median is:

A. 8

B. 7

C. 6

D. 5

Question 187

A missile travels at 1278 km/h. How many metres does it travel in one second?

A. 355 metres

B. 358 metres

C. 345 metres

D. 313 metres

Question 188

The length of a rectangle is increased by 25%. To maintain the same area, the breadth has to be decreased by

A. 20%

B. 25%

C. 30%

D. 40%

Question 189

A square park having a side 22 m has two roads each 2 m wide running in the middle of it and parallel to its length and breadth. What will be the cost of gravelling the path at the rate of Rs.100/sq.m?

A. Rs. 88

B. Rs. 8800

C. Rs. 84

D. Rs. 8400

Question 190

If the parallel sides of a trapezium are 8 cm and 4 cm, M and N are the mid points of the diagonals of the trapezium, then length of MN is

A. 12 cm

B. 6 cm

C. 1 cm

D. 2 cm

Question 191

In a triangle PQR, PQ = PR and angle Q is twice that of angle P. Then angle Q is equal to

A. 72 deg

B. 36 deg

C. 144 deg

D. 108 deg

Question 192

ΔXYZ is similar to ΔPQR. If ratio of perimeters of ΔXYZ : ΔPQR is 3:2 and if PQ = 6 cm then what is the length of XY (in cm)?

A. 4

B. 8

C. 12

D. 9

Question 193

A hall, whose length is 16 m and the breadth is twice its height, takes 168 m of paper with 2 m as its width to cover its four walls. The area of the floor is :

A. 96 m2

B. 190 m2

C. 192 m2

D. 216 m2

Question 194

What is the obtuse angle formed by the hands of a clock when the time in the clock is 2:30?

A. 95 deg

B. 120 deg

C. 105 deg

D. 165 deg

Question 195

The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height

A. 6

B. 7

C. 8

D. 9

Question 196

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3 and area of ΔABC is 100 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

A. 84

B. 16

C. 25

D. 75

Question 197

If the perimeter of a semicircle is 108 cm, then find its area (in cm²).

A. 1386

B. 512

C. 693

D. 1024

Question 198

The percentage increase in the area of a rectangle, if each of its sides is increased by 20%

A. 22%

B. 33%

C. 44%

D. 55%

Question 199

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?

A. 10ft

B. 20ft

C. 30ft

D. 40ft

Question 200

Find the area (in cm2) of a semi-circle of radius 28 cm.

A. 2464

B. 832

C. 1232

D. 1664

Question 201

You purchased two pieces of cloth measuring 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 202

The ratio of bases of two triangles is x:y and that of their areas is a:b. Then the ratio of their corresponding altitudes wll be

A. ay:bx

B. a:b

C. x:y

D. bx:ay

Question 203

The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side :

A. 39 cm

B. 40 cm

C. 41 cm

D. 42 cm

Question 204

The diagonal of the floor of a rectangular closet is 712 feet. The shorter side of the closet is 412 feet. What is the area of the closet in square feet?

A. 9

B. 18

C. 27

D. 36

Question 205

The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid in the one-third of the remaining and blue tiles in the rest, how many blue tiles will be there ?

A. 16

B. 24

C. 32

D. 48

Question 206

If the area of a square with side a s equal to the area of a triangle with base a, then the altitude of the triangle is

A. a

B. 2a

C. 5a

D. 3a

Question 207

The area of the largest circle, that can be drawn inside a rectangle with side 18 cm by 14 cm, is :

A. 49 cm2

B. 154 cm2

C. 378 cm2

D. 1078 cm2

Question 208

What is the area (in square units) of the figure enclosed by the graphs of the lines x = -4, x = 2, y = -2 and y = 3?

A. 12

B. 24

C. 15

D. 60

Question 209

If the radius of a circle is increased by 75%, then its circumference will increase by :

A. 25%

B. 50%

C. 75%

D. 100%

Question 210

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A. 16

B. 18

C. 20

D. 22

Question 211

In an equilateral triangle of side 24 cms, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is equal to

A. 36.6 sq. cm

B. 54.2 sq. cm

C. 72.8 sq. cm

D. 98.5 sq. cm

Question 212

Five angles of a hexagon measure 116 deg each. What is the measure of the remaining angle?

A. 152 deg

B. 116 deg

C. 140 deg

D. 126 deg

Question 213

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3 and area of ΔADE is 4 sq cm, what is the area (in sq cm) of quadrilateral BDEC.

A. 25

B. 21

C. 5

D. 9

Question 214

A circular road runs around a circular garden. If the difference between the circumference of the outer circle and the inner circle is 44 m, the width of the road is :

A. 3.5 m

B. 4 m

C. 7 m

D. 7.5 m

Question 215

From each corner of a square with an edge of 4 cm, a 1 cm segment was chopped off from each side containing a vertex. What is the perimeter and the area of the octagon thus created?

A. 4√2 cm, 14 sq.cm

B. (8 + 4√2) cm, 14 sq.cm

C. (4 + 4√2) cm, 14 sq.cm

D. 16 cm, 12 sq.cm

Question 216

In triangle ABC, AB = 10 cm. Angle A is bisected internally to intersect BC at D. BD = 6 cm and DC = 7.5 cm. What is the length of CA?

A. 12.5 cm

B. 10.5 cm

C. 12 cm

D. 10 cm

Question 217

The base of a triangle is five-sixth of the base of a parallelogram having the same area as that of the triangle. The ratio of the corresponding heights of the triangle to the parallelogram will be

A. 12:5

B. 5:12

C. 5:3

D. 6:5

Question 218

In an isosceles triangle, the length of each equal side is twice the length of the third side. The ratio of areas of the isosceles triangle and an equilateral triangle with same perimeter is

A. 30√5 : 100

B. 32√5 : 100

C. 36√5 : 100

D. 42√5 : 100

Question 219

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is

A. 200m

B. 300m

C. 400m

D. 100m

Question 220

The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.

A. 312 sq.cm

B. 128 sq.cm

C. 412 sq.cm

D. 246 sq.cm

Question 221

ABCD is a rectangle and E and F are the mid-points of AD and DC respectively. Then the ratio of the areas of EDF and AEFC would be :

A. 1 : 2

B. 1 : 3

C. 1 : 4

D. 2 : 3

Question 222

D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD:DB = 4:5, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF

A. 16:25

B. 16:81

C. 81:16

D. 4:9

Question 223

Two equal circle are drawn in square in such a way that a side of the square forms diameter of each circle. If the remaining area of the square is 42 cm2, how much will the diameter of the circle measure ?

A. 3.5 cm

B. 4 cm

C. 14 cm

D. 7.5 cm

Question 224

PQR is a triangle, whose area is 180 cm2. S is a point on side QR, such that PS is the angle bisector of ∠QPR. If PQ : PR = 2 : 3, then what is the area (in cm2) triangle PSR?

A. 90

B. 108

C. 144

D. 72

Question 225

The inner circumference of a circular race track, 14m wide is 440m. Find the radius of the outer circle.

A. 84m

B. 24m

C. 44m

D. 54m

Question 226

Find the total surface area (in cm2) of a cube of side 7.5 cm.

A. 364.5

B. 446

C. 337.5

D. 684

Question 227

The three sides of a triangular field are 20 metres, 21 metres and 29 metres long respectively. The area of the field is :

A. 210 m2

B. 215 m2

C. 230 m2

D. None of these

Question 228

Find the cost in rupees for carpeting a room 65 dm x 30 dm at Rs. 45 per sq.m

A. 877.5

B. 87750

C. 87.75

D. 8775

Question 229

The diagonal of the floor of a rectangular closet is 7.5 feet. The shorter side of the closet is 4.5 feet. What is the area of the closet in square feet?

A. 5.25

B. 13.5

C. 27

D. 37

Question 230

A rectangular lawn 80 metres by 60 metres has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. 30 per square metre.

A. Rs. 3600

B. Rs. 3900

C. Rs. 36000

D. Rs. 39000

Question 231

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A. 1

B. 2

C. 3

D. 4

Question 232

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

A. 55%

B. 65%

C. 75%

D. 85%

Question 233

X and Y are the mid points of sides AB and AC of a triangle ABC. If BC+XY=12 units, then BC-XY is

A. 8 units

B. 4 units

C. 6 units

D. 2 units

Question 234

In a trapezium, one diagonal divides the other in the ratio 2 : 9. If the length of the larger of the two parallel sides is 45 cm, then what is the length (in cm) of the other parallel side?

A. 10

B. 5

C. 18

D. 14

Question 235

PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ΔABC is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and QC = 16 cm .Then the length of the line joining the mid points of the sides AB and BC is

A. 4√2 cm

B. 5 cm

C. 6 cm

D. 10 cm

Question 236

The area of the largest triangle that can be inscribed in a semi-circle of radius r, is :

A. r2

B. 2r2

C. r3

D. 2r3

Question 237

ΔABC is an isosceles right angled triangle having ∠C = 90°. If D is any point on AB, then AD2+ BD2 is equal to

A. CD2

B. 2CD2

C. 3CD2

D. 4CD2

Question 238

A rectangle of certain dimension is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is :

A. 24 cm

B. 28 cm

C. 36 cm

D. 48 cm

Question 239

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

A. 40%

B. 42%

C. 44%

D. 46%

Question 240

Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.

A. 25 sq.cm

B. 16 sq.cm

C. 9 sq.cm

D. 4 sq.cm

Question 241

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

A. 18%

B. 28%

C. 38%

D. 48%

Question 242

If the diagonals of a rhombus are 24cm and 10cm the area and the perimeter of the rhombus are respectively.

A. 10

B. 11

C. 12

D. 13

Question 243

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

A. 844

B. 814

C. 840

D. 820

Question 244

Area of circle is equal to the area of a rectangle having perimeter of 50 cms. and length more than the breadth by 3 cms. What is the diameter of the circle?

A. 7 cms

B. 21 cms

C. 28 cms

D. 14 cms

Question 245

Find the circumference (in cm) of a circle of radius 10.5 cm

A. 84

B. 35

C. 70

D. 66

Question 246

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 7803 sq. mtr, what is the breadth of the rectangular plot ?

A. 51 m

B. 88 m

C. 104 m

D. 153 m

Question 247

If O is the orthocentre of a triangle ABC and ∠BOC = 100°, the measure of ∠BAC is

A. 100°

B. 180°

C. 80°

D. 200°

Question 248

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A. 30

B. 40

C. 50

D. 60

Question 249

Find the area of the rectangle or square with the given dimensions L = 5 inches, W= 3 inches?

A. 13

B. 14

C. 15

D. 16

Question 250

If the lengths of the two parallel sides of a trapezium are 4 cm and 6 cm and its area is 25 cm². Find the distance between its parallel sides (in cm).

A. 2.5

B. 10

C. 5

D. 7.5

Question 251

The area of the triangle whose vertices are given by (2,4), (-3,-1) and (5,3) is

A. 10 sq.units

B. 14 sq.units

C. 20 sq.units

D. 7 sq.units

Question 252

An angle is smaller than its supplementary angle by 50°. What is the measure of the angle?

