The period of  is

a)

b)

c)

d)

The domain of  is

a)  

b)  

c)  

d)  

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