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VIT – PAST PAPERS
MATHEMATICS - UNSOLVED PAPER - 2009
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
01If is defined by , then the range f(x) is
contained in the interval
a. [1, 12]
b. [12, 34]
c. [35, 50]
d. [-12, 12]
Problem
f : 2, 3 R 3f x x 3x 2
02The number of subsets of {1, 2, 3, ..... , 9} containing at least one odd number is
a. 324
b. 396
c. 496
d. 512
Problem
Problem03A binary sequence is an array of 0's and 1's.The number of n-digit binary
sequences which contain even number of 0's is
a.
b.
c.
d.
n 12
n2 1
n 12 1
n2
Problem04If x is numerically so small so that and higher powers of x can be neglected,
then is approximately equal to
a.
b.
c.
d.
2x
3/2
1/52x1 32 5x
3
32 31x64
31 32x64
31 32x64
1 2x64
Problem05The roots of (x - a) (x - a-1) + (x - a -1)(x - a - 2)+ (x - a) (x - a - 2) = 0 are always
a. equal
b. imaginary
c. nial and distinct
d. rational and equal
Problem06Let , where . If f(x) = 0 has all its roots
imaginary, then the roots of f(x) + f' (x) + f" (x) = 0 are
a. real and distinct
b. imaginary
c. equal
d. rational and equal
f x x2 ax b a, b R
Problem07If is divisible by , then (a, b) is
equal to
a. (-9, -2)
b. (6, 4)
c. (9, 2)
d. (2, 9)
4 2f x 2x 13x ax b 2x 3x 2
Problem08If x, y, z are all positive and are the pth, qth and , rth terms of a geometric
progression
respectively, then the value of the determinant ,
Equals
a. log xyz
b. (p -1)(q -1)(r -1)
c. pqr
d. 0
log x p 1
log y q 1
log z r 1
Problem09The locus of z satisfying the inequality ,where z = x + iy,is
a.
b.
c.
d.
z 2i1
2z i
2 2x y 1
2 2x - y 1
2 2x y > 1
2 22x 3y 1
Problem10If n is an integer which leaves remainder one when divided by three, then
Equals
a.
b.
c.
d.
n n
1 3 i 1 3i
n 12
n 12
n2
n2
Problem11The period of is
a.
b.
c.
d.
4 4sin x cos x
4
2
2
2
4
2
Problem12If , then the general solution of
is
a.
b.
c.
d.
3 cos x 2 sin x
2 2sin x cos x 2 sin 2x
nn ( 1) ,n Z2
n,n Z
2
4n 1 ,n Z2
2n 1 ,n Z
Problem13 equals:
a.
b.
c.
d.
1 1 1 11 1 1cos 2 sin 3 cos 4 tan 1
2 2 2
1912
3512
4712
4312
Problem14In
a.
b.
c.
d.
ABC
2 2
a b c b c a c a b a b c
4b c
2cos A
2cos B
2sin A
2sin B
Problem15The angle between the lines whose direction cosines satisfy' the equations 1+
m + n = 0 , is
a.
b.
c.
d.
2 2 2l m – n 0
6
4
3
2
Problem16 If are respectively the magnitudes of the vectors
, then the
correct order of is
a.
b.
c.
d.
1 2 3 4m , m , m and m
1 2 3 4ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆa 2i j k, a 3i 4j 4k, a i j k and a i 3j k
1 2 3 4m , m , m and m
3 1 4 2m m m m
3 1 2 4m m m m
3 4 1 2m m m m
3 4 2 1m m m m
Problem17If X is a binomial variate with the range {0, 1, 2, 3, 4, 5, 6} and P(X = 2) = 4P(X = 4),
then the parameter p of X is
a.
b.
c.
d.
13
12
23
34
Problem18The area (in square unit) of the circle which touches the lines 4x + 3y = 15 and 4x
+ 3y =5 is
a.
b.
c.
d.
4
3
2
Problem19The area (in square unit) of the triangle formed by x+ y + 1 = 0 and the pair of
straight lines is
a.
b.
c.
d.
