# NDA PAST QUESTIONS ON MATHEMATICS 2011

1. Give the sin Ɵ = 5/13 and Ɵ is an acute angle. find Cos Ɵ
A. 3/13
B. 4/13
C. 12/13
D. 8/13

3. Of the following, the one which is a cube root of i is
A. -
i
B.
Cos30°
C. Cos90°+
i sin 30°
D.
Cos120°+ i sin 120°

4. x2 -6x + 8 > 0 is true for all values of x where
A. 2 < x < 4
B. x < 2 or > 4
C. x < 4
D. x > 2

5. Find the area enclosed between the curves
y=4 - x2 and y= x2 - 2x
A. 22/3
B. 43/4
C. 131/2
D. 71/
4

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. 2
/3
B. 1/3
C. 5/6
D. 3/4

9. Let U be a universal set and let A and B be events such that
P(AB) = 3/4 P(Ac ) = 2/3 and P(AՈB) =1/4
Find P(B)
A.
2/3
B. 2
/5
C
.11/2
D. 3/7

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. 3/19
B. 4/19
C. 5/19
D. 9/19

11. Find the variance of the 6 numbers 4, 6, 6, 7, 9 and 10
A. 4
B. 3
C. 2
D.
5

12, A gun of mass
8kg 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

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 = 10
ms-2)
A. 20N
B. 18N
C. 15.4N
D. 25N

14. A particle of mass 3
kg 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

15. An open box with a square base is required to hold 108 c
m3 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)

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%

17. A body from rest with an acceleration of 10m
/s2. what is it velocity after 5 sec?
A. 25 m/sec
B. 50 m
/sec
C. 45 m
/sec
D. 32 m
/sec

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. 2
0π cm2 sec
C. 3π
2
D. None

19. A
curve passes through the point (4, -3). Its gradient is 2 — x. Find the equation of the curve.
A. 2y =
4x — x2 — 6
B. y =4x + 2x2 — 2
C. 2y
= 4x - x2 + 12 = 0
D. y + X2 - 6x +
11

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

22. if (x+iy) (2+i) = 3 then
A. x=2 and y=1
B. x.=-
1 and y= 2
C.
X= 6/5 and y = -3/5
D. x = -3/5 and y = 6/5

23. The roots (s) of the equation
is (are)
A. 9,
1
B. 9
C. (-
3/4, 1)
D. 3, -1

24. that is the area enclosed by the curve; Y = 4x — x
2, x= 1, x = 2, and the x-axis
A. 2/3
B. None
C. 21/4
D.
11/3

25. The area of a circle is increasing at a rate of 3 c
m/sec. Find the rate of change of the circumference when the radius is 2 cm
A. 4
cm/sec
B. 3
1/2 cm/sec
C. 1
1/2 cm/sec
D. 2
3/4 cm/sec

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

27. If the following, which one is a factor of (x99 +
1)?
A. (x+1)
B. (x- 1)
C. (x+3)
D. (x-3)

29. Simplify 1 + tan2Ɵ
A. Sin2 Ɵ
B. Sec2 Ɵ
C. Cos
Ɵ
D. Tan2
Ɵ

31. Which of the following is in descending order?
A. 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

32. Evaluate 2700 000 x 0.03 ÷ 18 000
A. 4.x
100
B. 4
.5 x 101
C. 4.5 x
102
D
. 4.5 x 103

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

34. If 12
e = X7, find X where = 12 find x if 92-x =T
A. 20
B. log a
C
. log
D. log
a

36. What is the difference between 0.007685 correct to three significant fig
ures and 0.007685 correct to four places of decimal?
A. 10
-5
B. 7x 10
-4
C. 8 x10-5
D
. 10-6

38. Oke deposited ₦800.00 in the bank at the rate of 121/2% 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
. 51/3
D. 8

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%

ANSWERS
1. B
2. D
3. C
4. A
5. C
6. A
7. D
8. C
9. B
10. A
11. A
12. B
13. A
14. A
15. B
16. D
17. A
18. B
19. C
20. C
21. A
22. A
23. D
24. A
25. D
26. D
27. C
28. D
29. A
30. D
31. A
32. B
33. B
34. B
35. C
36. D
37. B
38. D
39. D
40. D