A. 115°

B. 60°

C. 30°

D. 65°

Question 253

The area of a triangle is 216 cm2 and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is :

A. 6 cm

B. 12 cm

C. 36 cm

D. 72 cm

Question 254

The length of one side of a rhombus is 13 cm and one of the diagonals is 10 cm. What is the legth of the other diagonal?

A. 24 cm

B. 23 cm

C. 25 cm

D. 22 cm

Question 255

In ΔXYZ measure of angle Y is 90°. If cosecX = 17/15, and XY = 4cm, then what is the length (in cm) of side YZ?

A. 7.5

B. 8.5

C. 5

D. 6

Question 256

Area of a rectangle is 150 sq. metre. When the breadth of the same rectangle is increased by 2 metres and the length decreased by 5 metres the area of the rectangle decreases by 30 square metres. What is the perimeter of the square whose sides are equal to the length of the rectangle ?

A. 76 m

B. 72 m

C. 120 m

D. 60 m

Question 257

If a regular polygon has 6 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

A. 90°

B. 100°

C. 60°

D. 108°

Question 258

The different between the length and breadth of a rectangle is 6 m. If its perimeter is 64 m, then its area is:

A. 256 sq.m

B. 247 sq.m

C. 264 sq.m

D. 238 sq.m

Question 259

PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees)of POR?

A. 30

B. 45

C. 60

D. 90

Question 260

If the area of the trapezium whose parallel sides are 6 cm and 10 cm is 32 sq. cm, then the distance between the parallel sides is :

A. 2 cm

B. 4 cm

C. 5 cm

D. 8 cm

Question 261

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?

A. 44ft

B. 88ft

C. 22ft

D. 11ft

Question 262

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A. 15360

B. 153600

C. 30720

D. 307200

Question 263

A cylindrical vessel of height 5 cm and radius 4 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 6 cm. What will be the height of this cone? (Take π = 22/7)

A. 6.67 cm

B. 2.22 cm

C. 3.33 cm

D. 1.67 cm

Question 264

The number of sides of a regular polygon whose exterior angles are each 40 deg is

A. 7

B. 10

C. 9

D. 8

Question 265

If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the area of the square ?

A. 441 sq.m

B. 784 sq.m

C. 1225 sq.m

D. Cannot be determined

Question 266

A rectangular farm has to be fenced on one long side, one short side and the diagonal. If the cost of fencing is Rs. 100 per m, the area of the farm is 1200 m2 and the short side is 30 m long, how much would the job cost ?

A. Rs. 7000

B. Rs. 12000

C. Rs. 14000

D. Rs. 15000

Question 267

The length, breadth and height of the room are in the ratio 3 : 2 : 1. The breadth and height of the room are halved and length of the room is doubled. The area of the four walls of the room will :

A. decrease by 13.64%

B. decrease by 15%

C. decrease by 18.75%

D. decrease by 30%

Question 268

What must be the length (in cm) of the diagonal of a rectangle if its area and breadth are 60 cm² and 5 cm respectively?

A. 26

B. 8

C. 16

D. 13

Question 269

The magnitude of the area of a circle is seven times that of its circumference. What is the circumference (in units) of the circle ?

A. 88 units

B. 132 units

C. 616 units

D. Cannot be determined

Question 270

ABCDEF is a regular hexagon of side 12 cm. What is the area (in cm2) of the triangle ECD?

A. 18√3

B. 24√3

C. 36√3

D. 42√3

Question 271

Two small circular parks of diameters 16 m and 12 m are to be replaced by a Bigger circular park. What would be the radius of this new park. If the new park has to occupy the same space as the two small parks ?

A. 10 m

B. 15 m

C. 20 m

D. 25 m

Question 272

If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the largest angle.

A. 36 deg

B. 96 deg

C. 84 deg

D. 60 deg

Question 273

A ladder 20 m long is leaning against a vertical wall. It makes an angle of 30 deg with the ground. How high on the wall does the ladder reach?

A. 10 m

B. 17.32 m

C. 34.64 m

D. 3 m

Question 274

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A. 136

B. 236

C. 336

D. 436

Question 275

The base of a triangle is one-third of the base of a parallelogram having the same area as that of the triangle. The ratio of the corresponding heights of thr triangle to the parallelogram will be

A. 3:2

B. 4:1

C. 3:1

D. 6:1

Question 276

Find the perimeter of the rectangle or square with the given dimensions s = 3 cm

A. 12

B. 13

C. 14

D. 15

Question 277

What will be the area of 4 metres high wall on all four sides of a rectangular hall having perimeter 64 m ?

A. 256 m2

B. 328 m2

C. 384 m2

D. Cannot be determined

Question 278

Slope of the side DA of the rectangle ABCD is 5/3. What is the slope of the side AB?

A. 3/5

B. -5/3

C. 5/3

D. -3/5

Question 279

What is the area of the given rectangle? I. Perimeter of the rectangle is 60 cm. II. Breadth of the rectangle is 12 cm. III. Sum of two adjacent sides is 30 cm.

A. I only

B. II only

C. I and II only

D. II and either I or III

Question 280

An angle is smaller than its supplementary angle by 70°. What is the measure of the angle?

A. 125°

B. 55°

C. 80°

D. 10°

Question 281

The area of a circle is 616 sq cm, find its circumference?

A. 44 cm

B. 88 cm

C. 22 cm

D. 176 cm

Question 282

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A. 15360 m2

B. 153600 m2

C. 30720 m2

D. 307200 m2

Question 283

In a trapezium ABCD, AB and DC are parallel sides and ∠ ADC = 90°. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm. Then the area of the trapezium ABCD is

A. 245 cm2

B. 240 cm2

C. 247.5 cm2

D. 250 cm2

Question 284

If an angle of a triangle remains unchanged but each of its two including sides is doubled, then by what factor does the area get multiplied ?

A. 2

B. 3

C. 4

D. 6

Question 285

What is the area (in sq cm) of an equilateral triangle of side 14 cm?

A. 49√3

B. 98√3

C. (49/2)√3

D. (49/4)√3

Question 286

The length of each side of a rhombus is 25 m and the length of one of its diagonals is 14 m. Find the area of the rhombus?

A. 336 sq. m

B. 175 sq. m

C. 350 sq. m

D. 168 sq. m

Question 287

Δ DEF is right angled at E. If m∠D = 30°, what is the length of DE (in cm), if EF = 6√3 cm?

A. 18

B. 12√3

C. 18√3

D. 12

Question 288

The areas of a circle and square are equal. What is the square of the ratio of length of diameter to the length of diagonal?

A. 11/7

B. 7/9

C. 7/11

D. 9/7

Question 289

A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be

A. 7744

B. 8844

C. 5544

D. 4444

Question 290

The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle :

A. 30.6 cm2

B. 39 cm2

C. 42.4 cm2

D. 65.3 cm2

Question 291

The diameter of a circle is 3.5 cm. What is the circumference of the circle ?

A. 11 cm

B. 22 cm

C. 38.5 cm

D. 45.2 cm

Question 292

A right-angled triangle ABC is right-angled at B, and tan A = 4/3. If AC = 25 cm, the length of BC is

A. 33.3 cm

B. 24 cm

C. 20 cm

D. 18.75 cm

Question 293

The diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 64π sq cm?

A. 128 sq cm

B. 196 sq cm

C. 108 sq cm

D. 256 sq cm

Question 294

What is the reflection of the point (5, 3) in the line y = -2?

A. (-9 , 3)

B. (-5 , -7)

C. (-9 , -3)

D. (5 , -7)

Question 295

The length of the diagonal and the breadth of a rectangle is 26 cm and 10 cm respectively. Calculate its area (in cm2).

A. 480

B. 96

C. 240

D. 192

Question 296

What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?

A. 814

B. 714

C. 614

D. 713

Question 297

The ratio between the area of a square and that of a circle, when the length of a side of the square is equal to that of the diameter of the circle, is (take π=22/7)

A. 14 : 11

B. 28 : 11

C. 7 : 22

D. 22 : 7

Question 298

Of the two square fields, the area of one is 1 hectare while the other one is broader by 1%. The difference in their areas is :

A. 100 m2

B. 101 m2

C. 200 m2

D. 201 m2

Question 299

The number of sides of a regular polygon whose exterior angles are each 60 deg is

A. 7

B. 5

C. 6

D. 8

Question 300

A circular pond has area equal to 616 m2. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present ?

A. 454 sq. m

B. 462 sq. m

C. 532 sq. m

D. 564 sq. m

Question 301

If the radius of a circle is increased by 25%, its area increases by:

A. 50 percent

B. 25 percent

C. 28.125 percent

D. 56.25 percent

Question 302

The area of the shaded portion is :

A. 10 sq. cm

B. 14 sq. cm

C. 21 sq. cm

D. 25 sq. cm

Question 303

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

A. 10%

B. 10.08%

C. 20%

D. 28%

Question 304

The area of a rectangle is 448 sq.m. If the length is more than the breadth by 12%, find the breadth.

A. 14 m

B. 16 m

C. 18 m

D. 20 m

Question 305

If ABCDEF is a regular hexagon, then what is the value (in degrees) of ∠ADB?

A. 15

B. 30

C. 45

D. 60

Question 306

ABC is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the sides of the triangle, then the locus of the centre of the circle is an equilateral triangle of side is

A. 5 cm

B. (6 - 2√3) cm

C. 4 cm

D. (3 + √3) cm

Question 307

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A. 40m

B. 50m

C. 120m

D. None of the above

Question 308

Find the radius of the circle if the area of its sector is 30.8 sq cm whose corresponding central angle is 72°?

A. 3.5 cm

B. 7 cm

C. 14 cm

D. 10.5 cm

Question 309

If a cylinder of radius 4.3 cm and height 4.8 cm is melted and constructed into a cone of the same radius, what will be the height of this cone? (Use π = 22/7)

A. 28.8 cm

B. 14.4 cm

C. 7.2 cm

D. 21.6 cm

Question 310

ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8 cm. AD is perpendicular to BC. What is the area (in cm2) of triangle ABD?

A. 12

B. 6

C. 10

D. 20

Question 311

The circumference of a circle is 88 cm. Find its radius (in cm).

A. 28

B. 15

C. 14

D. 30

Question 312

The area of a rectangle is 42 sq.cm and its length is 7 cm. Find its perimeter.

A. 14 cm

B. 21 cm

C. 26 cm

D. 24 cm

Question 313

An octahedron has 6 vertices. How many edges does it have?

A. 8

B. 12

C. 6

D. 10

Question 314

The diameter of a circle is 28 cm find its area?

A. 616 sq cm

B. 308 sq cm

C. 154 sq cm

D. 77 sq cm

Question 315

A rectangular carpet has an area of 120 m2 and a perimeter of 46 metres. The length of its diagonal is :

A. 23 metres

B. 13 metres

C. 17 metres

D. 21 metres

Question 316

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A. 40

B. 20

C. 30

D. none of these

Question 317

Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be

A. 0.13 m

B. 0.4 m

C. 0.3 m

D. 0.41 m

Question 318

ΔPQR is right angled at Q. QS is the altitude. PQ is 2√13 cm and PS is 8 cm. What is the length of SR?

