Relations and Functions Test

Result

Relations and Functions Test - 56

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Weekly Quiz Competition

Question 1
1 / -0

If $$\dfrac {(2x+3)(3x-4)}{(x-1)(4x+5)}=f(x)-\dfrac {5i}{9(x-1)}+\dfrac {31}{18(4x+5)}$$, then $$f(x)=$$

A
$$1$$

B
$$\dfrac {1}{2}$$

C
$$\dfrac {-3}{2}$$

D
$$\dfrac {3}{2}$$

Solution
Question 2
1 / -0

Let $$f(x)$$ be a real function not identically zero in $$Z$$, such that $$f(x+y^{2n+1})=f(x)+(f(y))^{2n+1},\ n\ \epsilon \ N,\ xy\ \epsilon \ R$$. If $$f'(0)\ge 0$$ then $$f'(6)$$ is equal to

A
$$0$$

B
$$1$$

C
$$-1$$

D
$$None\ of\ these$$

Solution
Question 3
1 / -0

If $$A=\begin{pmatrix} \dfrac { -1+i\sqrt { 3 } }{ 2i } & \dfrac { -1-i\sqrt { 3 } }{ 2i } \\ \dfrac { 1+i\sqrt { 3 } }{ 2i } & \dfrac { 1-i\sqrt { 3 } }{ 2i } \end{pmatrix}, i=\sqrt{-1}$$ and $$f(x)=x^{2}+2$$. Then $$f(A)$$ equals

A
$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

B
$$\left( \dfrac { 3-i\sqrt { 3 } }{ 2 } \right) \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

C
$$\left( \dfrac { 5-i\sqrt { 3 } }{ 2 } \right) \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

D
$$\left( 2+i\sqrt { 3 } \right) \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

Solution
Question 4
1 / -0

Let $$f\left( x \right) =\begin{cases} { x }^{ 2 };\quad 0<x<2 \\ 2x-3;\quad 2\le x<3 \\ x+2;\quad x\ge 3 \end{cases}$$ Then:-

A
$$f\left\{ f\left( f\left( \dfrac { 3 }{ 2 } \right) \right) \right\} =f\left( \dfrac { 3 }{ 2 } \right) $$

B
$$1+f\left\{ f\left( f\left( \dfrac { 5 }{ 2 } \right) \right) \right\} =f\left( \dfrac { 2 }{ 2 } \right) $$

C
$$f\left\{ f\left( f\left( 1 \right) \right) \right\} =f\left( 1 \right) =1$$

D
$$none\ of\ these$$

Solution
Question 5
1 / -0

a real valued function $$f\left( x \right)$$ satisfied the functional equation $$f\left( x-y \right) =f\left( x \right) f\left( y \right) -f\left( a-x \right) f\left( a+y \right) $$ where a is given constant and $$f\left( 0 \right) =1,f\left( 2a-x \right) $$ is equal to:

A
$$f\left( -x \right) $$

B
$$f\left( a \right) +f\left( a-x \right) $$

C
$$f\left( x \right)$$

D
$$-f\left( x \right) $$

Solution
Question 6
1 / -0

Let $$f(x)$$ be a non-negative continuous function such that the area bounded by the curve $$y=f(x)$$, $$x$$-axis and the ordinates $$x=\dfrac { \pi }{ 4 }$$, $$x=\beta >\dfrac { \pi }{ 4 }$$ is $$\left( \beta \sin { \beta } +\dfrac { \pi }{ 4 } \cos { \beta +\sqrt { 2 } \beta -\dfrac { \pi }{ \sqrt { 2 } } } \right)$$. Then $$f\left( \dfrac { \pi }{ 2 } \right)$$ is:

A
$$\left( 1-\dfrac { \pi }{ 2 } -\sqrt { 2 } \right)$$

B
$$\left( 1-\dfrac { \pi }{ 4 } +\sqrt { 2 } \right)$$

C
$$\left( 1+\dfrac { \pi }{ 2 } -1 \right)$$

D
$$\left( 1-\dfrac { \pi }{ 2 } + \right)$$

Solution
Question 7
1 / -0

If $$g ( x ) = [ x ] + \sum _ { a = 1 } ^ { 2018 } \frac { x + a - [ x + a ] } { 2018 }$$ then $$g ( 100 ) = ( [ . ] G I F )$$

A
100

B
1

C
2018

D
0
Question 8
1 / -0

If $$f(x)+f(x+4)=f(x+2)+f(x+6) \forall x\epsilon R$$, and $$f(5)=10$$, then $$\sum _{ r=1 }^{ 100 }{ f\left( 5+8r \right) }$$ equal to

A
$$1000$$

B
$$100$$

C
$$10000$$

D
$$None$$

Solution
Question 9
1 / -0

The number of solutions of solutions of the equation: $${ x }^{ 3 }+\quad 2{ x }^{ 2 }\quad +\quad 5x\quad +\quad 2cosx\quad =\quad 0\quad in\quad \left[ 0,2\pi \right] $$ is:-

A
0

B
1

C
2

D
3
Question 10
1 / -0

If $$f(x)=ax^{4}-bx^{2}+x+5$$ and $$f(-3)=2$$, then $$f(3)$$is.

A
$$-5$$

B
$$-2$$

C
$$3$$

D
$$8$$

Solution