The domain of  is

a)  

b)  

c)  

d)  

For all real values of x,  is

a)  ≤1

b)  ≤2

c)  >1

d)  >2

The period of the function

 is

a)

b)

c)

d) None of these

The domain of definition of the function   is

a) [1, 4]

b) [1, 0]

c) [0, 5]

d) [5, 0]

The domain of the function

a)

b)

c)

d) None of these

In a statistical investigation of 1003 families of Kolkata, it was found that 63 families have neither a radio nor a T.V. 794 families have a radio and 187 have a T.V. The number of families in the group having both a radio and a T.V. is

a) 36

b) 32

c) 41

d) None of these

A survey shows that 63% of Americans like cheese and 76% apples. If x% of Americans like both cheese and apples then

a)

b)

c)

d) None of these

If  where[x] denotes the integral part of x, then

a) f is one–one

b) f is not one–one and not a constant function

c) f is a constant function

d) None of the above

If  be two sequences given by  for all n  then  is equal to

a)

b)

c)

d)

The range of the function  is

a)

b)

c)

d) None of these

The relation  on the set {1, 2, 3} is

a) reflexive and not symmetric

b) reflexive but not transitive

c) neither symmetric nor transitive

d) symmetric and transitive

Let
and

then

a) 1

b) 0

c) 3

d) does not exist

The value of x in the given equation  is

a)

b)

c)

d)

The solution set of the inequality  is

a)

b) (1, 2)

c)

d)

Let  be a function defined as  is

a) One–one and into

b) One–one and onto

c) Many one and onto

d) Many one and into

Statement 1 – The number of real solutions of the equation   is zero
Statement 2 -

a) Statement 1 is false, Statement 2 is true

b) Statement 1 is true, Statement 2 is true. Statement 2 is correct explanation of Statement1

c) Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation of Statement1

d) Statement 1 is true, Statement 2 is false

If  then the value of k is

a)

b)

c)

d)

If  are in arithmetic progression whose common difference is α then the value of  is equal to

a)

b)

c)

d)

If  then f is

a) an increasing function

b) a decreasing function

c) both increasing and decreasing function

d) none of the above

Statement 1 – a, b, c ε ℝ and equations  and  have a common root, then
Statement 2 – If both roots of  and  are common then

a) Statement 1 is false, Statement 2 is true

b) Statement 1 is true, Statement 2 is true. Statement 2 is correct explanation of Statement1

c) Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation of Statement1

d) Statement 1 is true, Statement 2 is false

The period of the function   is

a)  

b)  

c)  

d)  

The number of roots of the equation  is

a) 1

b) 2

c) 0

d) Infinitely many

If  then  is equal to

a)

b)

c)

d) None of these