# Advanced Mathematics – Paper VI – WBCS Main Question Paper

Contents

###### WBCS Advanced Mathematics

## WBCS Main Question Paper – 2021

1. Solve:

(A) 1/3

(B) ± 1/3

(C) 3

(D) ± 3

13. Find the minimum value of 5 sinθ + 12 cosθ

(A) 0

(B) -1

(C) –√3

(D) -13

20. If the length of a rectangle is increased by 30% and width by 20%; its area will increased by

(A) 50%

(B) 25%

(C) 56%

(D) 60%

21. The number of coconuts plucked from each tree is more than the number of coconut trees in Anil’s garden. The total number of coconut plucked is 132. The total number of coconut trees in the garden is

(A) 12

(B) 22

(C) 11

(D) 33

24. The value of the product (a-u) (b-u) (c-u) ….. (z-u) is

(A) 25

(B) 26

(C) 0

(D) 1

29. If P = 99, then P(P² + 3P + 3) = ?

(A) 999

(B) 9999

(C) 99999

(D) 999999

31. In △ABC, D, E and F are respectively the mid-points of sides BC, CA and AB; if △ABC=16 sq cm, then the area of the trapezium FBCE is

(A) 40 sq cm

(B) 8 sq cm

(C) 12 sq cm

(D) 24 sq cm

35. If a + 1/b = 1 and b + 1/c = 1 then find the value of c + 1/a

(A) -I

(B) 1

(C) b

(D) -b

39. The area of a regular hexagon with side 10 cm. is

(A) 50 √3 cm²

(B) 150 √3 cm²

(C) 50 cm²

(D) 300 cm²

47. The sum of opposite angles of a cyclic quadrilateral is

(A) 90°

(B) 120°

(C) 150°

(D) 180°

48. The angle between the external bisectors of two angles of a triangle is 60°, then the third angle of the triangle is

(A) 40°

(B) 50°

(C) 60°

(D) 80°

50. The length of the sides of a triangle are 5 cm, 12 cm and 13 cm. Its area is

(A) 30 cm²

(B) 37.5 cm²

(C) 60 cm²

(D) 78 cm²

56. The roots of the equation

B

57. The length of the longest rod that can be put in a room of dimensions 10m x 10m x 5m is

(A) 15√3 m

(B) 15m

(C) 10√2 m

(D) 5√3m

63. If the median drawn on the base of a triangle is half its base, the triangle will be

(A) equilateral

(B) right-angled

(C) acute-angled

(D) obtuse-angled

70. A room is 26 feet long and 10 feet wide. If its floor is to be covered by square tiles, how many minimum number of tiles will be required?

(A) 50

(B) 60

(C) 65

(D) 55

72. State in which of the following quadrants the point (√5-3, √5−2) lies.

(A) first

(B) second

(C) third

(D) fourth

75. The volume of a solid hemisphere is numerically equal to its total surface area. Its radius is

(A) 4½ units

(B) 9 units

(C) 3 units

(D) 1½ units

77. The Length of radius of spherical gas balloon increases from 7cm to 21cm as air being pumped into it. The ratio of surface areas of the balloon in two cases is

(A) 9 : 1

(B) 49 : 21

(C) 1 : 9

(D) 7 : 441

78. If area of circular field is X sq unit, perimeter is Y unit and length of diameter is Z unit, then the value of X/YZ is

(A) 1/2

(B) 1/4

(C) 1

(D) 1/8

81. What is the ratio between a square circumscribing a circle and that of the one inscribed in the circle?

(A) 2:1

(B) √2:1

(C) 2:3

(D) √2:√3

86. If cosecθ + cotθ = √3, find the value of

(A) √3/2

(B) √3

(C) 1/√3

(D) 2/√3

88.

then the value of

(A) 0

(B) 1

(C) -1

(D) 2

96. If cotθ = x/y, then what is the value of

B

98. Find the angle of the elevation of the Sun when the length of shadow of a vertical pole is √3 times its height.

(A) 45°

(B) 60°

(C) 30°

(D) 22½°

101. The height of a tower is 4h meter and the height of the observer is h meter. He finds the top of the tower from a distance √3 h meter from the tower. Find the angle of elevation of the tower as seen by the observer.

