If  be two arithmetic means and  be two geometric means between a and b then  is equal to

a)

b)

c)

d)

If α,  are roots of the equation  then the value of   is

a) 2

b) 0

c) 1

d) None of these

If  then

a)

b)

c)

d) None of these

Let a relation R be defined by  then  is

a)

b)

c)

d) None of these

Let

then for all x, f(g(x) ) is equal to

a) 0

b) 1

c) f(x)

d) g(x)

The function  by  is

a) One–one

b) Onto

c) Bijective

d) None of these

If then general value of  is

a)

b)

c)

d)

If  then  is equal to

a)  

b)  

c)  

d)  

The least integer satisfying  is

a) 2

b) 3

c) 4

d) None of these

In the polynomial  coefficient of  is

a)  5050

b)  –5050

c)  100

d)  99

For every natural number n,  is divisible by

a) 4

b) 6

c) 10

d) None of these

The greatest positive integer which divides  for all  is

a) 4

b) 120

c) 240

d) 24

Let the function f : ℝ  ℝ be defined by  then f is

a) One–one and onto

b) One–one but not onto

c) Onto but not one to one

d) Neither one–one nor onto

The number of solutions of the equation are

a) No solution

b) One solution

c) Two solutions

d) Infinitely many solutions

Consider the following relations

 x, y are real numbers and  for some rational numbers }
S = { m, n, p and q are integers such that n, q ≠ 0 and qm = pn }

Then

a) R is an equivalence relation but S is not an equivalence relation

b) Neither R nor S is an equivalence relation

c) S is an equivalence relation but R is not an equivalence relation

d) R and S are both equivalence relations

Let α and β are roots of the equation  then  is equal to

a) –2

b) –1

c) 1

d) 2

A person is to count 4500 currency notes. Let denotes the number of notes he counts in the  minutes. If  and   are in arithmetic progression with common difference –2 , then the time taken by him to count all notes is

a) 24 minutes

b) 34 minutes

c) 125 minutes

d) 135 minutes

Let f : ℝ  ℝ be a continuous function defined by  
Statement 1:   for some
Statement 2:   for all
 

a) Statement 1 is true. Statement 2 is a correct explanation of statement 1.

b) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation of statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true.

Let a, b, c be such that . If
  

Then the value of n is

a) Zero

b) Any even number

c) Any odd number

d) Any integer

If the roots of the equation  be imaginary, then for all real values of x,  is

a) greater than 4ab

b) less than 4ab

c) greater than –4ab

d) less than –4ab

For real x, let f(x) = x³ + 5x + 1, then

a) f is one – one but not onto ℝ

b) f is onto but not one – one

c) f is one to one and onto

d) f is neither one to one nor onto