Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 66

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Let $A$ consists $5$ different elements and set $B$ consists $4$ different elements. Number of mapping which can be defined from set $A$ to set $B$ which are surjective, is

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Important Questions on Relation and Functions

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 67

If the equation

| x - 1 | - | x - 13 | = k

has exactly one solution, then number of integral values of

k

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 68

Let

g (x) = \sin^{2} (\ln x) + \cos^{2} (\ln x)

then sum of least integral value of domain of

g (x)

and the integral values in range of

g (x)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 69

Let

f (x) = \max . \{x^{2}, (1 - x)^{2}, 2 x (1 - x)\}

, where

0 \leq x \leq 1

then

f (\frac{1}{5}) + f (\frac{1}{2}) + f (\frac{1}{\sqrt{2}})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 70

The range of $f (x) = \sqrt{x - 1} + 2 \sqrt{3 - x}$ is $[a, b]$ then $a^{2} + b^{2}$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 1

If

f (x) = \ln (x^{2} + 7 | x | + 10)

is a single valued real function then the range of

f (x)

in its natural domain will be

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 2

If

f (x)

is a real valued function defined as

f (x) = \{\begin{matrix} \min \{| x |, \frac{1}{x^{2}}, \frac{1}{x^{3}}\}, & x \neq 0 \\ 1 & x = 0 \end{matrix}

then range of

f (x)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 3

Let

f : (- 1, \frac{- 1}{\sqrt{3}}) \to B

, be a function defined by

f (x) = \tan^{- 1} \frac{3 x - x^{3}}{1 - 3 x^{2}}

, then

f

is both one-one and onto when

B

is the interval

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 4

Let

f : R \to R

and

g : R \to R

be two one-one and. onto functions such that they are mirror images of each other about the line

y = a

. If

h (x) = f (x) + g (x),

then

h (x)

is