A. 6√13 cm

B. 4√13 cm

C. 18 cm

D. 9 cm

Question 319

The length of the diagonal of a square is 14 cm. What is area of this square?

A. 49 sq cm

B. 196 sq cm

C. 98 sq cm

D. 77 sq cm

Question 320

Area of a square natural lake is 50 sq. kms. A driver wishing to cross the lake diagonally, will have to swim a distance of :

A. 10 miles

B. 12 miles

C. 15 miles

D. None of these

Question 321

The radius of the circle is 14 cm, an arc is subtend an angle 54 degree at center. Find the length of the arc (in cm).

A. 12.8

B. 13.2

C. 13.8

D. 14.2

Question 322

A slice from a circular pizza of diameter 14 inches is cut in asuch a way that each slice of pizza has a central angle of 45°. What is the area of each slice of Pizza(in square inches)?

A. 16.25

B. 19.25

C. 18.25

D. 17.25

Question 323

x, y be two acute angles, x + y < 90° and sin(2x - 20°) = cos(2y + 20°), the value of tan(x + y) is

A. √3

B. 1/√3

C. 1

D. 2+√2

Question 324

In a triangle PQR, ∠PQR = 90 deg, PQ = 10 cm and PR = 26 cm, then what is the value (in cm) of inradius of incircle?

A. 9

B. 4

C. 8

D. 6

Question 325

In order to reach his office on time, Mr. Roy goes through the middle passage of a round fort which he takes 14 minutes to pass through. However, on a certain day, due to repairs, the straight road being blocked, he had to take the roundabout way as a result of which he reached his office late. How late was he ?

A. 6 min

B. 8 min

C. 12 min

D. 7$$\frac{1}{2}$$ min

Question 326

There are 4 semi-circular gardens on each side of a square-shaped pond with each side 21 m. The cost of fencing the entire plot at the rate of Rs. 12.50 per metre is :

A. Rs. 1560

B. Rs. 1650

C. Rs. 3120

D. Rs. 3300

Question 327

What is the area (in cm2) of the circumcircle of a triangle whose sides are 6 cm, 8 cm and 10 cm respectively?

A. 275/7

B. 550/7

C. 2200/7

D. 1100/7

Question 328

A rectangular swimming pool of length 30 m and breadth 15 m has a uniformly sloping floor. It is 1 m in depth on one end of its length and 2 m at the other. How much water is needed to completely fill this pool?

A. 1350 cubic mts

B. 2025 cubic mts

C. 675 cubic mts

D. 2700 cubic mts

Question 329

The length of one side of a rhombus is 61 cm and its area is 1320 sq.cm. Find the sum of the lengths of its diagonals?

A. 120 cm

B. 122 cm

C. 142 cm

D. 71 cm

Question 330

The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m

A. 53800

B. 43800

C. 83800

D. 73800

Question 331

Point P is the midpoint of segment AB. Co-ordinates of P are (3 , 1) and B are (5, -4). What are the co-ordinates of point A?

A. (-1 , 7)

B. (1 , -7)

C. (1 , 6)

D. (-1 , -7)

Question 332

In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area, calculate from the those measurements.

A. .7%

B. 0.8%

C. 0.9%

D. 0.3%

Question 333

What is the area of the hall? I. Material cost of flooring per square metre is Rs. 2.50 II. Labour cost of flooring the hall is Rs. 3500 III. Total cost of flooring the hall is Rs. 14,500.

A. I and II only

B. II and III only

C. All I, II and III

D. Any two of the three

Question 334

In a Kite _____.

A. One diagonal bisects the other

B. Both diagonals form two congruent triangles

C. Adjacent angles are supplementary

D. Opposite sides are parallel

Question 335

A rectangular playground of length 125 m and width 75 m, has a walking strip of width 3 m in the middle of the ground, along the longer side. What is the area of the ground without the walking strip?

A. 9375 sq.m

B. 9000 sq.m

C. 9750 sq.m

D. 8625 sq.m

Question 336

Chord AB of a circle when extended meets the tangent to the circle at point P. PT is the tangent touching the circle at point T. If lengths of PT and PB are 6 cm and 4 cm respectively, what is the length of PA?

A. 12 cm

B. 11 cm

C. 10 cm

D. 9 cm

Question 337

The area of a triangle whose sides are of lengths 3 cm, 4 cm and 5 cm is :

A. 8 cm2

B. 6 cm2

C. 10 cm2

D. None of these

Question 338

The dimensions of a rectangle are 51 m and 49 m respectively while side of a square is 50 m. Which of the following statements is correct ?

A. Diagonal of the square and the rectangle are equal.

B. Diagonal of both the geometrical figures intersect at right angles.

C. The perimeters of both the geometrical figure are equal.

D. Both the geometrical figures are of the same area.

Question 339

Find the area of the trapezium, whose parallel sides are 12 cm and 10 cm, and distance between the parallel sides is 14 cm?

A. 121 sq.com

B. 154 sq.com

C. 186 sq.com

D. 164 sq.com

Question 340

Perimeter of a rectangular field is 160 metres and the difference between its two adjacent sides is 48 metres. The side of a square field, having the same area as that of the rectangle, is :

A. 4 metres

B. 8 metres

C. 16 metres

D. 32 metres

Question 341

What is the height of the triangle? I. The area of the triangle is 20 times its base. II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.

A. I alone sufficient while II alone not sufficient to answer

B. Either I or II alone sufficient to answer

C. Both I and II are not sufficient to answer

D. Both I and II are necessary to answer

Question 342

If each side of a square is increased by 10%, its area will be increased by :

A. 10%

B. 21%

C. 44%

D. 100%

Question 343

The area of a triangle with vertices A (0, 8) , O (0,0) and B (5, 0) is:

A. 8 sq. units

B. 13 sq. units

C. 20 sq. units

D. 40 sq. units

Question 344

What is the length of the side of a regular hexagon, if its area is 54√3 sq cm?

A. 12 cm

B. 9 cm

C. 6 cm

D. 15 cm

Question 345

All sides are congruent in a _____.

A. Rectangle

B. Parallelogram

C. Rhombus

D. Kite

Question 346

The angles of a triangle are in the ratio 1 : 1 : 4. If the perimeter of the triangle is k times its largest side, then what is the value of k?

A. 1 + 2/√3

B. 1 - 2/√3

C. 2 + 2/√3

D. 2

Question 347

ABCD is square and CDE is an equilateral triangle outside the square. What is the value (in degrees) of ∠BEC?

A. 15

B. 30

C. 25

D. 10

Question 348

If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is :

A. 1

B. 1.5

C. 2

D. 3

Question 349

How many square units in 13 by 9?

A. 13

B. 9

C. 117

D. 13/9

Question 350

In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 100% respectively, then its perimeter increases by

A. 40/3%

B. 20%

C. 25%

D. 27%

Question 351

If the two sides of obtuse angled triangle are 8 cm and 15 cm and the third side is x then,

A. 7 < x < 23

B. 7 < x < √161

C. 17 < x < 21

D. Cannot be determined

Question 352

The perimeters of a square and an equilateral triangle are equal. If the diagonal of the square is 9 cm, what is the area of the equilateral triangle?

A. 18√3 sq cm

B. 9√3 sq cm

C. 18√2 sq cm

D. 9√2 sq cm

Question 353

A piece of wire 132 cm long is bent successively in the shape of an equilateral triangle, a square and a circle. Then area will be longest in shape of

A. Circle

B. Equilateral triangle

C. Square

D. Equal in all the shapes

Question 354

The area and the length of one of the diagonals of a rhombus is 84 cm² and 7 cm respectively. Find the length of its other diagonal (in cm).

A. 12

B. 24

C. 48

D. 36

Question 355

The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the square is

A. 108 units

B. 36 units

C. 216 units

D. 288 units

Question 356

What is the area (in sq cm) of a rhombus if the lengths of its diagonals are 25 cm and 20 cm?

A. 500

B. 250

C. 125

D. 200

Question 357

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A. 25% increase

B. 50% increase

C. 50% decrease

D. 75% decrease

Question 358

The order of rotational symmetry of a trapezium is

A. 2

B. 0

C. 1

D. 3

Question 359

A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor.

A. 136

B. 146

C. 166

D. 176

Question 360

Triangle PQR is inscribed in the circle whose radius is 14 cm. If PQ is the diameter of the circle and PR = 10 cm, then what is the area of the triangle PQR?

A. 196

B. 30√19

C. 40√17

D. 35√21

Question 361

The measures of the four angles of a quadrilateral are in the ratio 1:2:3:4. What is the measure of the biggest angle?

A. 36°

B. 144°

C. 72°

D. 108°

Question 362

For triangle ABC, find equation of median AD if co-ordinates of A, B and C are (-1,-3), (5,-4) and (3,2) respectively?

A. 2x - 5y = 17

B. 2x - 5y = 13

C. 2x + 5y = 13

D. 2x + 5y = 17

Question 363

An equilateral triangle of side 6 cm is inscribed in a circle. Then radius of the circle is

A. 2√3 cm

B. 3√2 cm

C. 4√3 cm

D. √3 cm

Question 364

ΔGHI is similar to ΔKLM. If the ratio of Perimeter of Δ GHI : Perimeter of ΔKLM = 1:4, and length of GH is 2 cm, what is the length of the corresponding side KL?

A. 4 cm

B. 8 cm

C. 32 cm

D. 16 cm

Question 365

The area of the four walls of a room is 120 m2 and the length is twice the breadth. If the height of the room is 4 m, then the area of the floor is :

A. 48 m2

B. 49 m2

C. 50 m2

D. 52 m2

Question 366

Find the perimeter of the rectangle or square with the given dimensions l = 5 feet, w = 2 feet?

A. 11ft

B. 13ft

C. 14ft

D. 15ft

Question 367

If 1/4th of the wall is painted blue, 1/2 is painted yellow and remaining 3 m is painted white, what is the length of the wall?

A. 10

B. 8

C. 16

D. 12

Question 368

A semicircular shaped window has diameter of 63cm. Its perimeter equals

A. 162

B. 132

C. 142

D. 172

Question 369

The base of a parallelogram is twice its height. If the area of the parallelogram is 338 sq.cm. Find its height?

A. 13 cm

B. 14 cm

C. 16 cm

D. 12 cm

Question 370

The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.

A. 4:25

B. 3:25

C. 3:15

D. 5:25

Question 371

A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in its central part and grass has been grown in rest of the field. The area (in sq. metres) under the grass is :

A. 295 m2

B. 299 m2

C. 300 m2

D. 375 m2

Question 372

The area of a grassy plot is 480 sq. m. If each side had been 5 m longer, the area would have been increased by 245 sq. m. Find the length of the fence to surround it.

