Topic: Relations and Functions (Test 1)



Topic: Relations and Functions
Q.1
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

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Q.2
If f (x) =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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Q.3
The range of the function  is

A. [3, ∞∞)
B. [1/3,3]
C. none of these
D. R
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.4
If f(x) = ,then f (y) =

A. 1+x
B. 1-x
C. x
D. x-1
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.5
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.


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Q.6
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.


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Q.7
The minimum value of (x -α) (x – β) is
A. αβ
B. 14(αβ)2
C. 0
D. -14(αβ)2
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.8
If f(x) = then (fof) (2) is equal to
A. 3
B. 4
C. 2
D. 1
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.9
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.

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Q.10
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.

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