Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
VIT – PAST PAPERS MATHEMATICS - UNSOLVED PAPER - 2007
1. VIT – PAST PAPERS
MATHEMATICS - UNSOLVED PAPER - 2007
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 the normal to the curve y = f(x) at (3, 4) makes an angle with the positive x-
axis, then f' (3) is equal to :
a. -1
3
b. 4
c. 1
3
d.
4
4. 02 Problem
The function f x x2 e 2x
,x 0 . Then the maximum value of f(x) is:
1
a. e
1
b.
2e
1
c. e2
1
d. e2
5. 03 Problem
if u u is equal to :
x y sin u x 2 y 2 , then x y
x y
a. sin u
b. cosec u
c. 2 tan u
d. 3 tan u
6. 04 Problem
The angle between the tangents at those points on the curve
x t2 1 and y t2 t 6 where it meets x-axis is :
1 4
a. tan
29
1 5
b. tan
49
1 10
c. tan
49
1 5
d. tan
49
7. 05 Problem
4
The value of x 3 dx is equal to:
1
a. 2
5
b. 2
c. 1
2
3
d.
2
8. 06 Problem
The area of the region bounded by the straight lines x = 0 and x = 2, and the
curves y 2x and y 2x x 2 is equal to :
2 4
a.
log 2 3
3 4
b. log 2 3
1 4
c.
log 2 3
4 3
d.
log 2 2
9. 07 Problem
The value of dx is equal to:
2 2
0
a x
a.
2
b.
2a
c. a
1
d. 2a
10. 08 Problem
2
1 x
The value of the integral eX dx is:
1 x2
a. ex 1 x c
2
1 x
b. e x 1 x2 c
1 x
c. ex
c
1 x2
d. ex 1 x c
11. 09 Problem
If x sin y dy y sin
y
x dx and y 1 , then the value of is equal cos
y
x x 2 x
to:
a. x
1
b.
x
c. log x
d. ex
12. 10 Problem
The differential equation of the system of all circles of radius r in the xy plane is
:
2 2
3
dy d2 y
a. 1 r2
dx dx 2
2 3
3
dy d2 y
b. 1 r2
dx dx 2
3 2
2
dy 2 d2 y
c. 1 r
dx dx 2
3 3
2
dy d2 y
1 r2
d. dx dx 2
13. 11 Problem
The general solution of the differential equation d2 y dy
2 y 2e 3x
dx 2 dx
is given by :
x e3x
a. y c1 c2 x e
8
-x e-3x
b. y c1 c 2 x e
8
-x e3x
c. y c1 c2 x e
8
-x e3x
y c1 c 2 x e
d. 8
14. 12 Problem
The solution of the differential equation ydx x y3 dy 0 is :
1 3
a. xy y c
3
b. xy y4 c
c. y4 4xy c
d. 4y y3 c
15. 13 Problem
The number of integral solutions of x1 x2 x3 0, with xi 5 , is :
15
a. C2
b. 16
C2
17
c. C2
18
d. C2
16. 14 Problem
Let A = {1, 2, 3, ... , n} and B = {a, b, c}, then the number of functions from A to
E
B that are onto is :
a. 3n – 2n
n n
b. 3 – 2 1
n
c. 3 2 1
n
d. 3 3 2n 1
17. 15 Problem
Everybody in a room shakes hands with everybody else. The total number of
hand shakes is 66. The total number of persons in the room is :
a. 9
b. 12
c. 10
d. 14
18. 16 Problem
In a group G = {1, 3,7, 9} under multiplication modulo 10, the inverse of 7 is :
a. 7
b. 3
c. 9
d. 1
19. 17 Problem
A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from
the box one at a time, the probability that they are alternatively either
{odd, even, odd} or {even, odd, even} is :
5
a.
17
4
b. 17
5
c. 16
5
d. 18
20. 18 Problem
1 5 B 1 is equal to :
If P A ,P B and P , then P A B
12 12 A 15
89
a. 180
90
b. 180
91
c. 180
92
d. 180
21. 19 Problem
If the probability density function of a random variable X is
x
f x in a 0 x 2 ,then P(X > 1.5 | X > 1) is equal to :
2
7
a.
16
3
b.
