# NDA PAST QUESTIONS ON MATHEMATICS 2012

1. Evaluate (212)3 - (121)3 + (222)3
A. (313)3

B. (1000)3

C. (1020)3

D. (1222)3

2. If Musa scored 75 in Biology instead of 57, his average mark in four subjects would have
been 60. What was his total mark?

A. 282
B. 240
C. 222
D. 210

3. Divide the L.C.M of 48, 64, and 80 by their H.C.F
A. 20
B. 30
C. 48
D. 60

4. Find the smallest number by which 252 can be multiplied to obtain a perfect square

A. 2
B. 3
C. 5
D. 7

5. Find the reciprocal of

A. 4/5
B. 5/4
C. 2/5
D. 6/7

6. If x varies directly as yand x = 2 when y = 1. find x when y = 5

A. 2
B. 10
C. 125
D. 250

7. Factorize completely 3a + 125ax3

A. (2a + 5x2)(4 + 25ax)
B. a(2 + 5x)(4 -10x + 25x2)
C. (2a + 5x)(4 -10ax 25x2)
D. a(2 + 5 x)( 4 + 10ax 25x2)

8. If y = , find y when x=-2

A. -3/5
B. 3/5
C. -7/5
D. -2/5

9. Find all real numbers x which satisfy the inequality 1/5(x+1)-1>1/5(x+4)
A. x < 11
B. x < -1
C. x > 6
D. x > 11

10. Factorise x2 + 2a + ax + 2x

A. (x + 2a)(x + 1)
B. (x + 2a)(x - 1)
C. (x2 - 1)(x - a)
D. (x + 2)( x+a)

11. The 7th and 9th terms of an arithmetic progression are 346 and 328 respectively. Find the 2nd term
A. 12
B. 292
C. 301
D. 382

12. A letter is chosen at random from the word LIVELY. What is the probability that it is L?

A. 1/3
B. 1/6
C. 3/6
D. 1/2

13. All possible arrangement of the setters of the word MATHEMATICS are made. If one of these is picked at random, what is the probability that it will end with E?

A. 1/11
B. 2/11
C. 1/2
D. 4/11

14. Factorize Cosec2A+ 2CotA CosecA+ Cot2A

A. (CosecA + CotA)2
B. (Cot A — Cosec A)2
C. (Cot A - Sin A)
D. (Sin A Cot A)

15. Find dy/dn of

16. If tan A=
Find Sin 2A, where A is an acute angle
A. 3P
B. 2P
C. P
D. -P

17. If Cos 2A =4/ find tan A. where A is acute

A. 9/10
B. 1/10
C. 1/3
D. 1/5
18. If Sin q =0 = 90°, find cos q

19. Find the acute angle between the lines x + 4y =12 and y — 2x + 6 = 0

A. 76°
B. 72.47°
C. 77.47°
D. 78°

20. Find the equation or the tangent to the circle
x2 + y+ 2x +4y =15 at the point (-1 2)
A. y = x + 5
B. 3y = 2x + 5
C. 2y = x + 5
D. y = 2x + 5

21. If a dice is thrown. what is the probability of a total score of 7?

A. 1/18
B. 1/6
C. 1/4
D. 1/12

22. Find the median of the following set of  numbers

 x 5 6 7 8 9 10 f 3 4 3 3 3 2
A. 7.35
B. 6.25
C. 7.6
D. 6.50

23. Find the mean of the following scores

 Scores 0 1 2 3 4 5 Frequency 2 5 6 4 2 1

A. 3.2

B. 1.85
C. 2.1
D. 2.21

24. A number of the for An + bn + Cn + d where
A = 4, b = 2, c = 2, d = 1 and n=10), is divisible by
A. 2
B. 5
C. 7
D. 9

25. The set of values satisfying the inequality

A. 4 < x < 16
B. 4 > x > - 16
C. -4 > x > - 16
D. x <1

26. Which of the following is not true?

A. cos(180 - x) = -cos
B. cos(180 + x) = -cos
C. cos(360 -x)) = -cos
D. cos(-x) = cos

27. Which of the following is true about any rhombus

A. All the sided are equal
B. Two diagonal cut at right angles
C. The angle are bisected by the diagonals.
D. All of the above

28. Using trigonometric identities Cos 3 is same. as

A. Cos3x — 3 Cosx
B. 4Cos 3x — 3 Cosx
C. 3 Cos3x — 4 Cosx
D. Cosx — 3 Cosx

29. Sin x Cos y is same as

A. 1/2( Sin (x+y) Sin (x-y)]
B. 1/2[ Cos (x-y) +Sin(x - y)]
C. 1/2[ Sin (x - y) + Sin (x + y)]
D. 1/2[ Sin (x - y) + Sin (x + y)]

30. What is the area of the triangle RTS to the nearest whole number?

A. 26cm2

B. 27cm2

C. 25cm2

D. 28cm2

31. In a class of 40 students, 20 offer Physics. 35 offer Chemistry and 18 offer both Physics and Chemistry. How many students do not offer either Physics or Chemistry?
A. 5
B. 3
C. 4
D. 2

32. A point Q divides a line segment MN joining the point M(-2,3)and N (6, -4) externally in
the ratio 5:2. Find the coordinates of Q

A. (34/3), -26/3)
B. (34/5, -26/5)
C. (34/7, -26/7)
D. (34/11, 24/11)

33. Which of the following sets of points are col-linear?

A. (0, 1), (2, 2), (3. 4)
B. (-2, 3), (1, 5), (2, 1)
C. (6, 1), (0, -2), (4, 2)
D. (-2, 4), (-3, 2), (5, 0)

34. Chuka walks at a velocity of 4km/hr eastward. Ali walks 3krn/hr northwards. Find the velocity of Chuka relative to Ali.

A. 5km/h
B. 4km/h
C. 6km/h
D. 8km/h

35. A car of mass 1000kg has a uniform acceleration of 3m/s2 .Find the external force applied to the car.

A. 4 x 103N
B. 3 x103 N
C. 3 x 10-3 N
D. 4 x 10-3  N

36.In the figure above, what is the perimeter of the equilateral triangle ABC

A. 3
B. 9
C. 10
D. 30

37. A pie chart of total number of students in a school has a sector 35˚ representing 14 students.

How many students are there in the school altogether?
A. 200
B. 140
C. 144
D. 250

38. lf a block of height 2.5cm represents 100 goats, how high should the block be to represent

170 goats
A.4.50 cm
B. 5.00 cm
C. 4.00 cm
D. 4.25 cm

39. Define the co-efficient of rank correlation

40. Find the correlation co-efficient between x and y for the following data

 X 1 2 3 4 Y 2 4 6 8
A. -1.0
B. 1.0
C. 0.0
D. 2

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