A. 87 m

B. 88 m

C. 90 m

D. None of these

Question 373

The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.

A. 2808

B. 3808

C. 4808

D. 5808

Question 374

A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?

A. 4

B. 6

C. 8

D. None of the above

Question 375

The circumference of a circle, whose area is 24.64 sq.m

A. 14.64

B. 16.36

C. 17.6

D. 18.4

Question 376

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

A. 814

B. 820

C. 840

D. 844

Question 377

The two equal sides of an isosceles triangle is 20 cm each and the third side is 30 cm. What is the area(in cm2) of the triangle?

A. 50√5

B. 100

C. 75√7

D. 175

Question 378

A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm × 20 cm, the number of tiles required to cover the path is :

A. 200

B. 1800

C. 2000

D. 2150

Question 379

The diameter of a circle is equal to the perimeter of a square whose area is 3136 cm2 . What is the circumference of the circle ?

A. 352 cm

B. 704 cm

C. 39424 cm

D. 1024 cm

Question 380

What is the minimum number of identical square tiles required to tile a floor of length 6 m 24 cm and width 4 m 80 cm ?

A. 122

B. 130

C. 148

D. 165

Question 381

The length of a rectangular blackboard is 8 m more than its breadth. If its length is increased by 7 m and its breadth is decreased by 4 m, its area remains unchanged. The length and breadth of the rectangular blackboard is :

A. 24 m, 16 m

B. 20 m, 24 m

C. 28 m, 16 m

D. 28 m, 20 m

Question 382

One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?

A. 110

B. 120

C. 130

D. 140

Question 383

The ratios of areas of two squares, one having its diagonal double than the other is

A. 2:1

B. 2:3

C. 3:1

D. 4:1

Question 384

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A. 16 cm

B. 18 cm

C. 24 cm

D. Data inadequate

Question 385

The area of an equilateral triangle is 9√3 sq cm, find height of the triangle?

A. 6 cm

B. 6√3 cm

C. 3√3 cm

D. 9 cm

Question 386

The height of the equilateral triangle is 9 cm. What is the radius (in cm) of the circle circumscribing the three vertices?

A. 3

B. 6

C. 9

D. 12

Question 387

What is the ratio of radius of incircle and circumcircle for an equilateral triangle with an area of 22√3 sq. units?

A. 1/2

B. 1/4

C. 1/3

D. 2/3

Question 388

In Δ ABC, the median AD is 8 cm and CB is 16 cm, measure of angle CAB is_____ .

A. 90°

B. 30°

C. 60°

D. 120°

Question 389

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is

A. Rs. 258

B. Rs. 358

C. Rs. 458

D. Rs. 558

Question 390

The area of a right angled triangle ABC, right angled at B, is 46 sq units. A median is drawn from A to BC which intersects at D. Find the area (in sq. units)of triangle ABD.

A. 12

B. 23

C. 46

D. 88

Question 391

Area of 4 walls of a cuboid is 448 sq cm, its length is 18 cm and height is 8 cm. What is its breadth (in cm)?

A. 10

B. 9

C. 8

D. 7

Question 392

A rectangular parking space is marked out by painting three of its sides.If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?

A. 126sq.ft

B. 120sq.ft

C. 130sq.ft

D. 135sq.ft

Question 393

Three medians AD, BE and CF of ΔABC intersect at G; Area of ΔABC is 36 sq cm. Then the area of ΔCGE is

A. 12 sq cm

B. 6 sq cm

C. 9 sq cm

D. 18 sq cm

Question 394

The perimeter of a rectangle whose length is 6 m more than its breadth is 84 m. What will be the area of the rectangle?

A. 333 sq.mts

B. 330 sq.mts

C. 362 sq.mts

D. 432 sq.mts

Question 395

A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be :

A. 3520 cm2

B. 6400 cm2

C. 7744 cm2

D. 8800 cm2

Question 396

The length of a rectangle is 10 cm more than the breadth. Find the diagonal length of rectangle if perimeter is 44 cm ?

A. 12.50 cm

B. 14.21 cm

C. 15.98 cm

D. 17.08 cm

Question 397

The following squares represent the monthly income of two families If the monthly income of family A is Rs. 40000, the monthly income of family B is ?

A. Rs. 50000

B. Rs. 60000

C. Rs. 90000

D. Rs. 120000

Question 398

What is the length of the side of an equilateral triangle, if its area is 64√3 sq cm?

A. 8 cm

B. 16 cm

C. 16√3 cm

D. 8√3 cm

Question 399

The radii of two concentric circles are 68 cm and 22 cm. The area of the closed figure bounded by the boundaries of the circles is

A. 4140π sq.cm.

B. 4110π sq.cm.

C. 4080π sq.cm.

D. 4050π sq.cm.

Question 400

What will be the cost of painting the inner walls of a room if the rate of painting is Rs. 20 per square foot? I. Circumference of the floor is 44 feet. II. The height of the wall of the room is 12 feet.

A. I alone sufficient while II alone not sufficient to answer

B. Either I or II alone sufficient to answer

C. Both I and II are not sufficient to answer

D. Both I and II are necessary to answer

Question 401

If two complimentary angles are in the ratio of 11 : 7, find the smaller angle.

A. 35 deg

B. 55 deg

C. 45 deg

D. 25 deg

Question 402

What is the area (in sq cm) of a rectangle of perimeter 90 cm and breadth 20 cm?

A. 500

B. 400

C. 250

D. 450

Question 403

AB and AC are the two tangents to a circle whose radius is 6 cm. If ∠BAC = 60 deg, then what is the value (in cm) of √(AB2 + AC2)?

A. 6√6

B. 4√6

C. 9√3

D. 8√3

Question 404

What is the slope of the line parallel to the line passing through the points (4,-2) and (-3,5)?

A. 3/7

B. 1

C. -3/7

D. -1

Question 405

A plate on square base made of brass is of length x cm and width 1 mm. The plate weights 4725 gm. If 1 cubic cm cm of brass weight 8.4 grams, then the value of x is :

A. 75

B. 76

C. 72

D. 74

Question 406

The height of an equilateral triangle is 18 cm. Its area is

A. 36√3 sq. m.

B. 108√3 sq. cm.

C. 108 sq. cm.

D. 96√3 sq. m.

Question 407

If each side of a square is increased by 25%, find the percentage change in its area.

A. 56.25%

B. 36.25%

C. 16.25%

D. 12.25%

Question 408

If the perimeter of a semi-circle is 108 cm, then find its radius (in cm).

A. 42

B. 28

C. 56

D. 21

Question 409

A well of diameter 3 m and depth 14 m is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of embankment?

A. 7/8 m

B. 9/8 m

C. 3/8 m

D. 1/8 m

Question 410

Find the curved surface area (in cm²) of a hemisphere of diameter 28 cm

A. 1152

B. 1024

C. 956

D. 1232

Question 411

One angle of a triangle is 55 deg. If the other two angles are in the ratio 9:16, find the angles?

A. 65 and 115

B. 90 and 160

C. 55 and 165

D. 45 and 80

Question 412

The breadth of a rectangular field is 75% of its length. If perimeter of the field is 1050 m, what will be th area of field ?

A. 65700 sq.m

B. 54500 sq.m

C. 78700 sq.m

D. 67500 sq.m

Question 413

What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?

A. 13 m

B. 14 m

C. 15 m

D. 16 m

Question 414

What is the length of the side of an equilateral triangle, if its area is 36√3 sq cm?

A. 6 cm

B. 24 cm

C. 12 cm

D. 18 cm

Question 415

The rectangle having 10 cm and 6 cm as its dimensions was reconstructed to make a rhombus having the same perimeter as that of the rectangle and 60 deg as one of its angles. The area of the rhombus, in sq.cm was

A. 24√3

B. 8√3

C. 16√3

D. 32√3

Question 416

The diagonals of two squares are in the ratio of 2:5. Find the ratio of their areas.

A. 2:25

B. 3:25

C. 4:25

D. 6:25

Question 417

The length and breadth of a rectangle is in the ratio of 3 : 1. If its perimeter is 96 m, then what is the length of the rectangle?

A. 36m

B. 24m

C. 12m

D. 48m

Question 418

In Δ ABC, the median AD is 7 cm and CB is 14 cm, measure of ∠CAB is

A. 30°

B. 60°

C. 90°

D. 120°

Question 419

If the radius of a circle is decreased to 25% of its original value, calculate the percentage decrease in the area of the circle

A. 25%

B. 43.75%

C. 50%

D. 93.75%

Question 420

What is the area of a right-angled triangle? I. The perimeter of the triangle is 30 cm. II. The ratio between the base and the height of the triangle is 5 : 12. III. The area of the triangle is equal to the area of a rectangle of length 10 cm.

A. I and II only

B. II and III only

C. All I, II and III

D. Any two of the three

Question 421

The perimeter of a rectangular field is 480 metres and the ratio between the length and the breadth is 5 : 3. The area is :

A. 1350 sq. m

B. 1550 sq. m

C. 13500 sq. m

D. 15500 sq. m

Question 422

The perimeter of a rectangle is 60 metres. If its length is twice its breadth, then its area is :

A. 160 m2

B. 180 m2

C. 200 m2

D. 220 m2

Question 423

The diagonal of a rectangle is root(41) cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

A. 9 cm

B. 18 cm

C. 20 cm

D. 41 cm

Question 424

The difference between circumference and semidiameter of a circle is 37 cm. What is the diameter of the circle ?

A. 18 cm

B. 12 cm

C. 16 cm

D. 14 cm

Question 425

Let O be the orthocentre of the triangle ABC. If ∠BOC = 150°, Then ∠BAC is

A. 30°

B. 60°

C. 90°

D. 120°

Question 426

The length of a rope in meter by which a cow must be tethered in order that she may be able to graze an area of 2826 sq.m is ?

A. 15 mts

B. 30 mts

C. 24 mts

D. 36 mts

Question 427

The perimeter of a triangle is 28 cm. If the length is 5/2 times its breadth, find the length and breadth of the triangle.

A. 9 & 5

B. 10 & 4

C. 6 & 7

D. 11 & 3

Question 428

Area of 4 walls of a cuboid 400 sq cm, its length is 15 cm and height is 8 cm. What is its breadth (in cm)?

A. 12

B. 20

C. 24

D. 10

Question 429

There is a circular garden of radius 21 metres. A path of width 3.5 metres is constructed just outside the garden. What is the area (in metres2) of the path?

A. 50.05

B. 57.56

C. 52.12

D. none

Question 430

The point of intersection of all the three medians of a triangle is called its

A. orthocentre

B. incentre

C. centroid

D. circumcentre

Question 431

The area of a square is three-fifths the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square ?

A. 44 cm

B. 60 cm

C. 80 cm

D. Cannot be determined

Question 432

In ∆ABC, AB = 12 cm. ∠A is bisected internally to intersect BC at D. BD = 7 cm and DC = 8.75 cm. What is the length of CA?