(A) 60°

(B) 30°

(C) 45°

(D) 75°

103. If (a, b, c) * (d, e, f) = a × f + b × c + c/d, then (5, 7, 10) * (2, 3, 2) is

(A) 6

(B) 16

(C) 26

(D) 36

105. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is

(A) 12cm

(B) 13 cm

(C) 10 cm

(D) 11cm

109. A circular lawn has an area of 154 sq meter. A path of 7 meter width surrounds the lawn. What is the area of the lawn including the path? (in sq meter)

(A) 580

(B) 516

(C) 616

(D) 637

112. ABCD is a quadrilateral in which P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Then PQRS is

(A) trapezium

(B) parallelogram

(C) rectangle

(D) square

113.

(A) 1

(B) 2

(C) 4

(D) 16

118. Two angles of a triangle are 75° and 45°. What is the value of third angle in circular measure? (as per convention, we do not use the symbol of radian.)

(A) π/2

(B) π/3

(C) π/4

(D) π/5

122. then find the value of

C

129. A boy recorded the weight of some of his friends as 32kg, 30kg, 40kg, 65kg, 54kg, 38kg, 36kg, 45kg, 50kg, 52kg, 40kg. What is the median?

(A) 38kg

(B) 40kg

(C) 45kg

(D) 43.8kg

133. If x/2 + y/3 = 4 and 2/x + 3/y = 1 then what is x + y equal to?

(A) 11

(B) 10

(C) 9

(D) 8

134. The distance between the centers of two circles of radii 1 cm and 7 cm is 10 cm. The length of direct tangent (in cm) is

(A) 2

(B) 6

(C) 8

(D) 18

135. In a right-angled triangle XYZ, ∠Y = 90°, if XY=2 √6 and XZ-YZ=2, then sec X + tanY is

D

137. If each interior angle of a regular polygon is 144°, find the number of sides of the polygon is

(A) 10

(B) 20

(C) 24

(D) 36

140. In AABC, ZB = 90°, BC=7 cm, if AC-AB= 1cm, then the value of sine is

(A) 7/24

(B) 7/25

(C) 24/25

(D) 25/24

141.

then the value of K is

(A) 1/2 or 2

(B) –1 or 1/2

(C) -1/2 or 1

(D) 1/2 or -1

147. A hemisphere can with an internal radius of 9 cm is completely filled with water. Someone is requested to fill this water in a cylindrical bottle with a diameter of 3 cm and height of 4 cm. The number of bottles to be required to make the can empty is

(A) 54

(B) 128

(C) 36

(D) 256

150. If secθ=cosecΦ and 0°< (θ, Φ) < 90°, then the value of sin(θ + Φ) is

(A) 0

(B) 1/2

(C) 1/√ 2

(D) 1

156. If tanθ + secθ=4, then what is the value of cosθ ?

(A) 8/17

(B) 8/15

(C) 15/17

(D) 23/32

168. If the length of shadow on the ground of a post is 3-√3 times of its height, the angle of elevation of the Sun is

(A) 30°

(B) 45°

(C) 60°

(D) None of the above

170. If the edge of a cube is increased by 25% then percentage increase in its surface area is

(A) 25%

(B) 48-75%

(C) 50%

(D) 56.25%

177. The area of a triangle, the length of whose sides are 50m, 78m and 112m, is

(A) 1480m²

(B) 1600m²

(C) 1680m²

(D) 3360m²

181. If S=ut + 1/2ar² and u = 50, a = 9.8, t=2 the value of S is

(A) 119.6

(B) 109.8

(C) 69.6

(D) 139.2

183. If a = 999, b=998, c = 997, then the value of a³ + b³ + c³-3abc will be

(A) 8982

(B) 8980

(C) 8983

(D) 8985

186. If the surface areas of two spheres are in the ratio 4:9, then the ratio of their volumes will be

(A) 4:9

(B) 16:27

(C) 8:27

(D) 16:9

187. If sinθ: = 5/13, then what is the value of tanθ + secθ?

(A) 2.5

(B) 0.5

(C) 1.5

(D) 1.52

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

(A) 68

(B) 65

(C) 54

(D) 52

192. How many more words (not necessarily meaningful) can be formed using the letters of the word RYTHM taking all at a time?

(A) 24

(B) 25

(C) 119

(D) 120

195. The area of an equilateral triangle is 400√3 sq. m. Its perimeter is

(A) 120m

(B) 150m

(C) 90m

(D) 135m

196. is equal to

(A) 16.6

(B) 16

(C) 14

(D) 18.8

198. Three sets of books on Maths, Science and Social Studies have 240, 336, and 96 books in each set respectively. The books need to be stacked in such a way that all the books are stacked subject-wise and number of books in each stack is same. The total minimum number of stacks will then be.

