NDA MATHEMATICS 2011 PAST QUESTIONS AND ANSWERS
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
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 i is
A. -i
B. Cos30°
C. Cos90°+i sin 30°
D. Cos120°+ i sin 120°
A. -i
B. Cos30°
C. Cos90°+i sin 30°
D. Cos120°+ i sin 120°
ANSWER: C
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
A. 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 - x2 and y= x2 - 2x
A. 22/3
B. 43/4
C. 131/2
D. 71/4
B. 43/4
C. 131/2
D. 71/4
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. 2/3
B. 1/3
C. 5/6
D. 3/4
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(Ac ) = 2/3 and P(AՈB) =1/4
Find P(B)A.2/3
B. 2/5
C.11/2
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. 3/19
B. 4/19
C. 5/19
D. 9/19
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
B. 3
C. 2
D. 5
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 cm3 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)
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/s2. 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 cm2 sec
B. 20π cm2 sec
C. 3π2
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 — x2 — 6
B. y =4x + 2x2 — 2
C. 2y = 4x - x2 + 12 = 0
D. y + X2 - 6x + 11
A. 2y =4x — x2 — 6
B. y =4x + 2x2 — 2
C. 2y = 4x - x2 + 12 = 0
D. y + X2 - 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= 6/5 and y = -3/5
D. x = -3/5 and y = 6/5
B. x.=-1 and y= 2
C. X= 6/5 and y = -3/5
D. x = -3/5 and y = 6/5
ANSWER: A
23. The roots (s) of the equation
is (are)A. 9,1
B. 9
C. (-3/4, 1)
D. 3, -1
ANSWER: D
24. that is the area enclosed by the curve; Y = 4x — x2, x= 1, x = 2, and the x-axis
A. 2/3
B. None
C. 21/4
D.11/3
A. 2/3
B. None
C. 21/4
D.11/3
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. 31/2 cm/sec
C. 11/2 cm/sec
D. 23/4 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 (x99 + 1)?
A. (x+1)
B. (x- 1)
C. (x+3)
D. (x-3)
ANSWER: D
29. Simplify 1 + tan2Ɵ
A. Sin2 Ɵ
B. Sec2 Ɵ
C. CosƟ
D. Tan2 Ɵ
C. CosƟ
D. Tan2 Ɵ
ANSWER: A
ANSWER: D
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
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.x100
B. 4.5 x 101
C. 4.5 x 102
D. 4.5 x 103
A. 4.x100
B. 4.5 x 101
C. 4.5 x 102
D. 4.5 x 103
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 12e = X7, find X where = 12 find x if 92-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 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
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
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