A. 13.5 cm

B. 15 cm

C. 12.5 cm

D. 14.5 cm

Question 433

A room 5m 55cm long and 3m 74cm broad is to be paved with square tiles.Find the least number of square tiles required to cover the floor?

A. 156

B. 166

C. 176

D. 186

Question 434

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

A. 18

B. 28

C. 38

D. 48

Question 435

The least number that must be subtracted from 1294 so that the remainder when divided by 9, 11, 13 will leave in each case the same remainder 6 is:

A. 2

B. 3

C. 1

D. 4

Question 436

If a rope 84m long is divided in the ratio 7:5, then the length of the longer piece (in m) is

A. 50

B. 45

C. 42

D. 49

Question 437

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle (in cm) is

A. 15

B. 16

C. 17

D. 34

Question 438

What is the measure of an exterior angle of a regular polygon of 10 sides?

A. 30

B. 24

C. 36

D. 20

Question 439

A rectangular garden (60 m × 40 m) is surrounded by a road of width 2 m, the road is covered by tiles and the garden is fenced. If the total expenditure is Rs. 51600 and rate of fencing is Rs. 50 per metre, then the cost of covering 1 sq. m of road by tiles is :

A. Rs. 10

B. Rs. 50

C. Rs. 100

D. Rs. 150

Question 440

The area of a square is 100 sq cm, find length of its diagonal?

A. 10√2 cm

B. 10 cm

C. 20 cm

D. 20√2 cm

Question 441

The circumferences of two circle are 132 metres and 176 metres respectively. What is the difference between the area of the larger circle and the smaller circle ?

A. 1048 m2

B. 1076 m2

C. 1078 m2

D. 1090 m2

Question 442

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 ΔABC is 98 cm sq, what is the area (in sq cm) of quadrilateral BDEC?

A. 90

B. 98

C. 94

D. 86

Question 443

One side of a rectangle is 12 m and its diagonal is 13 m. Find its area.

A. 60 sq.m

B. 55 sq.m

C. 50 sq.m

D. 45 sq.m

Question 444

The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 800 per square metre.

A. Rs. 15000

B. Rs. 15500

C. Rs. 15600

D. Rs. 16500

Question 445

The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre.

A. Rs.15500

B. Rs.16500

C. Rs.17500

D. Rs.18500

Question 446

How many kilometers are there in one metre?

A. 0.01

B. 0.0001

C. 0.001

D. 0.1

Question 447

A small ring of negligible thickness and radius 2 cm moves on a bigger rung of radius 10 cm. How many rotations will the small ring take on the bigger ring to make a complete round ?

A. 5

B. 6

C. 7

D. 10

Question 448

Area of the circle inscribed in a square of diagonal 6√2 cm (in sq cm) is

A. 9 Π

B. 6 Π

C. 3 Π

D. 9√2 Π

Question 449

The wheel of a motorcycle 70cm in diameter makes 40 revolutions in every 10sec.What is the speed of motorcycle n km/hr?

A. 13.68kmph

B. 31.68kmph

C. 41.68kmph

D. 45.68kmph

Question 450

A cow s tethered in the middle of a field with a 14feet long rope.If the cow grazes 100 sq feet per day, then approximately what time will be taken by the cow to graze the whole field?

A. 616

B. 716

C. 816

D. 516

Question 451

What is the area of rectangular field? I. The perimeter of the field is 110 metres. II. The length is 5 metres more than the width. III. The ratio between length and width is 6 : 5 respectively.

A. I and II only

B. II and III only

C. All I, II and III

D. Any two of the three

Question 452

The length of the diagonal of a rectangle is 26 cm and that of one side is 10 cm. What is the area of this rectangle?

A. 260 sq cm

B. 120 sq cm

C. 130 sq cm

D. 240 sq cm

Question 453

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square ? (rounded off to two decimal places)

A. 23.57 cm

B. 38.57 cm

C. 42.46 cm

D. 47.47 cm

Question 454

The circumference of a circle is 110 cm. Find its radius (in cm).

A. 35

B. 19.5

C. 17.5

D. 39

Question 455

The length of a mirror arc is 2/9 of the circumference of the circle. Write the measure of the angle (in degrees) subtended by the arc at the centre of the circle.

A. 60

B. 50

C. 80

D. 30

Question 456

Find the volume (in cm3) of a right circular cylinder of diameter 21 cm and height 10 cm.

A. 3118

B. 3275

C. 3621

D. 3465

Question 457

Cost of fencing a circular plot at the rate of Rs. 15 per metre is Rs. 3300. What will be the cost of flooring the plot at the rate of Rs. 100 per square metre ?

A. Rs. 220000

B. Rs. 350000

C. Rs. 385000

D. Cannot be determined

Question 458

Find the length of the altitude of an equilateral triangle of side 33cm.

A. 4.5

B. 3.5

C. 2.5

D. 6.5

Question 459

A rectangular grassy plot 110m by 65cm has a gravel path .5cm wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq.mt

A. 680rs

B. 480rs

C. 340rs

D. 320rs

Question 460

Find the ratio of the areas of the incircle and circumcircle of a square.

A. 1:1

B. 1:2

C. 1:3

D. 1:4

Question 461

If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.

A. 110

B. 120

C. 130

D. 140

Question 462

The ratio between the length and breadth of a rectangular field is 5 : 4 if the breadth is 20m less than the length, the perimeter of the field is :

A. 260m

B. 280m

C. 360m

D. none of these

Question 463

The length of the radius of the circumference of a triangle having sides 9 cm, 12 cm and 15 cm is

A. 6 cm

B. 7.5 cm

C. 4.5 cm

D. 8 cm

Question 464

Diagonals of a Trapezium ABCD with AB || CD intersect each other at the point O. If AB = 2CD, then the ratio of the areas of ΔAOB and ΔCOD is

A. 4:1

B. 1:16

C. 1:4

D. 16:1

Question 465

If the ratio of two squares is 225:256,then the ratio of the perimeters is

A. 25:16

B. 15:16

C. 16:15

D. 17:16

Question 466

2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plots is 96 sq.m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction?

A. 20

B. 30

C. 40

D. data is inadequate

Question 467

The diagonals of 2 squares M and N are in the ratio 2:1. The ratio of their areas is

A. 1:2

B. 2:1

C. 1:4

D. 4:1

Question 468

A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq.ft per day, they approximately what time will be taken by the cow to graze the whole field ?

A. 2 days

B. 6 days

C. 18 days

D. 24 days

Question 469

A big rectangular plot of area 4320 m2 is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot ?

A. 160 m × 27 m

B. 240 m × 18 m

C. 120 m × 36 m

D. 135 m × 32 m

Question 470

In an old Palace there are 50 stairs to go on top floor. Each is 20 cm high, 30 cm wide and 60 cm long. If all the stairs are re-plastered at the rate of Rs. 4 per 100 sq.cm. What is the expenditure ?

A. Rs. 4680

B. Rs. 7600

C. Rs. 6000

D. Rs. 5480

Question 471

Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is

A. 12

B. 32

C. 42

D. 52

Question 472

A room 5m × 8 m is to be carpeted leaving a margin of 10 cm from each wall. If the cost of the carpet is Rs. 18 per sq. meter, the cost of carpeting the room will be :

A. Rs. 673.92

B. Rs. 682.46

C. Rs. 691.80

D. Rs. 702.60

Question 473

A solid sphere of radius 3 cm is melted to form a hollow right circular cylindrical tube of length 4 cm and external radius 5 cm. The thickness of the tube is

A. 1 cm

B. 9 cm

C. 0.6 cm

D. 1.5 cm

Question 474

The area of the circle is 220 sq.m, the area of the square inscribed in a circle will be

A. 49

B. 70

C. 140

D. 150

Question 475

The ratio of length and breadth of a rectangle is 3 : 2 respectively. The respective ratio of its perimeter and area is 5 : 9. What is the breadth of the rectangle in metres ?

A. 6 m

B. 8 m

C. 9 m

D. 13 m

Question 476

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 110 deg then the angle POA is

A. 50 deg

B. 70 deg

C. 35 deg

D. 45 deg

Question 477

The area of a square is 49 mm. What is the length of each side?

A. 5mm

B. 6mm

C. 7mm

D. 8mm

Question 478

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is :

A. 1520 m2

B. 2420 m2

C. 2480 m2

D. 2520 m2

Question 479

What is the area (in sq cm) of a circle whose circumference is 26.4 cm?

A. 55.44

B. 44.55

C. 33.44

D. 44.33

Question 480

What is the angle between centripetal acceleration and tangential acceleration?

A. 90°

B. 45°

C. 0°

D. 180°

Question 481

A piece of wire when bent to from a circle will have a radius of 84 cm. If the wire is bent to form a square, the length of a side of the square is :

A. 216 cm

B. 133 cm

C. 132 cm

D. 168 cm

Question 482

The perimeter of a square is 40 meters. Find the length of one side of the square

A. 10m

B. 20m

C. 30m

D. 40m

Question 483

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 1:4 and area of ΔADE is 6 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

A. 1:12

B. 1:6

C. 1:16

D. 1:24

Question 484

A triangle has a perimeter of 200. If two of its sides are equal and the third side is 20 more than the equal sides, what is the length of the third side?

A. 60

B. 50

C. 80

D. 70

Question 485

If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be :

A. 1% increase

B. 1% decrease

C. 10% increase

D. No change

Question 486

ΔABC is similar to ΔPQR. Length of AB is 36 cm and length of the corresponding side PQ is 16 cm. If area of ΔABC is 1296 sq cm, what is the area of ΔPQR?

A. 128 sq cm

B. 512 sq cm

C. 64 sq cm

D. 256 sq cm

Question 487

In triangle PQR, C is the centroid. PQ = 30 cm, QR = 36 cm and PR = 50 cm. If D is the midpoint of QR, then what is the length (in cm) of CD?

A. (4√86)/3

B. (2√86)/3

C. (5√86)/3

D. (5√86)/2

Question 488

The area of a square with perimeter 48 cm, is :

A. 144 sq. cm

B. 156 sq. cm

C. 170 sq. cm

D. 175 sq. cm

Question 489

The circumferences of the front and rear wheels of a bicycle are 3.5 m and 3 m respectively. If the vehicle is moving at a speed of 15 m/sec, the shortest time in which both the wheels will make a whole number of turns is :

A. 1.4 seconds

B. 2.1 seconds

C. 4 seconds

D. 6.4 seconds

Question 490

A solid copper sphere of radius 9 cm is melted and reformed into a wire of radius 1 mm. What will be the length of this wire? (Take π = 22/7)

A. 1166.4 metres

B. 1458 metres

C. 777.6 metres

D. 972 metres

Question 491

A coaching institute wants to execute tiling work for one of its teaching halls 60 m long and 40 m wide with a square tile of 0.4 m side. If each tile costs Rs. 5, the total cost of tiles would be :

A. Rs. 60000

B. Rs. 65000

C. Rs. 70000

D. Rs. 75000

Question 492

If each side of a rectangle is increased by 50%, its area will increase by :

A. 50%

B. 125%

C. 150%

D. 200%

Question 493

What is the measure of central angle of the arc whose length is 11 cm and radius of the circle is 14 cm?

