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Explore the Back-Story**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)

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