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Sl.
No.
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Questions
(partly) & Answers
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1
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If
(2, 3,5) is one end of a diameter of the sphere x2
+ y2 + z2 -
6x -
12y -
2z + 20 = 0, ……
Answer: (4, 9, -
3)
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2
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Let
 =
 and
 . If the vector
 ……
Answer:
-
2
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3
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Let A
(h, k), B (1, 1) and C (2, 1) be the vertices of a right angled triangle with
AC …..
Answer:
{-
1, 3}
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4
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Let P
= (-
1, 0) Q = (0, 0) and R =
 be three points. The
equation …..
Answer:
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5
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If
one of the lines of my2 + (1 -
m2) xy -
mx2
= 0 is a bisector of the ….
Answer:
1
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6
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Let
F(x) =
 , where
 . Then F(e) equals …….
Answer:
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7
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Let f:R ®
R be a function defined by f(x) =
Min {x + 1, |x| + 1}. Then …..
Answer: f(x) is differentiable everywhere
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8
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The
function f: R \ {0} ®
R given by
 can be made ……
Answer:
1
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9
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The
solution for x of the equation
 is ……
Answer:
-
(not
given)
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10
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 equals
…..
Answer:
 + C
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11
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The
area enclosed between the curves y2 = x and ……..
Answer:
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12
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If
the difference between the roots of the equation x2 + ax + 1 = 0
is less than
 , then ….
Answer:
(-
3, 3). Assuming:- A Square minus
Four Greater than ZERO
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13
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In a
geometric progression consisting of positive terms, each term equals the sum
of …..
Answer:
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14
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If
 then a value of x is
…..
Answer:
3
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15
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In
the binomial expansion of (a -
b)n,
n ³
5, the sum of ……
Answer:
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16
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The set
S : = {1, 2, 3, …., 12} is to be partitioned into
three sets A, B, C of ……
Answer:
Twelve Factorial DIVIDED
BY (Four
Factorial) Cube
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17
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The
largest interval lying in
 for which …..
Answer:
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18
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A
body weighing 13 kg is suspended by two strings 5 m and 12 m long, their
other ends …..
Answer: 5 kg and 12 kg
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19
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A
pair of fair dice is thrown independently three times. The probability of …..
Answer:
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20
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Consider
a family of circles which are passing through the point (-
1, 1)
and are tangent …..
Answer:
k
³
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21
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Let L
be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z =
2. If L makes …..
Answer:
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22
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The
differential equation of all circles passing through the origin and having
…..
Answer:
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23
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If p
and q are positive real numbers such that p2 + q2 = 1,
then the ……
Answer:
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24
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A
tower stands at the centre of a circular park. A and B are
two points on the boundary ……
Answer:
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25
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The
sum of the series 20C0 -
20C1 +
20C2 -
20C3 + …..-
…+ 20C10
is ….
Answer:
20C10
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26
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The
normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from
the origin …..
Answer: hyperbola
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27
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If |z
+ 4| £
3, then the maximum value of …..
Answer:
6
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28
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The
resultant of two forces P N and 3 N is a force of 7 N. If the direction of
the 3 N …..
Answer:
5N
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29
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Two
aeroplanes I and II bomb a target in succession. The probabilities of I and
II scoring ……
Answer:
0.14.
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30
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If D
=
 for x ¹
0, y ¹
0
then …..
Answer:
divisible by both
x and y
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31
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For
the Hyperbola
 , which of the following …..
Answer:
Abscissae of foci
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32
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If a
line makes an angle of
 with the positive
directions of each of x=axis and y-axis, …..
Answer:
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33
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A
value of C for which the conclusion of Mean Value Theorem holds ……
Answer:
2 log3
e
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34
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The
function f(x) = tan-
1 (sin x + cos x) is an increasing
function ……
Answer:
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35
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Let A
=
 If |A2| = 25, then …..
Answer:
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36
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The
sum of the series
 upto infinity …..
Answer:
e-
1
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37
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If
 and
 are unit vectors and q
is the acute angle between them,
then …..
Answer:
Exactly one value of q
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38
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A
particle just clears a wall of height b at a distance a and strikes the
ground at …..
Answer:
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39
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The
average marks of boys in a class is 52 and that of
girls is 42. The average ….
Answer: 80
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40
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The
equation of a tangent to the parabola y2 = 8x is y = x + 2. The
point …
Answer:
(-
2, 0)
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