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A cube whose edge is 14 cm long has on each of its faces a circle of 7 cm radius painted yellow. What is the total area of unpainted surface ? (Take π = 22/7)
CDS I 2024
126 square cm
189 square cm
252 square cm
315 square cm
In a quadrilateral ABCD, AB = 6 cm, BC = 18 cm, CD = 6 cm and DA = 10 cm. If the diagonal BD = x, then which one of the following is correct?
CDS I 2024
8 < x < 12
12 < x < 16
16 < x < 18
18 < x < 20
The length, breadth and height of a cuboid are increased by 10%, 20% and 50% respectively. What is the percentage increase in volume of the cuboid ?
CDS I 2024
100%
99%
98%
50%
A solid cube is cut into two cuboids of equal volume. What is the ratio of total surface area of the given cube to that of one of the cuboids ?
CDS I 2023
2 : 1
3 : 2
4 : 3
5 : 3
The length of a diagonal of a cuboid is 11 cm. 63. The surface area is 240 square cm. What is the sum of its length, breadth and height ?
CDS I 2023
16 cm
17 cm
18 cm
19 cm
How long will a man take to walk around the boundary of a square field of area 25 hectares at the rate of 5 km/hr ?
CDS I 2023
36 minutes
30 minutes
24 minutes
18 minutes
If the length of a rectangle is increased by 200/3 %, then by what percent should the width of the rectangle be decreased in order to maintain the same area ?
CDS I 2023
50%
45%
40%
30%
The volume of a cuboid is 3600 cubic cm. The areas of two adjacent faces are 225 square cm and 144 square cm. What is the area of the other adjacent face ?
CDS I 2023
400 square cm
360 square cm
320 square cm
300 square cm
The perimeter and the area of a right-angled triangle are 36 cm and 54 square cm respectively. What is the length of the hypotenuse ?
CDS I 2023
12 cm
14 cm
15 cm
16 cm
The length of a room is 21/16 times its breadth and breadth is 4/3 times its height. If H is the height of the room and L is the longest rod that can be placed in the room, then which one of the following is correct?
CDS II 2022
12L= 29H
9L= 25H
7L= 23H
5L= 13H
Two parallel sides of a trapezium are 29 cm and 21 cm. Non-parallel sides are equal and each is of length 8.5 cm. What is the area of the trapezium?
CDS II 2022
187.5 square cm
227.5 square cm
375 square cm
455 square cm
The area of a rhombus is 96 square cm and one of its diagonals is of length 12 cm. What is the perimeter of the rhombus ?
CDS II 2022
36 cm
40 cm
44 cm
48 cm
A square and a rectangle have same perimeter. They differ in areas by 1 square cm. The length of the rectangle exceeds its breadth by
CDS II 2022
1 cm
2 cm
3 cm
4 cm
Two rectangles are of same area equal to 480 square cm. They differ in lengths by 6 cm and breadths by 4 cm. What is the difference in their perimeters?
CDS II 2022
2 cm
4 cm
6 cm
10 cm
X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?
CDS II 2022
9 cm
9.5 cm
10 cm
10.5 cm
What is the time taken by a person to cover one round of a circular park of diameter 210 m if he walks at a speed of 6 km/hr? (Take π = 22/7)
CDS II 2022
6.6 minutes
5.5 minutes
4.4 minutes
3.3 minutes
A triangle has side lengths x cm, x + 31 cm and x + 26 cm. If its area is 126 square cm, then what is the value of x ?
CDS II 2022
18
17
16
15
A closed box is built of wood of uniform thickness. Its external dimensions are 12 cm, 10 cm and 8 cm. If the inner surface area is 376 square cm, then what is the thickness of the wood ?
CDS II 2022
0.5 cm
1 cm
1.5 cm
2 cm
A rectangular metal sheet is of length 24 cm and breadth 18 cm. From each of its corners a square of side x cm is cut off, and an open box is made of the remaining sheet. If the volume of the box is 640 cubic cm, then what is the value of x ?
CDS II 2022
2
3
4
6
The perimeter of a rhombus is 52 m and its shorter diagonal is 10 m. The length of the longer diagonal is
67th BPSC
12 m
18 m
24 m
None of the above
Which of the following statements is false?
68th BPSC
Every square is a rectangle
Every rhombus is a parallelogram
Every square is a rhombus
None of the above
A rectangle has an area 30 cm square, and perimeter is 26 cm. Its side (in cm) are
68th BPSC
10, 3
5, 6
2, 15
None of the above
If the radii of circles A and B are in the ratio 1.5: 1, then the areas of the circles A and B will be in the ratio
65th BPSC
1.5 : 1
2.5 : 1
2.25 :1
None of the above
If x^2 – y^2 = 7 and x – y = 1, then the length of a diagonal of a rectangle with length and width respectively x cm and y cm will be
65th BPSC
5 cm
6 cm
7 cm
None of the above
The length of the longest pole that can be placed in a room 12 meters long, 9 meters wide, and 8 meters high is
64th BPSC
10 m
17 m
29 m
None of the above
The lengths of the diagonals of a rhombus are 10 cm and 24 cm. Its perimeter is
67th [RE] BPSC
52 cm
56 cm
60 cm
None of the above
Two equal arcs of different circles C1 and C2 subtend angles of 60° and 75° respectively, at the centres. What is the ratio of the radius of C1 to the radius of C2?
CDS II 2023
4 : 5
5 : 4
1 : 1
None of the above
ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF?
CDS II 2023
63 square cm
45 square cm
31.5 square cm
None of the above
A triangle has sides 13 cm, 14 cm and 15 cm long. What is the length of the smallest altitude of the triangle?
CDS II 2023
11 cm
11.2 cm
12 cm
None of the above
The circumference of a circle exceeds the diameter by 16.8 cm. What is the diameter of the circle? (Take π = 22/7)
CDS II 2023
6.24 cm
7.64 cm
7.84 cm
None of the above
If a, b and c are the sides of a right-angled triangle, where a > b > c, then what is the value of the expression (a + b + c) (a + b - c) (a - b + c) (a - b - c)?
CDS II 2023
4b²c²
-4b²c²
-4a²b²
None of the above
A solid sphere of radius 3 cm is melted to form a hollow cylinder of height 4 cm and external diameter 10 cm. What is the thickness of the cylinder?
CDS II 2023
1.00 cm
0.46 cm
0.52 cm
0.42 cm
If 2s = a + b + c, then what is s² + (s- a)(s-b) + (s -b)(s-c) + (s - c)(s - a) equal to?
CDS II 2023
(a + b + c)²
ab + bc + ca
2(ab + bc + ca)
None of the above
If the difference between the interior and exterior angles of a regular polygon is 144°, then what is the number of sides of the polygon ?
CDS I 2024
12
16
18
20
A plank of wood 4.25 m long and 3.4 m wide is to be cut into square pieces of equal size. How many square pieces of largest size can be cut from the plank, if no wastage is allowed ?