2 2x 3xy 2y 0
712
512
112
16
Problem20The pairs of straight lines
form a
a. square but not rhombus
b. rhombus
c. parallelogram
d. rectangle but not a square
2 2 2 2x 3xy 2y 0 and x 3xy 2y x 2 0
Problem21The equations of the circle which pass through the origin and makes intercepts of
lengths 4 and 8 on the x and y-axes respectively are
a.
b.
c.
d.
2 2x y 4x 8y 0
2 2x y 2x 4y 0
2 2x y 8x 16y 0
2 2x y x y 0
Problem22The point (3, - 4) lies on both the circles
Then, the angle between the circles is
a.
b.
c.
d.
2 2 2 2x y - 2x 8y 13 0 and x y 4x 6y 11 0
60
1 1tan
2
1 3tan
5
135
Problem23The equation of the circle which passes through the origin and cuts orthogonally
each of the circles
is
a.
b.
c.
d.
2 2 2 2x y 6x 8 0 and x y 2x 2y 7
2 23x 3y 8x 13y 0
2 23x 3y 8x 29y 0
2 23x 3y 8x 29y 0
2 23x 3y 8x 29y 0
Problem24The number of normals drawn to the parabola from the point (1, 0)is
a. 0
b. 1
c. 2
d. 3
Problem25If the circle
, for i = 1, 2, 3 and 4, then equals
a. 0
b. c
c. a
d.
2 2 2 2i ix y a intersects the hyperbola xy c in four points X , y
1 2 3 4y y y y
4c
Problem26The mid point of the chord 4x - 3y = 5 of the hyperbola is:
a.
b. (2, 1)
c.
d.
2 22x 3y 12
50,
3
5,0
4
11,2
4
Problem27The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is
a. 3
b. 2
c.
d.
2 2
2 3
Problem28If a line in the space makes angle with the coordinate axes, then
equals
a. -1
b. 0
c. 1
d. 2
, and 2 2 2cos 2 cos 2 cos 2 sin sin sin
Problem29The radius of the sphere is
a. 13/2
b. 13
c. 26
d. 52
2 2 2x y z 12x 4y 3z
Problem30 equals
a. e
b.
c.
d.
x 3
x
x 5lim
x 2
2e
3e
5e
Problem31If is defined by
then the value of a so that f is continuous at 0 is
a. 2
b. 1
c. -1
d. 0
2sin x sin2 x
,if x 0f x 2x cosx
a if x=0
f : R R
Problem32 is equal to
a. 0
b. tan t
c. 1
d. sin t cost
1 1
2 2
1 t dyx cos ,y sin
dx1 t 1 t
Problem33 is equal to
a. 1
b. -1
c. 0
d. 2
14
d x 1 1a tan x b log a 2b
dx x 1 x 1
Problem34 is equal to
a.
b.
c.
d.
1asin x 2n 2 n 1y e 1 x y 2n 1 xy
2 2nn a y
2 2nn a y
2 2nn a y
2 2nn a y
Problem35The function has
a. one maximum value
b. one minimum value
c. no extreme value
d. one maximum and one minimum value
3 2 2f x x ax bx c, a 3b
Problem36. is equal to
a.
b.
c.
d.
x2 sin2xe dx
1 cos2x
x e cot x c
x e cot x c
x 2e cot x c
x -2e cot x c
Problem37If equals
a.
b.
c.
d.
nn n 2In sin x dx, then nI n 1 I
n 1 sin x cos x
n 1cos x sin x
n 1 -sin x cos x
n 1-cos x sin x
Problem38The line divides the area of the region bounded by y = sin x, y = cos x
and x-axis into two regions of areas
equals
a. 4: 1
b. 3: 1
c. 2: 1
d. 1: 1
x 4
0 x 2
1 2 1 2A and A .Then A : A
Problem39The solution of the differential equation is
a. cosec (x + y)+ tan (x + y)= x + c
b. x + cosec(x + y)=c
c. x + tan (x + y)=c
d. x + sec (x + y) = c
dy sin x y tan x y 1
dx
Problem40If is false, the truth value of p and q are respectively
a. F, T
b. F, F
c. T, F
d. T, T
P ~p v q
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