4
7
c. 12
21
d. 64
22. 20 Problem
1
If X follows a binomial distribution with parameters n = 100 and p , then P(X
3
=r) is maximum when r is equal to
a. 16
b. 32
c. 33
d. none of these
23. 21 Problem
If A 1 tan and AB =1, then sec 2 B is equal to:
-tan 1
a. A
b. A
2
c. A
d. A 2
24. 22 Problem
2x 1 4 8
If x=-5 is a root of then the other roots are :
2 2x 2 0
7 6 2x
a. 3, 3.5
b. 1, 3.5
c. 1, 7
d. 2, 7
25. 23 Problem
The simultaneous equations Kx + 2y - z = 1,(K -I)y - 2z = 2and (K + 2) z =3 have
only one solution when:
a. k = -2
b. k = -1
c. k = 0
d. k = 1
26. 24 Problem
If the rank of the matrix 1 2 5 is 1,then the value of a is:
2 -4 a-2
1 -2 a+1
a. -1
b. 2
c. -6
d. 4
27. 25 Problem
2
If b 4ac for the equation ax 4 bx 2 c 0 ,then all the roots of the equation
will be real if:
a. b>0,a<0,c>0
b. b<0,a>0,c>0
c. b>0,a>0,c>0
d. b>0,a>0,c<0
28. 26 Problem
8 16
If x>0 and log3 x log3 x +log3 4
x +log3 x +log3 x . 4 ,then x
equals:
a. 9
b. 81
c. 1
d. 27
29. 27 Problem
3
the number of real roots of equation 1 1 is:
x x 0
x x
a. 0
b. 2
c. 4
d. 6
30. 28 Problem
H H
If H is the harmonic mean between P and Q, then the value of is:
P Q
a. 2
PQ
b.
P Q
c. 1
2
P Q
d. PQ
31. 29 Problem
If b is a unit vector, then a.b b bx axb is:
a. 2
a b
b. a.b a
c. a
d. b
32. 30 Problem
If is the angle between the lines AB and AC where A, Band C are the three
points with coordinates (1, 2, -1), (2, 0, 3), (3, -1, 2) respectively, then
462 cos is equal to:
a. 20
b. 10
c. 30
d. 40
33. 31 Problem
Let the pairs a,b and c, d each determine a plane. Then the planes are
parallel, if:
a. a x c x b x d 0
b. a x c . b x d 0
c. a x b x c x d 0
d. a x b . c x d 0
34. 32 Problem
ˆ
The area of a parallelogram with 3i ˆ
j ˆ
2k and ˆ
i ˆ
3j ˆ
4k as diagonals
is :
a. 72
b. 73
c. 74
d. 75
35. 33 Problem
If cos x cos 2 x 1, then the value of sin12 x 3 sin10 x 3 sin8 x sin6 x 1
is equal to:
a. 2
b. (b)1
c. (c) -1
d. (d)0
36. 34 Problem
3/5
The product of all values of cos i sin is:
a. 1
b. cos i sin
c. cos 3 i sin 3
d. cos 3 i sin 3
37. 35 Problem
2
The imaginary part of 1 i is:
i 2i 1
4
a. 5
b. 0
2
c. 5
4
d. 5
38. 36 Problem
If sin 1
x sin 1
y , then cos 1 x cos 1
y is equal to :
2
a.
2
b. 4
c.
3
d. 4
39. 37 Problem
The equation of a directrix of the ellipse x2 y2 is:
+ 1
16 25
a. 3y = 5
b. y = 5
c. 3y = 25
d. y = 3
40. 38 Problem
2
If the normal at ap2 , 2ap on the parabola y 4ax , meets the
parabola again at aq2 , 2aq , then:
a. p2 pq 2 0
b. p2 - pq 2 0
c. q2 pq 2 0
p2 pq 1 0
d.
41. 39 Problem
2
The length of the straight line x - 3y = 1 intercepted by the hyperbola x 4y 2 1
is :
a. 10
6
b.
5
1
c.
10
6
10
d. 5
42. 40 Problem
The curve described parametrically by x t2 2t 1 , y = 3t + 5
represents:
a. an ellipse
b. a hyperbola
c. a parabola
d. a circle
