Problem 1:
The domain of definition of is
(a)
(b)
(c)
(d)
Problem 2:
is a right-angled triangle with the right angle at B. If
and
, then the length of the perpendicular from
to
is
(a)
(b)
(c)
(d)
Problem 3:
If the points and
are on the circles
and
respectively and the angle included between these vectors is
, then
equals
(a)
(b)
(c)
(d)
Problem 4:
Let and
be positive integers such that
and
If
, then
equals
(a) 55
(b) 23
(c) 89
(d) 93
Problem 5 :
for :
(a) All .
(b) No .
(c) .
(d)
Problem 6 :
If and
where
, then the equation
has :
(a) Only real roots.
(b) No real roots.
(c) At least two real roots.
(d) Exactly two real roots.
Problem 7:
as x
is equal to
(a)
(b) 0
(c)
(d) 2
Problem 8:
where
runs from 1 to
as
is equal
(a) 0
(b)
(c) 2
(d) 1
Problem 9:
Let f: is given by
. Then,
(a) is
and onto
(b) is neither
nor onto
(c) is
but not onto
(d) is onto but not
Problem 10:
The last digit of is :
(a)
(b)
(c)
(d)
Problem 11:
The average scores of students in a test is
. The lowest score is
. Then the highest score is at most
(a)
(b)
(c)
(d)
Problem 12:
The coefficient of in the expansion of
is
(a)
(b)
(c)
(d)
problem 13:
Let be polynomials defined by
and
for
. Then
equals
(a)
(b)
(c)
(d)
Problem 14:
Suppose are matrices satisfying
. Then
is equal to
(a) 0
(b)
(c)
(d)
Problem 15:
The number of terms in the expansion of
is
(a)
(b)
(c)
(d)
Problem 16:
If are positive real numbers satisfying
,
then the maximum value of is
(a) 8
(b) 9
(c) 6
(d) 12
Problem 17:
If at least percent students in a class are good in sports, and at least
percent are good in music and at least
percent are good in studies, then the percentage of students who are good in all three is at least
(a)
(b)
(c)
(d)
Problem 18:
If , then
is
(a)
(b)
(c)
(d) 2/3
Problem 19:
Let Then
equals
(a)
(b) 2010
(c)
(d) None of the above
Problem 20:
If each side of a cube is increased by , then the surface area of the cube increased by
(a)
(b)
(c)
(d)
Problem 21:
If , then
(a)
(b)
(c)
(d) None of the above is true.
Problem 22:
The number of complex numbers w such that and imaginary part of
is 0 , is
(a) 4
(b) 2
(c) 8
(d) Infinite
Problem 23:
Let for all
Suppose
(summation is running from to
for all
. Then
(a)
(b)
(c)
(d)
Problem 24:
The number of points at which the function
) if
and
if
is not differentiable, is
(a) 1
(b) 0
(c) 2
(d) None of the above.
Problem 25:
The greatest value of function
(a)
(b)
(c)
(d)
problem 26:
Let (integration running from
to
for all
. Then
(a) is not differentiable.
(b) is constant.
(c) is increasing in
.
(d) is decreasing in
.
Problem 27:
Let be a continuous function which is positive for all
and
(first integration is running from 2 to 3 and second integration running from 0 to 2). Then
(a)
(b)
(c)
(d)
Problem 28:
Let be a continuous function. Let
for
. Then, the equation
has
(a) No solution.
(b) All points in as solutions.
(c) At least one solution.
(d) None of the above.
Problem 29:
Let be two angles. Then the equation
(a) Determines uniquely in terms of
(b) Gives two value of for each value of
(c) Gives more than two values of for each value of
(d) None of the above.
Problem 30:
Ten players are to pay a tennis tournament. The number of pairings for the first round is
(a)
(b)
(c)
(d)
Problem 1:
The domain of definition of is
(a)
(b)
(c)
(d)
Problem 2:
is a right-angled triangle with the right angle at B. If
and
, then the length of the perpendicular from
to
is
(a)
(b)
(c)
(d)
Problem 3:
If the points and
are on the circles
and
respectively and the angle included between these vectors is
, then
equals
(a)
(b)
(c)
(d)
Problem 4:
Let and
be positive integers such that
and
If
, then
equals
(a) 55
(b) 23
(c) 89
(d) 93
Problem 5 :
for :
(a) All .
(b) No .
(c) .
(d)
Problem 6 :
If and
where
, then the equation
has :
(a) Only real roots.
(b) No real roots.
(c) At least two real roots.
(d) Exactly two real roots.
Problem 7:
as x
is equal to
(a)
(b) 0
(c)
(d) 2
Problem 8:
where
runs from 1 to
as
is equal
(a) 0
(b)
(c) 2
(d) 1
Problem 9:
Let f: is given by
. Then,
(a) is
and onto
(b) is neither
nor onto
(c) is
but not onto
(d) is onto but not
Problem 10:
The last digit of is :
(a)
(b)
(c)
(d)
Problem 11:
The average scores of students in a test is
. The lowest score is
. Then the highest score is at most
(a)
(b)
(c)
(d)
Problem 12:
The coefficient of in the expansion of
is
(a)
(b)
(c)
(d)
problem 13:
Let be polynomials defined by
and
for
. Then
equals
(a)
(b)
(c)
(d)
Problem 14:
Suppose are matrices satisfying
. Then
is equal to
(a) 0
(b)
(c)
(d)
Problem 15:
The number of terms in the expansion of
is
(a)
(b)
(c)
(d)
Problem 16:
If are positive real numbers satisfying
,
then the maximum value of is
(a) 8
(b) 9
(c) 6
(d) 12
Problem 17:
If at least percent students in a class are good in sports, and at least
percent are good in music and at least
percent are good in studies, then the percentage of students who are good in all three is at least
(a)
(b)
(c)
(d)
Problem 18:
If , then
is
(a)
(b)
(c)
(d) 2/3
Problem 19:
Let Then
equals
(a)
(b) 2010
(c)
(d) None of the above
Problem 20:
If each side of a cube is increased by , then the surface area of the cube increased by
(a)
(b)
(c)
(d)
Problem 21:
If , then
(a)
(b)
(c)
(d) None of the above is true.
Problem 22:
The number of complex numbers w such that and imaginary part of
is 0 , is
(a) 4
(b) 2
(c) 8
(d) Infinite
Problem 23:
Let for all
Suppose
(summation is running from to
for all
. Then
(a)
(b)
(c)
(d)
Problem 24:
The number of points at which the function
) if
and
if
is not differentiable, is
(a) 1
(b) 0
(c) 2
(d) None of the above.
Problem 25:
The greatest value of function
(a)
(b)
(c)
(d)
problem 26:
Let (integration running from
to
for all
. Then
(a) is not differentiable.
(b) is constant.
(c) is increasing in
.
(d) is decreasing in
.
Problem 27:
Let be a continuous function which is positive for all
and
(first integration is running from 2 to 3 and second integration running from 0 to 2). Then
(a)
(b)
(c)
(d)
Problem 28:
Let be a continuous function. Let
for
. Then, the equation
has
(a) No solution.
(b) All points in as solutions.
(c) At least one solution.
(d) None of the above.
Problem 29:
Let be two angles. Then the equation
(a) Determines uniquely in terms of
(b) Gives two value of for each value of
(c) Gives more than two values of for each value of
(d) None of the above.
Problem 30:
Ten players are to pay a tennis tournament. The number of pairings for the first round is
(a)
(b)
(c)
(d)