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# VIT - Mathematics -2010 Unsolved Paper

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### VIT - Mathematics -2010 Unsolved Paper

1. 1. VIT – PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 2010
2. 2. SECTION – I Single Correct Answer Type  There are five parts in this question. Four choices are given for each part and one of them is correct. Indicate you choice of the correct answer for each part in your answer-book by writing the letter (a), (b), (c) or (d) whichever is appropriate
3. 3. 01 Problem If F is function such that F (0) = 2, F (1) = 3, F(x+2)=2F(x)-F(x+1) for x 0 then F (5) is equal to a. - 7 b. - 3 c. 17 d. 13
4. 4. 02 Problem Let S be a set containing n elements. Then,number of binary operations on S is a. nn n2 b. 2 n2 c. n 2 d. n
5. 5. 03 Problem 11 1 The numerically greatest term in the expansion of 3 5x when x is 5 a. 55 x 39 b. 55x 36 c. 45 x 39 d. 45 x 36
6. 6. 04 Problem The number of solutions of the equation ,is a. 0 b. 1 c. 2 d. infinitely many
7. 7. 05 Problem If ax by cz du and a, b, c, d are in GP, then x, y, z, u are in a. AP b. GP c. HP d. None of these
8. 8. 06 Problem If z satisfies the equation z z 1 2 i , then z is equal to 3 a. 2i 2 b. 3 2i 2 c. 3 2 i 2 3 d. 2+ i 2
9. 9. 07 Problem If 1 i 3 then arg(z)is z 1 i 3 a. 60 b. 120 c. 240 d. 300
10. 10. 08 Problem If f x log10 x2 .The set of all values of x , for which f (x) is real, is a. [- 1, 1] b. 1, c. , 1 d. , 1 1,
11. 11. 09 Problem 2 For what values of m can the expression, 2x mxy 3y 2 5y – 2 be expressed as the product of two linear factors? a. 0 b. ± 1 c. ±7 d. 49
12. 12. 10 Problem 1 If B is a non-singular matrix and A is a square matrix, then det B AB is equal to 1 a. det A 1 b. det B c. det (A) d. det (B)
13. 13. 11 Problem f x g x h x If f (x), g (x) and h (x) are three polynomials of degree 2 and x f x g x h x ,then x is a polynomial of degree f x g x h x a. 2 b. 3 c. 0 d. atmost 3
14. 14. 12 Problem The chances of defective screws in three boxes A, B, C are 1 , 1 , 1 5 6 7 respectively. A box is selected at random and a screw drawn from it at random is found to be defective. Then, the probability that it came from box A, is 16 a. 29 b. 1 15 27 c. 59 42 d. 107
15. 15. 13 Problem The value of cos is equal to 1 sin a. tan - 2 4 b. tan 4 2 c. tan 4 2 d. tan 4 2
16. 16. 14 Problem If 3 sin 5 cos 5 , then the value of 5 sin 3 cos is equal to a. 5 b. 3 c. 4 d. None of these
17. 17. 15 Problem The principal value of 1 5 is sin sin 6 a. 6 b. 5 6 c. 7 6 d. None of these
18. 18. 16 Problem A rod of length 1slides with its ends on two perpendicular lines. Then, the locus of its mid point is 2 2 l2 a. x y 4 2 2 l2 b. x y 2 c. x 2 2 l2 y 4 d. None of these
19. 19. 17 Problem The equation of straight line through the intersection of line 2x + y = 1 and 3x + 2y =5 and passing through the origin is a. 7x + 3y =0 b. 7x - y =0 c. 3x + 2y=0 d. x + y=O
20. 20. 18 Problem The line joining is divided internally in the ratio 2 : 3 at P. If varies, then the locus of P is a. a straight line b. a pair of straight lines c. a circle d. None of the above