(A) 14

(B) 48

(C) 22

(D) 21

## WBCS Main Question Paper – 2020

## WBCS Main Question Paper – 2018

2. If a square and a rectangle having the same perimeter and their areas are S and R respectively then

(A) S = R

(B) S > R

(C) S < R

(D) None of the above

3. A parallelogram, a rectangle and triangular region stands on same base and between same parallel and if their area are P, R and T respectively, then

(A) P = R = 2T

(B) P = R = T/2

(C) 2P = 2R = T

(D) P = R = T

6. Which of the following geometric figure has diagonals equal in length ?

(A) Parallelogram

(B) Rhombus

(C) Trapezium

(D) Rectangle

14. The measures of two angles of a triangle are 35°57’4″ and 39°2’56”, then circular value of third angle is

(A) 7π / 12

(B) π / 20

(C) 5π / 12

(D) π

15. If the length of shadow on the ground of a post is √3 times of its height, the angle of elevation of the Sun is

(A) 30°

(B) 45°

(C) 60°

(D) None of the above

16. If the numerical values of total surface area and volume of a cube are equal, then the length of its diagonal is

(A) 6√3

(B) 6

(C) 6√2

(D) 3√6

22. A hemisphere can with internal radius of 9 cm is completely filled with water. Someone is requested to fill this water in a cylindrical bottle with a diameter of 3 cm and height of 4 cm. The number of bottles to be required to make the can empty is

(A) 54

(B) 128

(C) 36

(D) 256

23. The Length of radius of spherical gas balloon increases from 7 cm to 21 cm as air being pumped into it. The ratio of surface areas of the balloon in two cases is

(A) 9 : 1

(B) 49 : 21

(C) 1 : 9

(D) 7 : 441

37. What is the volume of the cube (in cubic cm) whose diagonal measures 4√3 cm ?

(A) 8

(B) 16

(C) 27

(D) 64

52. If the length of radius of a right circular cylinder is doubled and height is halved, the lateral surface area will be

(A) equal

(B) double

(C) half

(D) 4 times

53. The length of a radius of a circle is 13 cm. and the length of a chord of the circle is 10 cm., the distance of the chord from the center of the circle is

(A) 12.5 cm.

(B) 12 cm.

(C) √69 cm.

(D) 24 cm.

54.

The diagonals PR and QS of the rhombus intersect each other at the point O. What is the value of ∠POS∠POS ?

(A) Insufficient information

(B) 90°

(C) Any angle

(D) 45°

55. If (0,0), (4, -3) and (x, y) are collinear then

(A) x = 8, y = – 6

(B) x = 8, y = 6

(C) x = 4, y = – 6

(D) x = – 8, y = 6

56.

In the above figure AD | | BC, AD = 10 cm, BC = 5cm, CD = 10 cm. The area of ABCD is

(A) 150 sq.cm

(B) 75 sq.cm

(C) 500 sq.cm

(D) 250 sq.cm

60. If area of circular field is X sq. unit, perimeter is Y unit and length of diameter is Z unit then the value of X/YZ is

(A) 1/2

(B) 1/4

(C) 1

(D) 1/8

63. A circular lawn has an area of 154 sq. meter. A path of 7 meter width surrounds the lawn. What is the area of the lawn including the path ? (in sq. meter)

(A) 580

(B) 516

(C) 616

(D) 637

70. The area of a circle is 2464 square meters. What will be its circumference ?

(A) 132 m

(B) 176 m

(C) 231 m

(D) 272 m

87. The poles of heights 6m and 11m stand vertically on a plane ground. If the distance between their feet is 12m, what is the distance between their tops ?

(A) 12.8m

(B) 13m

(C) 14m

(D) 15m

91. A circular copper wire of radius 7 cm is bent to form a rectangle. If breadth and length of the rectangle are in the ratio of 4 : 7 respectively, what is the breadth of the rectangle ? (in cm.)

(A) 8 cm.

(B) 14 cm.

(C) 10 cm.

(D) 12 cm.

96. A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88 m when it traces 72° at the centre, then the length of the rope is

(A) 35m

(B) 70m

(C) 17.5m

(D) 22m

45. A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic meter) is

(A) 3150

(B) 31500

(C) 6300

(D) 63000