Relations and Functions Test

Result

Relations and Functions Test - 65

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Weekly Quiz Competition

Question 1
1 / -0

Events A and B associated with an experiment are said to be independent iff

A
$$P(A\bigcap B)=P(A)+P(B)$$

B
$$P(A\bigcap B)=P(A)P(B)$$

C
$$P(A\bigcap B)= \phi$$

D
None of these

Solution
Question 2
1 / -0

If $$f(x)=1+x+\dfrac { { x }^{ 2 } }{ 2 } +......+\dfrac { { x }^{ 100 } }{ 100 } ,$$ then I'(1) is equal to

A
$$\dfrac { 1 }{ 100 } $$

B
100

C
0

D
does not exist

Solution
Question 3
1 / -0

If $$h=\left\{ ((x,y),(x-y, x+y))/ x,y \epsilon N \right\} $$ is a relation on NxN, then domain of h

A
$$\left\{ (x,y):\quad x

B
$$\left\{ (x,y):\quad x\le y,x,y\epsilon N \right\} $$

C
$$\left\{ (x,y):\quad x>y,x,y\epsilon N \right\} $$

D
$$\left\{ (x,y):\quad x \ge y,x,y\epsilon N \right\} $$
Question 4
1 / -0

If y = f (x) = $$\dfrac{ax -+ b}{cx - a}$$, then x is equal to

A
1 /f (x)

B
1/ f (x)

C
yf (x)

D
f (y) s
Question 5
1 / -0

If $$f\left(x\right)+2f\left(1-x\right)={ x }^{ 2 }+2$$ , $$ \forall x\in R$$,then$$ f\left (x\right)=$$

A
$$-{ x }^{ 2 }+\dfrac{4x}{3}$$

B
1

C
$$\dfrac { 1 }{ 3 } { (x-2) }^{ 2 }$$

D
none

Solution
Question 6
1 / -0

If the Period of $$f(x)=\dfrac { cos\left( sin\left( nx \right) \right) }{ tan\left( \dfrac { x }{ n } \right) } ,n\epsilon N$$ is $$6\pi $$ , then n is equal to

A
3

B
2

C
6

D
1

Solution
Question 7
1 / -0

If $$A = \left \{1, 2, 3, 4, 5\right \}$$ then

A
The number of relation on $$A$$ is $$2^{25}$$

B
The number of relation on $$A$$ is $$2^{20}$$

C
The number of reflexive relation on $$A$$ is $$20^{20}$$

D
The number of reflexive relation on $$A$$ is $$2^{15}$$

Solution
Question 8
1 / -0

If $$A=\left\{1,2,4 \right\}$$, $$B=\left\{1,4,6,9 \right\}$$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by $$x$$ is greater than $$y$$. The rangle of $$R$$ is :

A
$$\left\{1,4,6,9 \right\} $$

B
$$\left\{4,6,9 \right\} $$

C
$$\left\{ 1 \right\} $$

D
none of these

Solution
Question 9
1 / -0

$$f(x)$$ is a linear function. If $$f(x)=-1$$ and $$f(2)=14$$ find the value of $$f(15)$$

A
$$214$$

B
$$201$$

C
$$213$$

D
$$209$$

Solution
Question 10
1 / -0

If $$f ( x ) = \log _ { a } x$$ and $$F ( x ) = a ^ { x } ,$$ then $$F [ f ( x ) ]$$ is

A
$$f [ F ( x ) ]$$

B
$$f [ F (2 x ) ]$$

C
$$F\left| f(2x) \right| $$

D
$$F [ ( x ) ]$$

Solution

$$\textbf{Step 1 : Find the required function}$$

$$\text{Given , } f(x) = \log_{a}{x} \text{ and }$$ $$ F(x) = a^x $$

$$\therefore F[f(x)] = F ( \log_{a}{x} ))$$
$$ = a^{\log_{a}{x}}$$
$$ = x $$ $$\boldsymbol{[\because e^{\log_{e}{a}} = a]}$$

$$\therefore f[F(x)] = f[ a^x] $$
$$ = \log_{a}{a^x} $$
$$ = x$$ $$\boldsymbol {[ \because \log_{e}{e^a} = a]}$$

$$\Rightarrow F[f(x)] = f [ F{x} ]$$

$$\textbf{Hence , option A is correct}$$