# NDA MATHEMATICS 2011 PAST QUESTIONS AND ANSWERS

1. Give the sin Ɵ =

^{5}/_{13}and Ɵ is an acute angle. find Cos Ɵ
A.

B.

C.

D.

^{3}/_{13}B.

^{4}/_{13}C.

^{12}/_{13}D.

^{8}/_{13}**ANSWER: B**

_{}

**ANSWER: D**

3. Of the following, the one which is a cube root of

A. -i

B. Cos30°

C. Cos90°+i sin 30°

D. Cos120°+ i sin 120°

*i*isA. -i

B. Cos30°

C. Cos90°+i sin 30°

D. Cos120°+ i sin 120°

**ANSWER: C**

4. x

A. 2 < x < 4

B. x < 2 or > 4

C. x < 4

D. x > 2

^{2}-6x + 8 > 0 is true for all values of x whereA. 2 < x < 4

B. x < 2 or > 4

C. x < 4

D. x > 2

**ANSWER: A**

5. Find the area enclosed between the curves y=4 - x

^{2}and y= x

^{2}- 2x

A. 2

B. 4

C. 13

D. 7

^{2}/_{3}B. 4

^{3}/_{4}C. 13

^{1}/_{2}D. 7

^{1}/_{4}**ANSWER: C**

**ANSWER: A**

**ANSWER: D**

8. A class contains 10 men and 20 women of which half the men and half the women have brown eyes. Find the probability that a person chosen at random is a man.

A.

B.

C.

D.

A.

^{2}/_{3}B.

^{1}/_{3}C.

^{5}/_{6}D.

^{3}/_{4}**ANSWER: C**

9. Let U be a universal set and let A and B be events such that P(AꓴB) = ^{3}/_{4} P(A^{c} ) = ^{2}/_{3} and P(AՈB) =^{1}/_{4}

A.

^{2}/

_{3}

B.

^{2}/

_{5}

C.1

^{1}/

_{2}

D.

^{3}/

_{7}

**ANSWER: B**

10. Two groups of male students cast their votes on a particular proposal. The results are as follows:

In favour against

Group A 128 32

Group B 96 48

If a student is chosen at random, what is the probability that he is against the proposal?

A.

B.

C.

D.

Group A 128 32

Group B 96 48

If a student is chosen at random, what is the probability that he is against the proposal?

A.

^{3}/_{19}B.

^{4}/_{19}C.

^{5}/_{19}D.

^{9}/_{19}**ANSWER: A**

11. Find the variance of the 6 numbers 4, 6, 6, 7, 9 and 10

A. 4

B. 3

C. 2

D.

B. 3

C. 2

D. 5

**ANSWER: A**

12. A gun of mass8kg fires a bullet of mass 80g at a speed 300m/s. with what initial speed does the gun recoil

A. 3ms

^{-1}

B. 6ms

^{-1}

C. 8ms

^{-1}

D. 7ms

^{-1}

**ANSWER: B**

13. An object whose weight is 10ke is placed on a smooth plane inclined at 30˚ to the horizontal, what force parallel to the plane is required to hold the mass at rest. (Take g = 10ms

^{-2})
A. 20N

B. 18N

C. 15.4N

D. 25N

B. 18N

C. 15.4N

D. 25N

**ANSWER: A**

14. A particle of mass 3kg on a smooth surface is acted upon by a force F. If the acceleration produced in the particle is 2ms

^{-}

^{2}, find the magnitude of F.

A. 8N

B. 5N

C. 7N

D. 6N

**ANSWER: A**

15. An open box with a square base is required to hold 108 cm

A (6,6,3)

B. (8,8,4)

C. (4,4,2)

D. (2,2,4)

^{3}What should be the dimension if the area of cardboard used is as small as possible?A (6,6,3)

B. (8,8,4)

C. (4,4,2)

D. (2,2,4)

**ANSWER: B**

16. lf each side of a cube expands by r% find the approx. percentage change in the volume of the cube

A. 4%

B. 5%

C. 3r%

D.

^{5}/

_{2}%

**ANSWER: D**

17. A body from rest with an acceleration of 10m/s

^{2}. what is it velocity after 5 sec?

