(Paper) E Litmus Fresher Job Interview Placement Paper part - 1: 26-jul-2011

e litmus

Job Interview Placement Paper

TEST PAPER 1

Total Questions: 75 Time allotted 90 minutes

1. The set of all integers x such that |x – 3| < 2 is equal to
(a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4}
(c) {2, 3, 4} (d) {-4, -3, -2}

2. The Range of the function f(x) = x 22 x−−is
(a) R (b) R – {1}
(c) (-1) (d) R – {-1}

3. The value of (i)i is
(a) ω (b) ω2
(c) e-π/2 (d) 2√2

4. ( )( )45cos sincos sinθ + θθ + θis equal to
(a) cos− sin θ (b) cos9θ − isin9θ
(c) sin θ − cosθ (d) sin 9θ − icos9θ

5. The roots of the quadratic equation ax2 + box + c = 0 will be reciprocal to each other if
(a) a = 1/c (b) a = c
(c) b = ac (d) a = b

6. If α, β are the roots of ax2 − 2bx + c = 0 then α3β3 + α2β3 + α3β2 is
(a) 2 ( )3c c 2ba+
(b)33bca
(c)23ca
(d) None of these

7. The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is
(a) 1/39 (b) 1/28
(c) 1/17 (d) 1/6

8. Let Sn denote the sum of first n terms of an A.P.. If S2n = 3Sn, then the ratio S3n / 5n is equal to
(a) 4 (b) 6
(c) 8 (d) 10

9. Solution of |3 – x| = x – 3 is
(a) x < 3 (b) x > 3
(c) x > 3 (d) x < 3

10. If the product of n positive numbers in 1, then their sum is
(a) a positive integer
(b) divisible by n
(c) equal to n 1n+
(d) never less than n

11. A lady gives a dinner party to six quests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
(a) 112 (b) 140
(c) 164 (d) None of these

12. For 1 ≤ r ≤ n, the value of n 1 n 2 rr r r nCr + − C + − C + _ _ _ + C is
(a) r 1 nC +
(b) n 1r + C
(c) n 1r 1 + C+
(d) None of them.

13. 2.42n+1 + 33n+1 is divisible by
(a) 2 (b) 9
(c) 11 (d) 27

14. If Pn denotes the product of the binomial coefficients in the expansions of (1 + x)n, the n 1nPP+ equals
(a) n !n!+
(b)nnn!
(c) ( )n 1 n 1n!+ +
(d) ( )( )n 1!n 1n 1+ ++

15. If x is very large and n is a negative integer or a proper fraction, then an approximate value of n 1 x x + is
(a) 1 x n+
(b) 1 n x+
(c) 1 1x+
(d) n 1 1x +

16. If 4 log93 + 9 log24 = 10log x 83, (x ∈ R)
(a) 4 (b) 9
(c) 10 (d) None of these

17. The sum of the series 2 2 2 4 8 16 log − log + log _ _ _ _ to∞is
(a) e2 (b) loge2 + 1
(c) loge3 – 2 (d) 1 – loge2

18. tan 5x tan 3x tan2x is equal to
(a) tan5x − tan3x − tan 2x
(b) sin5x sin3x sin 2x cos5x cos3x cos2x − −− −
(c) 0
(d) None of these

19. If a = tan60 tan 420 and B = cot660 cot 780
(a) A = 2B (b) A 1 B3=
(c) A = B (d) 3A = 2B.

20. The value of cos 2 cos 4 cos 6 7 7 7 π π π + + is
(a) 1 (b) -1
(c) 1/2 (d) -1/2

21. If tan 1 andsin 1 ,7 10α = β = where 0 ,2π< α β < , then 2β is equal to
(a)4π− α
(b) 34π− α
(c)8π− α
(d) 38 2π π−

22. If sin θ + cosθ = 2 sin θ , then
(a) 2 cosθ (b) − 2 sin θ
(c) − 2 cosθ (d) None of these

23. Value of 2 0 4 0 4 0 2 0 sin 20 cos 20sin 20 cos 20++is
(a) 1 (b) 2
(c) ½ (d) None of these

24. Value of 32cos6 200 − 48cos4 200 +18cos2 200 −1 is
(a) 12−
(b) 12
(c) 32
(d) None of these

25. If sinθ + cosecθ = 2 , then value of sin3 θ + cosec3θ is
(a) 2 (b) 4
(c) 6 (d) 8

26. If cosecθ + cot θ = 5 2 , then the value of tanθ is
(a) 1516
(b) 2120
(c) 1521
(d) 2021

27. General value of x satisfying the equation 3sin x + cos x = 3 is given by
(a) n6π π ±
(b) ( )n n 14 3π ππ + − +
(c) n3π π ±
(d) ( )n n 13 6π ππ + − −

28. If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ∠ABC is
(a) 120 2 cm23
(b) 60 2 cm23
(c) 30 2cm23
(d) None of these

29. A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of depression of 300. After sometimes, the angle of depression becomes 600. The distance (in metres) traveled by the car during this time is
(a) 100 3
(b) 200 33
(c) 100 33
(d) 200 3

30. The shadow of a tower of height (1+ 3) metre standing on the ground is found to be 2 metre onger when the sun’s elevation is 300, then when the sun’s elevation was
(a) 300 (b) 450
(c) 600 (d) 750

31. cos 1 cos 54− π is equal to
(a) 4−π
(b) 4π
(c) 34π
(d) 54π

32. If cos 1 x cos 1 y 2 3 6− − π+ = , then value of x2 xy y24 2 3 9− + is
(a) 34
(b) 12
(c) 14
(d) None of these

33. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
(a) 7/2 (b) 7/3
(c) 7/5 (d) 7/10

34. The straight lines x + y – 4 = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a traigle which is
(a) isosceles (b) right angled
(c) equilateral (d) None of these

35. Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is
(a) 9 , 92 2
(b) 7 , 72 2
(c) 11,11 2 2
(d) None of these

Next

ANSWER KEYS : 1. (c) 2. (c) 3. (c) 4. (d) 5. (b) 6. (a) 7. (d) 8. (b)  9. (d) 10. (d) 11. (b) 12. (c) 13. (c) 14. (d) 15. (b) 16. (c) 17. (d) 18. (b) 19. (c) 20. (c) 21. (c) 22. (a) 23. (a) 24. (a) 25. (a)  26. (d) 27. (d) 28. (a) 29. (b)  30. (b) 31. (c) 32. (c) 33. (d) 34. (a) 35. (a)


Company Name: e litmus
No of Rounds:
Aptitude Test
Exam/Interview Date: 26-Jul-2011
Location : Delhi