The document is an unsolved mathematics past paper from 2010 containing 33 multiple choice questions. The questions cover a range of mathematics topics including functions, sets, sequences and series, coordinate geometry, trigonometry, calculus, and vectors.

1. VIT – PAST PAPERS
MATHEMATICS - UNSOLVED PAPER - 2010

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. 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. 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. 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. 04 Problem
The number of solutions of the equation ,is
a. 0
b. 1
c. 2
d. infinitely many

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. 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. 07 Problem
If 1 i 3 then arg(z)is
z
1 i 3
a. 60
b. 120
c. 240
d. 300

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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