21. 21. 19 Problem If 2x + y + k = 0 is a normal to the parabola , then the value of k, is a. 8 b. 16 c. 24 d. 32
22. 22. 20 Problem 1 1 1 1 is equal to lim ....... n 1.2 2.3 3.4 n n 1 a. 1 b. -1 c. 0 d. None of these
23. 23. 21 Problem The condition that the line lx +my = 1 may be normal to the curve y 2 4ax , is a. al3 2alm2 m2 2 b. al 2alm3 m2 3 c. al 2alm2 m3 3 d. al 2alm2 m2
24. 24. 22 Problem 2 If f x dx f x , then f x dx is equal to a. 1 2 f x 2 3 b. f x 3 c. f x 3 2 d. f x
25. 25. 23 Problem 2x 2 is equal to sin 1 , dx 2 4x 8x 13 1 2x 2 3 4x 2 8x 13 a. x 1 tan log c 3 4 9 3 1 2x 2 3 4x 2 8x 13 b. tan log c 2 3 4 9 1 2x 2 3 c. x 1 tan log 4x 2 8x 13 c 3 2 3 2x 2 3 d. x 1 tan 1 log 4x 2 8x 13 c 2 3 4
26. 26. 24 Problem If the equation of an ellipse is 3x 2 2y 2 6x 8y 5 0 , then which of the following are true? 1 e a. 3 b. centre is (-1, 2) c. foci are (- 1, 1) are (- 1, 3) d. All of the above
27. 27. 25 Problem x2 y2 y2 x2 The equation of the common tangents to the two hyperbolas 1 and 2 1 a2 b2 a b2 ,are a. y x b2 a2 b. y x a2 b2 c. y x a2 b2 d. y x a2 b2
28. 28. 26 Problem Domain of the function f x logx cos x , is a. , 1 2 2 b. , 1 2 2 c. , 2 2 d. None of these
29. 29. 27 Problem Range of the function 1 x2 , is y sin 1 x2 a. 0, 2 b. 0, 2 c. 0, 2 d. 0, 2
30. 30. 28 Problem If x sec cos , y sec n cos n , then x 2 dy 2 is 4 dx equal to a. n2 y 2 4 b. n2 4 y 2 2 2 c. n y 4 d. None of these
31. 31. 29 Problem If dy is equal to y x y x y ...... , then dx a. y 2 x y 2x y3 x b. 2 2y 2xy 1 y3 x c. 2y 2 x d. None of these
32. 32. 30 Problem x dt If then x can be equal to (a) - 1 t t2 1 6 2 a. 3 b. 3 c. 2 d. None of these
33. 33. 31 Problem The area bounded by the curve y sin x , x-axis and the lines x , is a. 2 sq unit b. 1 sq unit c. 4 sq unit d. None of these
34. 34. 32 Problem The degree of the differential equation of all curves having normal of constant length c is a. 1 b. 3 c. 4 d. None of these
35. 35. 33 Problem      If a ˆ 2i ˆ 2j ˆ b 3k, ˆ i ˆ 2j ˆ and c k ˆ 3i ˆ then a j, tb is perpendicular to , if t is equal to a. 2 b. 4 c. 6 d. 8
36. 36. 34 Problem The distance between the line   r 2ˆ i ˆ 2j ˆ 3k ˆ i ˆ j ˆ and the plane r. ˆ 4k i ˆ 5j ˆ k 5 is a. 10 3 10 b. 3 10 c. 3 3 10 d. 9
37. 37. 35 Problem The equation of sphere concentric with the sphere x2 y2 z2 4x 6y 8z 5 0 and which passes through the origin, is a. x 2 y2 z2 4x 6y 8z 0 2 b. x y2 z2 6y 8z 0 c. x 2 y2 z2 0 2 d. x y2 z2 4x 6y 8z 6 0
38. 38. 36 Problem If the lines x 1 y 1 z 1 x 3 y k z intersect, then the value of and 2 3 4 2 2 1 k, is 3 a. 2 b. 9 2 c. 2 9 3 d. 2
39. 39. 37 Problem The two curves y 3x and y 5x intersect at an angle log 3 log 5 a. tan 1 1 log 3 log 5 b. tan 1 log 3 + log 5 1 - log 3 log 5 c. tan 1 log 3 + log 5 1 + log 3 log 5 log 3 - log 5 d. tan 1 1 - log 3 log 5
40. 40. 38 Problem The equation x2 4xy y2 X 3y 2 0 represents a parabola, if is a. 0 b. 1 c. 2 d. 4
41. 41. 39 Problem If two circles 2x 2 2y 2 3x 6y k 0 and x 2 y2 4x 10y 16 0 cut orthogonally, then the value of k is a. 41 b. 14 c. 4 d. 1
42. 42. 40 Problem If A (- 2, 1), B (2, 3)and C (- 2, -4)are three points. Then, the angle between BA and BC is a. tan 1 2 3 3 b. tan 1 2 1 1 c. tan 3 1 1 d. tan 2
43. 43. FOR SOLUTION VISIT WWW.VASISTA.NET