Question(s) from Search: IIT

Evaluate

a)

b)

c)

d)

Let [.] denotes the greatest integer function and

f(x) =  then

a)  does not exist

b) f (x) is continuous at x = 0

c) f (x) is not differentiable at x = 0

d)

Evaluate

a)

b)

c)

d)

 is

a) 2

b) – 2

c)

d)

Evaluate

a)

b)

c)

d)

For x ε R,  is equal to

a) e

b)

c)

d)

Evaluate if sin |x| - |x| is differentiable at x = 0.

a) Yes

b) No

Prove that  Hence or otherwise evaluate the integral .

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

The value of  is

a) 0

b) 1

c) 2

d) 4

For n > 0,  is

a)

b) π

c)

d)

Evaluate

a) 0

b)

c)

d) 1

Evaluate

a) 2asina

b) a²cosa

c) 2asina + a²cosa

d) 2a

For 2 ≤ r ≤ n,  is equal to

a)

b)

c)

d)

Let

Determine the function g (x) = f (f(x)) and hence find the points of discontinuity of g if any.

a) g(x) is continuous for all x except x = 1 and x = 2

b) g(x) is continuous for all x except x = 1

c) g(x) is continuous for all x except x = 2

d) g(x) is continuous for all x

Let f (x) be a continuous function satisfying  If  exists, find its value.

a) 0

b) 1

c) 2

d) 4

The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in the English dictionary. The number of words that appear before the word COCHIN is

a) 360

b) 192

c) 96

d) 48

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many different ways can we place the balls so that no box is empty?

Let

Test whether

f(x) is continuous at x = 0

f(x) is differentiable at x = 0

a) f(x) is differentiable and continuous at x = 0

b) f(x) is continuous but not differentiable at x = 0

c) f(x) is neither continuous nor differentiable at x = 0

A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select at least one book is 63, find the value of n?

Let p be a prime and m be a positive integer. By mathematical induction on m, or otherwise, prove that whenever r is an integer such that p does not divide r, p divides

P(x) is a polynomial function such that P(1) = 0, > P(x)

 x > 1. Then  x > 1,

a) P(x) > 0

b) P(x) = 0

c) P(x) < 1

Prove that

The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is .  .  .  .