A. 45°

B. 60°

C. 75°

D. 90°

Question 494

Two concentric circles form a ring. The inner and outer circumference of the ring are 352/7 m and 528/7m respectively.Find the width of the ring.

A. 5

B. 4

C. 3

D. 2

Question 495

In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is

A. 2√2 cm

B. 3√2 cm

C. 2√3 cm

D. 3√3 cm

Question 496

In a circle with centre O, AB is the diameter and CD is a chord such that ABCD is a trapezium. If angle BAC = 40 deg , then angle CAD is equal to

A. 15 deg

B. 20 deg

C. 50 deg

D. 10 deg

Question 497

The length of the two parallel sides of a trapezium are 16 m and 20 m respectively. If its height is 10 m, its area in square metres is

A. 360

B. 260

C. 240

D. 180

Question 498

A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make the larger one makes 15 revolutions ?

A. 18

B. 20

C. 25

D. 30

Question 499

The areas of two similar triangles ΔXYZ and ΔPQR are 100 sq cms and 25 sq cms respectively. If PQ = 4 cm then what is the length of XY (in cm)?

A. 16

B. 14

C. 8

D. 20

Question 500

ΔPQR is right angled at Q. QS is the altitude. PQ is 4√29 cm and PS is 8 cm. Find length of SR?

A. 10√29 cm

B. 8√29 cm

C. 50 cm

D. 20 cm

Question 501

The lengths of the two diagonals of a rhombus are 8 cm and 15 cm respectively. Find its area (in cm²).

A. 30

B. 120

C. 90

D. 60

Question 502

In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is

A. 2√13 cm

B. 5√3 cm

C. 4√6 cm

D. 6√5 cm

Question 503

The area of a trapezium is 21 sq cm, the distance between the parallel sides is 3 cm and one of the parallel sides is 8.3 cm. What is the length of the other parallel side?

A. 12.7 cm

B. 7.7 cm

C. 10.7 cm

D. 5.7 cm

Question 504

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

A. 1.04

B. 2.04

C. 3.04

D. 4.04

Question 505

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

A. 20

B. 30

C. 40

D. 50

Question 506

In which of the following quadrilaterals both pairs of opposite sides are parallel?

A. Rhombus

B. Cyclic quadrilateral

C. Kite

D. Isosceles trapezium

Question 507

If a parallelogram with area p, a triangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then

A. P=R

B. P=A

C. P=A/2

D. P=2R

Question 508

If the length and breadth of a rectangular field are increased, the area increases by 50%. If the increase in length was 20 %, by what percentage was the breadth increased ?

A. 20%

B. 25%

C. 30%

D. Data inadequate

Question 509

In a triangle the length of the side opposite the right angle is 9√3 cm, what is the length of the side opposite to the angle which measures 30 degree?

A. 9 cm

B. 3√3 cm

C. 6 cm

D. (9√3)/2 cm

Question 510

Which of the following triangle has the maximum area when inscribed inside the circle of same radius?

A. Scalene

B. Isosceles

C. Equilateral

D. Right angled

Question 511

A path of 2.5 m width surrounds a rectangular garden of length 10 m and breadth 8 m. Area of the garden, inclusive of the path is

A. 130.25 sq.m

B. 131.25 sq.m

C. 195.00 sq.m

D. 162.50 sq.m

Question 512

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

A. 22

B. 44

C. 66

D. 88

Question 513

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8cm and breadth 7cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?

A. 55.12 cm

B. 22.54 cm

C. 42.51 cm

D. 38.57 cm

Question 514

PQRS is a square whose side is 20 cm. By joining opposite vertices of PQRS are get four triangles. What is the sum of the perimeters of the four triangles?

A. 40√2

B. 80√2 + 80

C. 40√2 + 40

D. 40√2 + 80

Question 515

The circumferences of two circles are touching externally. The distance between their centres is 12 cm. The radius of one circle is 7 cm. Find the diameter(in cm) of the other circle.

A. 12

B. 10

C. 8

D. 5

Question 516

In ΔABC, the angle bisector of ∠A cuts BC at E. Find the length of AC if lengths of AB, BE and EC are 9.6 cm, 4 cm and 3 cm?

A. 4.8 cm

B. 9.8 cm

C. 7.8 cm

D. 7.2 cm

Question 517

Two identical hemispheres of maximum possible size are cut from a solid cube of side 14 cm. The bases of the hemispheres are part of the two opposite faces of cube. What is the total volume (in cm3) of the remaining part of the cube?

A. 1556.33

B. 898.5

C. 1467.33

D. 1306.67

Question 518

A steel rod of length 20 3/26 is cut out from a rod of length 56 1/5. What then is the remaining length of the rod?

A. 36 3/130

B. 36 7/130

C. 36 1/130

D. 36 11/130

Question 519

The order of rotational symmetry of a rectangle is

A. 1

B. 4

C. 2

D. 0

Question 520

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A. 2520

B. 2420

C. 2320

D. 2620

Question 521

The order of rotational symmetry of a parallelogram is

A. 1

B. 4

C. 2

D. 0

Question 522

The area of a circle is increased by 22 sq. cm if its radius is increased by 1 cm. The original radius of the circle is :

A. 3 cm

B. 3.2 cm

C. 3.5 cm

D. 6 cm

Question 523

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar ?

A. 720

B. 600

C. 660

D. 6000

Question 524

If the radius of a circumscribed circle in an equilateral triangle is 14 cm. Then what will be the radius (in cm) of the inscribed circle?

A. 7

B. 14

C. 28

D. 35

Question 525

The area of an equilateral triangle is 9√3 sq cm, find its perimeter?

A. 18 cm

B. 9 cm

C. 9√3 cm

D. 6√3 cm

Question 526

Triangle ABC ~ Triangle EDF and ar(ABC) : ar(DEF) = 4 : 9. If AB = 6 cm, BC = 8 cm and AC = 10 cm, then DF is equal to:

A. 9 cm

B. 12 cm

C. 15 cm

D. 18 cm

Question 527

An angle is 30 deg more than one half of its complement. Find difference between the greater and the smaller angles.

A. 10 deg

B. 20 deg

C. 30 deg

D. 25 deg

Question 528

If the circumference of a circle is 44 cm, then what must be its area (in cm²)?

A. 308

B. 240

C. 154

D. 480

Question 529

What is the equation of the line whose y-intercept is -3 and makes an angle of 45° with the positive x-axis?

A. x - y = -3

B. x + y = 3

C. x - y = 3

D. x + y = -3

Question 530

The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?

A. 150

B. 250

C. 350

D. 550

Question 531

ΔABC is right angled at B. BD is the altitude. AD is 18 cm and DC is 50 cm. Find length of BD?

A. 30 cm

B. 25 cm

C. 35 cm

D. 15 cm

Question 532

A quadrilateral is inscribed in a circle. If the opposite angles of the quadrilateral are equal and length of its adjacent sides are 6 cm and 8 cm, what is the area of the circle?

A. 64π sq cm

B. 25π sq cm

C. 36π sq cm

D. 49π sq cm

Question 533

The base of a parallelogram is twice its height. If the area is 392 sq.m. What is its height?

A. 14 m

B. 28 m

C. 12 m

D. 24 m

Question 534

Two circles touch each other at point X. A common tangent touch them at two distinct points Y and Z. If another tangent passing through X cut YZ at A and XA= 16 cm, then what is the value (in cm) of YZ?

A. 18

B. 24

C. 16

D. 32

Question 535

A triangle with sides 13 cm, 14 cm and 15 cm is inscribed in a circle. The radius of the circle is :

A. 2 cm

B. 3 cm

C. 4 cm

D. 8.125 cm

Question 536

When 472 pieces of plywood, each 0.23 cm thick, are piled on top of each other, what would be the height of the pile in meter?

A. 108.56

B. 1.0856

C. 1.856

D. 10.856

Question 537

The length of the diagonal and the breadth of a rectangle are 17 cm and 8 cm respectively. Find its perimeter (in cm).

A. 92

B. 46

C. 42

D. 84

Question 538

If the ratio of area of rectangle to its perimeter is 60:11. And length and breadth are in the ratio 6 : 5. Find length of rectangle.

A. 40 units

B. 30 units

C. 13 units

D. 24 units

Question 539

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A. 20%

B. 30%

C. 40%

D. 50%

Question 540

Find measure of central angle of the arc whose length is 22 cm and radius of the circle is 28 cm?

A. 60°

B. 45°

C. 75°

D. 90°

Question 541

The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle.

A. 24

B. 48

C. 60

D. 72

Question 542

The area of a triangle is equal to the area of a square whose each side is 60 metres. The height of the triangle is 90 metres. The base of the triangle will be :

A. 65 m

B. 75 m

C. 80 m

D. 85 m

Question 543

Three circle of radius 3.5 cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is :

A. 1.967 cm2

B. 1.975 cm2

C. 19.67 cm2

D. 21.21 cm2

Question 544

One of the diagonals of a rhombus is double the other diagonal. Its area is 25 sq. cm. The sum of the diagonal is ?

A. 10 cm

B. 12 cm

C. 15 cm

D. 16 cm

Question 545

The base of a triangle of 15cm and height is 12cm. The height of another triangle of double the area having the base 20cm is

A. 16

B. 17

C. 18

D. 20

Question 546

The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?

A. 47500

B. 37500

C. 57500

D. 77500

Question 547

The radius of a circle is 20% more than the height of a right-angled triangle. The base of the triangle is 36 cm. If the area of triangle and circle be equal, what will be area of circle ?

A. 72 cm2

B. 128 cm2

C. 144 cm2

D. 216 cm2

Question 548

The four walls and ceiling of a room of length 25 m, breadth 12 m and height 10 m are to be painted. Painter A can paint 200 m2 in 5 days, Painter B can paint 250 m2 in 2 days. If A and B work together, they will finish the job in

A. 6 days

B. 6 10/33 days

C. 7 10/33 days

D. 8 days

Question 549

The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved, then by what percent the total area of the 4 walls of the room will be increased ?

A. 90%

B. 88%

C. 85%

D. 84%

Question 550

A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is?

A. 50

B. 60

C. 70

D. 80

Question 551

The total cost of flooring a room at Rs. 8.50 per square metre is Rs. 510. If the length of the room is 8 m, its breadth is :

A. 7.5 m

B. 8.5 m

C. 10.5 m

D. 12.5 m

Question 552

If two circles touch each other internally. The greater circle has its radius as 6 cm and the distance between the centres of the circles is 2 cm. The radius of the other circle is

A. 3 cm

B. 4 cm

C. 2 cm

D. 5 cm

Question 553

The area of a circle whose radius is the diagonal of a square whose area is 4 sq. units is :

A. 16π sq. units

B. 4π sq. units

C. 6π sq. units

D. 8π sq. units

Question 554

What is the measure of the central angle of the sector whose area is 462 sq cm and radius of the circle is 21 cm?

