Maths Solved Test for UPSC, SSC Railway exams

Maths Solved Test for UPSC, SSC Railway exams

Maths Objective Questions With Answers

1. If a+b+c =0 then a³+b³+c³ is equal to

(a) 3abc

(b) 3/abc

(c) 3a³b³c³

(d) Zero

Ans. (a)

2. A sphere of radius 3 cm and a cone of same radius and height 5 cm are melted to

        make a cylinder of the same radius, then its height is

(a) 12cm

(b) 10cm

(c) 9 cm

(d) 8 cm

Ans. (c)

3. A solid in the form of a cube, has a hemisphere touching four edges of the surface

    on every surface. If the side of the cube is 4 cm, then its volume is

(a) 250.15 cm³

(b) 132.16 cm³

(c) 125 cm³

(d) 164.57 cm³

Ans. (d)

4. The number of coins, of radius 0.75 cm and thickness 0.2 cm, to be melted to make

         a right circular cylinder of height 8 cm and radius 3 cm, is

(a) 640

(b) 650

(c) 675

(d) 700

Ans. (a)

5. The height of a parallelogram of area 350 cm² and base 25 cm is

(a) 12 cm

(b) 13 cm

(c) 14 cm

(d) 15 cm

Ans. (c)

6. The area of a sector of perimeter 45 cm and radius 6 cm is

(a) 44 cm²

(b) 66 cm²

(c) 88 cm²

(d) 99 cm²

Ans. (d)

7. A hall has dimensions 24 m × 8 m × 6 m. The length of the longest pole which can

        be accommodated in the hall is

(a) 26 m

(b) 28 m

(c) 30 m

(d) 36 m

Ans. (a)

8. If the area of 4 walls of the hall whose breadth is 15 m and height is 8 m is 1068 m²,

        then the length of the hall is

(a) 18 m

(b) 17m

(c) 16 m ,

(d) none of these

Ans. (d)

9. The slant height of a conical tent is 35 m and its diameter is 56 m. Then the cost of

         constructing it at 20 paise per m³ is

(a) Rs 3600.50

(b) Rs 3616.00

(c) Rs 620

(d) Rs 3449.60

Ans. (d)

10. A square whose diagonal is 10 cm long has area equal to

(a) 28 cm²

(b) 34 cm²

(c) 50 cm²

(d) none of these

Ans. (c)

11. The base of a right angled triangle is 8 m and its hypotenuse is 10 m. Then its area is

(a) 48 m²

(b) 40 m²

(c) 30 m²

(d) 24 m²

Ans. (d)

12. The tangent at a point P on a circle with centre Q, meets the diameter AR produced at Q. If ∟AQP = 40° then the measure of ∟APO is

(a) 20°

(b) 25°

(c) 30°

(d) 35°

Ans. (d)

13. If O is the centre of circle, PA and PB are tangents. Q is a point on the circumference on the opposite side of AR on which O lies of ∟APB 50° then the measure of ∟AQB is

(a) 115°

(b) 110°

(c) 105°

(d) 103°

Ans. (a)

14. In a cyclic quadrilateral ABCD, ∟ABC = 60° and if O be the centre of the circle then the measure of ∟OAC is

(a) 20°

(b) 30°

(c) 40°

(d) 50°

Ans. (b)

15. The length of diagonal of a square whose area is 16900 m2 is

(a) 130 m

(b) 130 √2 m

(c) 169 m

(d) 144 m

Ans. (b)

16. The base of an isosceles right triangle is 30cm. Its area is

(a) 225 cm²

(b) 225 cm²

(c) 5 √2 cm²

(d) None

Ans. (a)

17. The simplified value of (√3 + 1) ² — 2(2 + √3) is

(a) 2

(b) -1

(c) 1

(d) 0

Ans. (d)

18. The value of x, y and z respectively on simplifying the equation 2x + 3y =0, 3y + 4z = 14. 2x + 4z = 26 is

(a) 3, -2, 5

(b) -3, 2, 5

(c) -3, 2, -5

(d) 3, 2, 5

Ans. (a)

19. If the difference of the squares of two numbers is 45, the square of the smaller number is 4 times the larger number, then the numbers are

(a) 9, 6 or 9,-6

(b) 5, 6 or 5,-6

(c) 9, 5 or 9,-5

(d) None of these

Ans. (a)

20. If the index of any power function is zero, then the value of that function is

(a) 0

(b) 1

(c) -l

(d) none of these

Ans. (b)

21. Twelve years hence a man will be four times as he was 12 years ago, then his present age is

(a) 25 years

(b) 20 years

(c) 28 years

(d) 30 years

Ans. (b)

22. If 2^2x-y=32 and 2^x+y= 16 then x²+y² is equal to

(a) 9

(b) 10

(c) 11

(d) 13

Ans. (b)

23. If a^x=b, b^y=c, c^z=a, then the value of xyz is

(a) 0

(b) 1

(c) 1/abc

(d) abc

Ans. (b)

25. A leap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of coconuts in the leap is

(a) 11

(b) 21

(c) 3l

(d) 41

Ans. (a)