The domain of the function is

**A. ** none of these.

**B. ** R

**C. ** { }

**D. ** {2 n π: n ∈ I}

**Answer : ****Option D**

**Explaination / Solution: **

This function exists only if cosx−1≥0 ⇒cosx≥1 ⇒cosx>1 OR cosx=1 since maximum value of cosine function is 1 so, cos x >1 is not possible

This function exists only if cosx−1≥0 ⇒cosx≥1 ⇒cosx>1 OR cosx=1 since maximum value of cosine function is 1 so, cos x >1 is not possible

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If f (x) =, then domain of fof is

**A. ** (−∞,∞)

**B. ** (−∞,0)

**C. ** none of these

**D. ** (0,∞)

**Answer : ****Option C**

**Explaination / Solution: **

is defined only if

will be non negative.

Hence is defined only for 0.

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The range of the function is

No Explaination.

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If f(x) = then f (y) =

No Explaination.

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If f : R R is given by f (x) = | x | and , then equals

**A. ** R

**B. ** A U {0}

**C. ** ϕ

**D. ** A

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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For all x ∈ (0, 1)

**A. ** loge(1+x)<x
**B. ** sin x >> x

**C. ** ex<1+x
**D. ** logex>x
**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The minimum value of (x -α) (x – β) is

**A. ** αβ

**B. ** 14(α−β)2
**C. ** 0

**D. ** -14(α−β)2
**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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If f(x) = then (fof) (2) is equal to
**A. ** 3

**B. ** 4

**C. ** 2

**D. ** 1

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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A relation R in a set A is called universal relation, if

**A. ** one element of A is related to all elements of A

**B. ** each element of A is related to every element of A

**C. ** every element of A is related to one element of A

**D. ** no element of A is related to any element of A

**Answer : ****Option B**

**Explaination / Solution: **

The relation R = A x A is called Universal relation.

The relation R = A x A is called Universal relation.

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Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following is a function from A to B?

**A. ** {(0, 3), (2, 4)}

**B. ** {(1, 3), (2, 3), (3, 3)}

**C. ** {(1, 2), (2, 3), (3, 4), (3, 2)}

**D. ** {(1, 2), (1, 3), (2, 3), (3, 3)}

**Answer : ****Option B**

**Explaination / Solution: **

{(1, 3), (2, 3), (3, 3)} is a function ,because for each x ∈ A , there is a unique y ∈ B such that ( x , y) ∈f., i.e. xfy.

{(1, 3), (2, 3), (3, 3)} is a function ,because for each x ∈ A , there is a unique y ∈ B such that ( x , y) ∈f., i.e. xfy.

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