A. 90°

B. 60°

C. 30°

D. 120°

Question 555

A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?

A. 315

B. 385

C. 415

D. 485

Question 556

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A. 1520 m2

B. 2420 m2

C. 2480 m2

D. 2520 m2

Question 557

Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.

A. 30

B. 40

C. 50

D. 60

Question 558

Point A divides segment BC in the ratio 1:3. Co-ordinates of B are (4,-4) and C are (0,6). What are the co-ordinates of point A?

A. (-3, 1.5)

B. (-1.5, 3)

C. (3, -1.5)

D. (1.5, 3)

Question 559

The length of the diagonal and the breadth of a rectangle are 26 cm and 10 cm respectively. Find its perimeter (in cm).

A. 68

B. 136

C. 43

D. 86

Question 560

The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq.cm. Find its height?

A. 3 cm

B. 4 cm

C. 6 cm

D. 8 cm

Question 561

What is the area (in sq cm) of a rectangle if its diagonal is 25 cm and one of its sides is 24 cm?

A. 186

B. 144

C. 132

D. 168

Question 562

A rectangular playground ground of length 125 m and width 75 m, has a walking strip of width 3 m in the middle of the ground, along the longer side. What is the area of the ground without the walking strip?

A. 9375 sq.m

B. 9000 sq.m

C. 9750 sq.m

D. 8625 sq.m

Question 563

The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is

A. 49

B. 154

C. 378

D. 1078

Question 564

A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π

B. 3π

C. 5π

D. 4π

Question 565

The area of a circular cricket ground is 24.64 hectares. Find the cost of making rope boundary at the rate of Rs. 5.40 per metre.

A. Rs. 9,600

B. Rs. 9,504

C. Rs. 9,802

D. Rs. 9,876

Question 566

A cone of radius 3.5 cm and height 27 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 2.1 cm. What will be the height of water in this vessel? (Take π = 22/7)

A. 50 cm

B. 25 cm

C. 12.5 cm

D. 37.5 cm

Question 567

The area of a circle is 346.5 cm². Find its radius (in cm).

A. 10.5

B. 21

C. 7.5

D. 15

Question 568

A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :

A. 5 m

B. 12 m

C. 13 m

D. 14.5 m

Question 569

The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square in cm2 is

A. 20

B. 10

C. 4√5

D. 10√2

Question 570

What is the area of the square, if the length of its diagonal is 13√2 units?

A. 104 sq.units

B. 169 sq.units

C. 338 sq.units

D. 676 sq.units

Question 571

If the length of the side of an equilateral triangle is 8 cm, what is its area?

A. 32√3 sq cm

B. 16 sq cm

C. 16√3 sq cm

D. 32 sq cm

Question 572

An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?

A. Rs. 4082.40

B. Rs. 1024.21

C. Rs. 2810.6

D. Rs. 3214

Question 573

The point at which the perpendicular bisectors of the sides of a triangle intersect is known as _____________________

A. circum-centre

B. orthocenter

C. centroid

D. in-center

Question 574

What is the area (in sq cm) of a rectangle if its diagonal is 51 cm and one of its sides is 24 cm?

A. 540

B. 810

C. 1080

D. 360

Question 575

What will be the cost of levelling a circular ground of diameter 28 m, if charges are Rs. 125 per sq.m?

A. Rs. 76000

B. Rs. 76400

C. Rs. 76800

D. Rs. 77000

Question 576

The length of a room is double its breadth. The cost of colouring the ceiling at Rs. 25 per sq. meter is Rs. 5000 and the cost of painting the four walls at Rs. 240 per sq. metre is Rs. 64800. Find the height of the room :

A. 3.5 m

B. 4 m

C. 4.5 m

D. 5 m

Question 577

Area of _____ equals square of its side.

A. Rhombus

B. Cyclic quadrilateral

C. Rectangle

D. Square

Question 578

What is the area (in sq cm) of a regular hexagon of side 6 cm?

A. 27√3

B. 54√3

C. 54

D. 27

Question 579

The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field?

A. 20 m

B. 30 m

C. 40 m

D. 50 m

Question 580

The area of a rectangle is 252 cm2 and its length and breadth are in the ratio of 9 : 7 respectively. What is its perimeter ?

A. 64 cm

B. 68 cm

C. 96 cm

D. 128 cm

Question 581

The lengths of diagonals of a rhombus are 24cm and 10cm the perimeter of the rhombus (in cm ) is :

A. 52

B. 56

C. 68

D. 72

Question 582

A solid right circular cone of radius 4 cm and height 7 cm is put inside a cylindrical vessel of radius 5 cm and height 8 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A. 1022.48 cubic cms

B. 1533.72 cubic cms

C. 511.24 cubic cms

D. 255.62 cubic cms

Question 583

The lengths of the diagonals of a rhombus are 8 cm and 6 cm. The area of rhombus is:

A. 96 cm2

B. 60 cm2

C. 48 cm2

D. 24 cm2

Question 584

If the perimeter of a semi-circle is 36 cm, then find its radius (in cm).

A. 7

B. 14

C. 13

D. 26

Question 585

ABCD is a kite where m∠A is 90° and m∠C is 60°. If length of AB is 6 cm, what is the length of diagonal AC?

A. 6(√2+√3) cm

B. 2(√3+√6) cm

C. 2(√2+√3) cm

D. 3(√2+√6) cm

Question 586

The perimeters of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

A. 12

B. 24

C. 36

D. 48

Question 587

A square and rectangle have equal areas. If their perimeters are p and q respectively. Then

A. p

B. p>q

C. p=q

D. none of these

Question 588

The length of the diagonal of a square is 12 cm. Find its area (in cm2).

A. 36

B. 72

C. 144

D. 48

Question 589

The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is :

A. 29.46 km/hr

B. 31.68 km/hr

C. 32.72 km/hr

D. 36.25 km/hr

Question 590

From a square plate with each side 7 cm, squares of area 0.25 sq. cm are cut out at each corner and the remaining plate is folded along the cuts to form a cuboid. The volume of this open-top cuboid will be ......... . cub.cm

A. 21

B. 16

C. 18

D. 20

Question 591

A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?

A. 65m

B. 45m

C. 55m

D. 56m

Question 592

The perimeter of an isosceles triangle is 32 cm and each of the equal sides is 5/6 times of the base. What is the area (in cm2 ) of the triangle ?

A. 39

B. 48

C. 57

D. 64

Question 593

Area of _____ equals half the product of its diagonal.

A. Parallelogram

B. Rectangle

C. Kite

D. Cyclic quadrilateral

Question 594

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

A. 34

B. 40

C. 68

D. 88

Question 595

Point P is the midpoint of segment AB. Co-ordinates of point P are (2,1) and point A are (11,5). Co-ordinates of point B are

A. (-7,-3)

B. (6.5,3)

C. (7,3)

D. (-6.5,-3)

Question 596

A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of the room leaving 1.5 feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per squire feet?

A. 378

B. 472.5

C. 496

D. 630

Question 597

The perimeter and the breadth of a rectangle are 60 cm and 14 cm respectively. Find its area (in cm²)

A. 112

B. 448

C. 224

D. 336

Question 598

A diagonal of a rhombus is 6 cm. If its area is 24 cm2 then the length of each side of the rhombus is :

A. 5 cm

B. 6 cm

C. 7 cm

D. 8 cm

Question 599

One of the internal angle of a rhombus is 60° and length of its shorter diagonal is 8 cm. What is the area of the rhombus?

A. 64√3 sq cm

B. 32√2 sq cm

C. 64√2 sq cm

D. 32√3 sq cm

Question 600

If the sum of the measures of all the interior angles of polygon is 2340°. What is the number of sides of the polygon?

A. 13

B. 15

C. 17

D. 11

Question 601

The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 104 cm. The length of the longest side (in cm) is

A. 52

B. 48

C. 32

D. 26

Question 602

If the area of a circle is 9π sq.cm then its circumference is

A. 9 cm

B. 6π cm

C. 3π cm

D. 6 cm

Question 603

A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is

A. rs.58

B. rs.158

C. rs.258

D. rs.358

Question 604

A tent is to be built in the form of a cylinder of radius 10 m surmounted by a cone of the same radius. If the height of the cylindrical part is 5 m and slant height of the conical part is 15 m, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. (Take π = 22/7)

A. 4714.43 sq m

B. 3772.14 sq m

C. 6783.86 sq m

D. 2451.42 sq m

Question 605

The length of a class room floor exceeds its breadth by 25 m. The area of the floor remains unchanged when the length is decreased by 10 m but the breadth is increased by 8 m. The area of the floor is

A. 5100 sq.m

B. 4870 sq.m

C. 4987 sq.m

D. 4442 sq.m

Question 606

The slopes of two lines are 1/√3 and √3. What is the angle between these two lines?

A. 15°

B. 45°

C. 60°

D. 30°

Question 607

An artist has completed one-fourth of a rectangular oil painting. When he paint another 100 square centimetres of the painting, he would complete three-quarters of the painting. If the height of the oil painting is 10 cm, determine the length (in cm) of the oil panting.

A. 10 cm

B. 15 cm

C. 20 cm

D. 25 cm

Question 608

The length of a rectangle is 12 cm. What is the width if the area is 72 cm ?

A. 6cm

B. 5cm

C. 3cm

D. 4cm

Question 609

The circumference of a circular ground is 88 metres. A strip of land, 3 metres wide, inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling costs Rs. 7 per square metre ?

A. Rs. 1050

B. Rs. 1125

C. Rs. 1325

D. Rs. 1650

Question 610

If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area ?

A. No change

B. 8% decrease

C. 16% increase

D. 16% decrease

Question 611

From the four corners of a rectangular sheet of dimensions 25 cm x 20 cm, square of side 2 cm is cut off from four corners and a box is made. The volume of the box is

A. 828 cm3

B. 672 cm3

C. 500 cm3

D. 1000 cm3

Question 612

A horse is tied at the corner of a rectangular field whose length is 20 m and width is 16 m, with a rope whose length is 14 m. Find the area which the horse can graze :

A. 144 sq. m

B. 154 sq. m

C. 156 sq. m

D. 164 sq. m

Question 613

The cost of leveling a triangular piece of land whose sides are 72 m. 30 m and 78 in respectively at the rate of 20 paisa per square metre is:

A. ₹ 220

B. ₹ 200

C. ₹ 216

D. ₹ 210

Question 614

A sector of 120 degrees, cut out from a circle, has an area of 66/7 sq cm. Find the radius of the circle.

A. 1cm

B. 2cm

C. 3cm

D. 4cm

Question 615

Δ LMN is right angled at M. If m∠N = 45°, what is the length of MN (in cm), if NL = 9√2 cm?

A. 9√2

B. 9/√2

C. 18

D. 9

Question 616

The diagonal of a square is 12 cm what is the length (in cm) of its side?

A. 6√2

B. 12√2

C. 6

D. 9

Question 617

If the perimeters of a square and a rectangle are the same, then the area a & b enclosed by them would satisfy the condition:

A. a

B. a>b

C. a=b

D. none

Question 618

If each side of a square is increased by 25%, find the percentage change in its area?