A. 25 m/sec

B. 50 m/sec

C. 45 m/sec

D. 32 m/sec

B. 50 m/sec

C. 45 m/sec

D. 32 m/sec

**ANSWER: A**

18. Suppose the radius of a circle is 3cm at a certain instant and it is increasing at the rate of 0-5cm/s at what rate will the area be increasing at the instant

A. 16π cm

^{2}sec

B. 20π cm

^{2}sec

C. 3

*π*

^{2}

D. None

**ANSWER: B**

19. A curve passes through the point (4, -3). Its gradient is 2 — x. Find the equation of the curve.

A. 2y =4x — x

B. y =4x + 2x

C. 2y = 4x - x

D. y + X

A. 2y =4x — x

^{2}^{ }— 6B. y =4x + 2x

^{2}— 2C. 2y = 4x - x

^{2}+ 12 = 0D. y + X

^{2}- 6x + 11**ANSWER: C**

20. A line passes through the point (5, -2) and its gradient is -3. Find the equation of the line.

A. y +3x — 16=0

B. y+ 3x — 13=0

C. y = -3x + 1

D. y = 3x — 1

**ANSWER: C**

**ANSWER: A**

22. if (x+iy) (2+i) = 3 then

A. x=2 and y=1

B. x.=-1 and y= 2

C. X=

D. x = -

B. x.=-1 and y= 2

C. X=

^{6}/_{5}and y = -^{3}/_{5}D. x = -

^{3}/_{5}and y =^{6}/_{5}**ANSWER: A**

**ANSWER: D**

24. that is the area enclosed by the curve; Y = 4x — x

A.

B. None

C. 2

D.1

^{2}, x= 1, x = 2, and the x-axisA.

^{2}/_{3}B. None

C. 2

^{1}/_{4}D.1

^{1}/_{3}**ANSWER: A**

25. The area of a circle is increasing at a rate of 3 cm/sec. Find the rate of change of the circumference when the radius is 2 cm

A. 4cm/sec

B. 3

^{1}/

_{2}cm/sec

C. 1

^{1}/

_{2}cm/sec

D. 2

^{3}/

_{4}cm/sec

**ANSWER: D**

26. if log 2 = 03010 and Log 5 = 0.6992 then log 50 equals

A. 1.6622

B. 1.6990

C. 1.7357

D. 1.7525

**ANSWER: D**

27. If the following, which one is a factor of (x

^{99}+ 1)?

A. (x+1)

B. (x- 1)

C. (x+3)

D. (x-3)

**ANSWER: C**

**ANSWER: D**

29. Simplify 1 + tan

^{2}Ɵ
A. Sin

^{2}Ɵ
B. Sec

C. CosƟ

D. Tan

^{2}ƟC. CosƟ

D. Tan

^{2}Ɵ**ANSWER: A**

**ANSWER: D**

31. Which of the following is in descending order?

A.

B.

C.

D.

^{9}/_{10},^{4}/_{5}, ¾^{17}/_{10}B.

^{4}/_{5}^{9}/_{10},^{3}/_{4},^{17}/_{20}C.

^{9}/_{10},^{17}/_{20},^{4}/_{5},^{3}/_{4}D.

^{4}/_{5},^{9}/_{10},^{17}/_{10},^{3}/_{4}**ANSWER: A**

32. Evaluate 2700 000 x 0.03 ÷ 18 000

A. 4.x10

B. 4.5 x 10

C. 4.5 x 10

D. 4.5 x 10

A. 4.x10

^{0}B. 4.5 x 10

^{1}C. 4.5 x 10

^{2}D. 4.5 x 10

^{3}**ANSWER: B**

33. The prime factors of 2520 are ___.

A. 2,9,5

B. 2,9.7

C. 2,3,5,7

D. 2,3,7,9

**ANSWER: B**

34. If 12

_{e}= X

_{7}, find X where = 12 find x if 9

^{2}

^{-}

^{x }=T

A. 20

B. log a

C. log

D. log a

**ANSWER: B**

**ANSWER: C**

36. What is the difference between 0.007685 correct to three significant figures and 0.007685 correct to four places of decimal?

A. 10

^{-5}

B. 7x 10

^{-}

^{4}

C. 8 x10

^{-5}

D. 10

^{-}

^{6}

**ANSWER: D**

38. Oke deposited ₦800.00 in the bank at the rate of 12

^{1}/

_{2}% simple interest. After some time, the total amount was one and half times the principal. For how many years was the money left in the bank?

A. 2

B. 4

C. 5

^{1}/

_{3}

D. 8

**ANSWER: D**

39. If the surface area of a sphere of radius r, when r=5cm it is decreased by 2%. Find the percentage decreased in the surface area

A. 4%

B. 30%

C. 22%

D. 20%

**ANSWER: D**

**ANSWER: D**

**Share This Post:**If you believe this post will be helpful to others, please share it using the buttons below!