vit - mathematics -2010 unsolved paper
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VIT – PAST PAPERS
MATHEMATICS - UNSOLVED PAPER - 2010
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 F is function such that F (0) = 2, F (1) = 3, F(x+2)=2F(x)-F(x+1) for then F
(5) is equal to
a. - 7
b. - 3
c. 17
d. 13
Problem
x 0
02Let S be a set containing n elements. Then,number of binary operations on S is
a.
b.
c.
d.
Problem
nn
2n2
2nn
2n
Problem03The numerically greatest term in the expansion of is
a.
b.
c.
d.
11 13 5x when x
5
955 x 3
655x 3
945 x 3
645 x 3
Problem04The number of solutions of the equation ,is
a. 0
b. 1
c. 2
d. infinitely many
Problem05If 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
x y z ua b c d
Problem06If z satisfies the equation , then z is equal to
a.
b.
c.
d.
z z 1 2 i
3 2i
2
3 2i
2
32 i
2
32+ i
2
Problem07If then arg(z)is
a.
b.
c.
d.
1 i 3z
1 i 3
60
120
240
300
Problem08If .The set of all values of x , for which f (x) is real, is
a. [- 1, 1]
b.
c.
d.
210f x log x
1,
, 1
, 1 1,
Problem09For what values of m can the expression, be
expressed as the product of two linear factors?
a. 0
b. ± 1
c. ± 7
d. 49
2 22x mxy 3y 5y – 2
Problem10If B is a non-singular matrix and A is a square matrix, then is
equal to
a.
b.
c. det (A)
d. det (B)
1det B AB
1det A
1det B
Problem11If f (x), g (x) and h (x) are three polynomials of degree 2 and
,then is a polynomial of degree
a. 2
b. 3
c. 0
d. atmost 3
f x g x h x
x f ' x g' x h' x
f '' x g'' x h'' x
x
Problem12The chances of defective screws in three boxes A, B, C are
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
a.
b.
c.
d.
1 1 1, ,
5 6 7
1629
115
2759
42107
Problem13The value of is equal to
a.
b.
c.
d.
cos1 sin
tan - 2 4
tan 4 2
tan 4 2
tan 4 2
Problem14If , then the value of is equal to
a. 5
b. 3
c. 4
d. None of these
3 sin 5 cos 5 5 sin 3 cos
Problem15The principal value of is
a.
b.
c.
d. None of these
1 5sin sin
6
6
56
76
Problem16A rod of length 1slides with its ends on two perpendicular lines. Then, the locus
of its mid point is
a.
b.
c.
d. None of these
22 2 l
x y 4
22 2 l
x y 2
22 2 l
x y 4
Problem17The 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
Problem18The 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
Problem19If 2x + y + k = 0 is a normal to the parabola , then the value of k, is
a. 8
b. 16
c. 24
d. 32
Problem20 is equal to
a. 1
b. -1
c. 0
d. None of these
n
1 1 1 1lim .......
1.2 2.3 3.4 n n 1
Problem21The condition that the line lx +my = 1 may be normal to the curve
, is
a.
b.
c.
d.
2y 4ax
3 2 2al 2alm m
2 3 2al 2alm m
3 2 3al 2alm m
3 2 2al 2alm m
Problem22If is equal to
a.
b.
c.
d.
2f x dx f x , then f x dx
21f x
2
3f x
3f x
3
2f x
Problem23 is equal to
a.
b.
c.
d.
1
2
2x 2sin , dx
4x 8x 13
2
1 2x 2 3 4x 8x 13x 1 tan log c
3 4 9
213 2x 2 3 4x 8x 13
tan log c2 3 4 9
1 22x 2 3x 1 tan log 4x 8x 13 c
3 2
1 23 2x 2 3x 1 tan log 4x 8x 13 c
2 3 4
Problem24If the equation of an ellipse is , then which of
the following are true?
a.
b. centre is (-1, 2)
c. foci are (- 1, 1) are (- 1, 3)
d. All of the above
2 23x 2y 6x 8y 5 0
1e
3
Problem25The equation of the common tangents to the two hyperbolas
,are
a.
b.
c.
d.
2 2 2 2
2 2 2 2
x y y x1 and 1
a b a b
2 2y x b a
2 2y x a b
2 2y x a b
2 2y x a b
Problem26Domain of the function , is
a.
b.
c.
d. None of these
xf x log cos x
, 12 2
, 12 2
,2 2
Problem27Range of the function , is
a.
b.
c.
d.
21
2
xy sin
1 x
0, 2
0,2
0,2
0,2
Problem28If , then is
equal to
a.
b.
c.
d. None of these
n nx sec cos , y sec cos 2
2 dyx 4
dx
2 2n y 4
2 2n 4 y
2 2n y 4
Problem29If is equal to
a.
b.
c.
d. None of these
dyy x y x y ...... , then
dx
2
y xy 2x
3
2
y x2y 2xy 1
3
2
y x2y x
Problem30If then x can be equal to (a) -
a.
b.
c. 2
d. None of these
x
1 2
dt6t t 1
2
3
3
Problem31The area bounded by the curve , x-axis and the lines , is
a. 2 sq unit
b. 1 sq unit
c. 4 sq unit
d. None of these
y sin x x
Problem32The 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
Problem33If is
perpendicular to , if t is equal to
a. 2
b. 4
c. 6
d. 8
ˆ ˆˆ ˆ ˆ ˆ ˆ ˆa 2i 2j 3k, b i 2j k and c 3i j, then a t b
Problem34The distance between the line
is
a.
b.
c.
d.
ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆr 2i 2j 3k i j 4k and the plane r. i 5j k 5
103
10
3
10
3 3
109
Problem35The equation of sphere concentric with the sphere
and which passes through the origin, is
a.
b.
c.
d.
2 2 2x y z 4x 6y 8z 5 0
2 2 2x y z 4x 6y 8z 0
2 2 2x y z 6y 8z 0
2 2 2x y z 0
2 2 2x y z 4x 6y 8z 6 0
Problem36If the lines intersect, then the value of k,
is
a.
b.
c.
d.
x 1 y 1 z 1 x 3 y k zand
2 3 4 2 2 1
32
92
29
32
Problem37The two curves intersect at an angle
a.
b.
c.
d.
x xy 3 and y 5
1 log 3 log 5tan
1 log 3 log 5
1 log 3 + log 5tan
1 - log 3 log 5
1 log 3 + log 5tan
1 + log 3 log 5
1 log 3 - log 5tan
1 - log 3 log 5
Problem38The equation represents a
parabola, if is
a. 0
b. 1
c. 2
d. 4
2 2x 4xy y X 3y 2 0
Problem39If two circles
cut orthogonally, then the value of k is
a. 41
b. 14
c. 4
d. 1
2 2 2 22x 2y 3x 6y k 0 and x y 4x 10y 16 0
Problem40If A (- 2, 1), B (2, 3)and C (- 2, -4)are three points. Then, the angle between BA
and BC is
a.
b.
c.
d.
1 2tan
3
1 3tan
2
1 1tan
3
1 1tan
2
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