A. 65.25

B. 56.25

C. 65

D. 56

Question 619

What is the measure of an interior angle of a regular polygon of 10 sides?

A. 150

B. 156

C. 144

D. 160

Question 620

In a rhombus _____.

A. Diagonals are equal and perpendicular

B. Consecutive angles are equal

C. Consecutive angles are supplementary

D. Adjacent sides are not equal

Question 621

The area of a rectangle is 120 sq cm and its perimeter 140 cm. What is the length of its diagonal?

A. 50 cm

B. 30 cm

C. 40 cm

D. 60 cm

Question 622

A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before, is :

A. 20 min

B. 25 min

C. 50 min

D. 100 min

Question 623

Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq meters.

A. 56m

B. 16m

C. 14m

D. 76m

Question 624

The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides.

A. 27 and 23

B. 24 and 23

C. 25 and 23

D. 22 and 23

Question 625

A line cuts two concentric circles. The lengths of chords formed by that line on the two circles are 4 cm and 16 cm. What is the difference (in cm2) in squares of radii of two circles?

A. 240

B. 120

C. 60

D. 90

Question 626

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?

A. 56m

B. 65m

C. 34m

D. 36m

Question 627

In a Rhombus ABCD, measure of angle CAB is 25°, what is the measure of angle ABC?

A. 65°

B. 50°

C. 40°

D. 130°

Question 628

Total area of 64 small squares of a chessboard is 400 sq. cm. There is 3 cm wide border around the chess board. What is the length of the side of the chess board ?

A. 17 cm

B. 20 cm

C. 23 cm

D. 26 cm

Question 629

A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?

A. 115

B. 117

C. 116

D. 114

Question 630

The area of a rectangle is equal to the area of right-angles triangle. What is the length of the rectangle? I. The base of the triangle is 40 cm. II. The height of the triangle is 50 cm.

B. Either I or II alone sufficient to answer

C. Both I and II are not sufficient to answer

D. Both I and II are necessary to answer

Question 631

The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter

A. Rs.16500

B. Rs.15500

C. Rs.17500

D. Rs.18500

Question 632

Find the perimeter (in cm) of a semicircle of radius 28 cm.

A. 288

B. 144

C. 121

D. 242

Question 633

ax + 5y = 8 has slope of -4/3. What is the value of a?

A. 20/3

B. 3/20

C. -20/3

D. -3/20

Question 634

Find the area of a square, one of whose diagonals is 3.8 m long

A. 7.22

B. 6.22

C. 4.22

D. 3.22

Question 635

The area of a rectangle field is 52000 m2 . This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is :

A. 150 m

B. 160 m

C. 200.5 m

D. 300.5 m

Question 636

A typist uses a sheet measuring 20cm by 30cm lengthwise.If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is

A. 64%

B. 74%

C. 84%

D. 94%

Question 637

A rectangular lawn of dimensions 80 m x 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m ?

A. Rs. 3600

B. Rs. 3800

C. Rs. 3900

D. Rs. 3700

Question 638

What is the reflection of the point (-0.5, 6) in the x-axis?

A. (0.5, -6)

B. (-6, -0.5)

C. (6, -0.5)

D. (-0.5, -6)

Question 639

Area of 4 walls of a cuboid is 57 sq m, if its length is 5.5 m and height is 3 m. What is its breadth (in m)?

A. 4.5

B. 4

C. 3

D. 3.5

Question 640

The length and the breadth of rectangular field are in the ratio of 8 : 7. If charges of the painting the boundary of rectangle is at Rs. 10 per meter is Rs. 3000. What is the area of rectangular plot?

A. 5600 sq.m

B. 1400 sq. m

C. 4400 sq.m

D. 3600 sq.m

Question 641

A boundary wall around a rectangular plot is constructed at a total cost of Rs. 46000 at the rate of Rs. 200 per metre. What is the area of the plot if the respective ratio between the breadth and the length of the plot is 10 : 13 ? (in sq. metre)

A. 3750 sq. m2

B. 3250 sq. m2

C. 3000 sq. m2

D. 3900 sq. m2

Question 642

An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?

A. 1:2

B. 1:3

C. 2:3

D. 3^(1/2) :2

Question 643

A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?

A. 5

B. 6

C. 8

D. 9

Question 644

What is the measure of the smaller of the two angles formed between the hour hand and the minute hand of a clock when it is 6:44 p.m?

A. 62.5 deg

B. 62 deg

C. 84 deg

D. 83.5 deg

Question 645

The ratio of the outer and the inner perimeters of a circular path is 23 : 22. If the path is 5 metres wide, the diameter of the inner circle is :

A. 55 m

B. 110 m

C. 220 m

D. 230 m

Question 646

If the length of the side of an equilateral triangle is 6 cm, what is its area?

A. 18√3 sq cm

B. 36√3 sq cm

C. 27√3 sq cm

D. 9√3 sq cm

Question 647

The area of a rectangle is 80 cm.If its length is 16 cm, what is its width?

A. 5cm

B. 10cm

C. 15cm

D. 20cm

Question 648

If the area of a square increase by 69%, then the side of the square increases by :

A. 13%

B. 30%

C. 39%

D. 69%

Question 649

In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is

A. 80°

B. 40°

C. 90°

D. 50°

Question 650

ΔABC is right angled at B. BD is an altitude. AD = 9 cm and DC = 16 cm. What is the value of BD (in cm)?

A. 6

B. 18

C. 21

D. 12

Question 651

The length of the diagonal of a square is 10 cm. What is area of this square?

A. 50 sq cm

B. 100 sq cm

C. 200 sq cm

D. 25 sq cm

Question 652

The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :

A. 35%

B. 42%

C. 62%

D. 82%

Question 653

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A. rs.458

B. rs,558

C. rs.658

D. rs.758

Question 654

The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.

A. 30

B. 40

C. 50

D. 60

Question 655

Two sides of a rectangle were measured. One of the sides (length) was measured 10% more than its actual length and the other side (width) was measured 5% less than its actual length. The percentage error in measure obtained for the area of the rectangle is :

A. 4.50%

B. 5%

C. 7.56%

D. 15%

Question 656

What is the measure of an interior angle of a regular decagon?

A. 120°

B. 140°

C. 144°

D. 150°

Question 657

An order was placed for supply of carpet of breadth 3 metres, the length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 percent respectively. At the rate of 45 per square metre, what would be the increase in the cost of the carpet ?

A. Rs. 398.80

B. Rs. 437.40

C. Rs. 583.20

D. Rs. 1020.60

Question 658

The edge of three cubes of metal is 3 m, 4 m and 5 m. They are melted and formed into a single cube. Find the edge of the new cube ?

A. 15 m

B. 4 m

C. 6 m

D. 9 m

Question 659

The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm what is the length of the side of the equilateral triangle?

A. 22/3 cm

B. 44/3 cm

C. 44 cm

D. 22 cm

Question 660

If the length of one side and the diagonal of a rectangle are 5 cm and 13 cm respectively, then find its perimeter (in cm).

A. 68

B. 34

C. 25

D. 50

Question 661

What is the slope of the line parallel to the line passing through the points (-2, -1) and (4, -3)?

A. 1/3

B. -1/3

C. -3

D. 3

Question 662

The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter is 32cm. Find the area of the triangle?

A. 50

B. 60

C. 70

D. 80

Question 663

A wheelchair slalom event, athletes weave around cones and race to the finish line. A diagram of the rectangular course 30m length &16m bredth is shown. Find the the area of the course

A. 480

B. 560

C. 180

D. 460

Question 664

A man walking at the speed of 4 kmph crosses a square field diagonally in 3 meters.The area of the field is

A. 10000

B. 20000

C. 30000

D. 40000

Question 665

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 2:3, and area of Δ APQ is 8 sq cm, what is the area of trapezium PQCB?

A. 50 sq cm

B. 18 sq cm

C. 42 sq cm

D. 14 sq cm

Question 666

If each of the two equal angles of an isosceles triangle is twice the third angle, the measure of the third angle is

A. 90 deg

B. 72 deg

C. 45 deg

D. 36 deg

Question 667

If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?

A. 108 sq.cm

B. 112 sq.cm

C. 116 sq.cm

D. 120 sq.cm

Question 668

The length of a string is 8 feet and 9 inches, which is divided into 3 equal parts. What is the length of each part in inches?

A. 31

B. 33

C. 35

D. 37

Question 669

The curved surface area and the slant height of a right circular cone are 99 sq.cm and 9 cm respectively. Find its diameter (in cm)

A. 3.5

B. 7

C. 14

D. 10.5

Question 670

The area of a circle is 616 cm². What is its circumference (in cm).

A. 176

B. 88

C. 70

D. 140

Question 671

What is the area (in sq cm) of a rhombus if the lengths of the diagonals are 12 cm and 14 cm?

A. 42

B. 168

C. 84

D. 63

Question 672

Let A(O,-1), B(0,3) and C(2,1) be three points. Let △1 be the area of the triangle ABC and △2 be the area of the triangle formed by the mid points of the sides of the triangle whose vertices are A, B and C such that △1=1 ,△2=x Find the value of x .

A. 4

B. 5

C. 2

D. 3

Question 673

The length of the rectangle is 20% more than its breadth . what will be the ratio of the area of the rectangle to that of the square whose side is equal to the breadth of the rectangle?

A. 2:1

B. 5:6

C. 6:5

D. data is inadequate

Question 674

In a triangle PQR, PX, QY and RZ be altitudes intersecting at O. If PO = 6 cm, PX = 8 cm and QO = 4 cm, then what is the value (in cm) of QY?

A. 6.3

B. 5.8

C. 6

D. 7

Question 675

The perimeter of a circular field and a square field are equal. If the area of the square field is 12100 m2, the area of the circular field will be :

A. 15200 m2

B. 15300 m2

C. 15400 m2

D. 15500 m2

Question 676

Find the greatest length which can be used to measure exactly three cloth pieces of lengths 1.26 m, 1.98 m and 1.62 m respectively.

A. 12 cm

B. 14 cm

C. 16 cm

D. 18 cm

Question 677

The areas of two similar triangles ΔABC and ΔPQR are 36 sq cms and 9 sq cms respectively. If PQ = 4 cm then what is the length of AB (in cm)?

A. 16

B. 12

C. 8

D. 6

Question 678

Find the ratio of the areas of the incircle and circumcircle of a square ?

A. 1 : 4

B. 4 : 1

C. 2 : 1

D. 1 : 2

Question 679

If the cost of 17 m of cloth is Rs. 77 5/7, find its cost per meter in Rs.?

A. 4 4/7

B. 7 5/7

C. 5 5/7

D. 4 5/7

Question 680

The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle

A. 44

B. 22

C. 33

D. 84

Question 681

The area of an equilateral triangle is 25√3 sq.cm. Find its side (in cm).

A. 10

B. 5

C. 20

D. 30