Relations and Functions Test

Result

Relations and Functions Test - 62

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If $$f\left( x+\cfrac { 1 }{ x } \right) ={ x }^{ 3 }+\cfrac { 1 }{ { x }^{ 2 } } -4\left( { x }^{ 3 }+\cfrac { 1 }{ { x }^{ 2 } } \right) +13$$ then the value of $$f(2+\sqrt { 3 } )=$$

A
9

B
10

C
11

D
12

Solution
Question 2
1 / -0

Let $$\frac { d }{ dx } f(x)=\frac { { e }^{ sin\quad x } }{ x } .x>0.If\int _{ x }^{ 4 }{ \frac { 3 }{ x } { e }^{ sin{ x }^{ 3 } } } dx=F(k)-F(I)$$ then one of the possible value of K is

A
63

B
64

C
16

D
32
Question 3
1 / -0

If $$f\left( x \right) = \cos \left[ {{\pi ^{^2}}} \right]x + \cos \left[ { - {\pi ^{^2}}} \right]x,$$ then

A
$$f\left( {\frac{\pi }{4}} \right) = 2$$

B
$$f\left( { - \pi } \right) = 2$$

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

D
$$f\left( {\frac{\pi }{2}} \right) = -1$$

Solution
Question 4
1 / -0

If $$f(x)=cos(log,x),\quad then\quad f(x)f(x)-\cfrac { 1 }{ 2 } \left[ f\left( \cfrac { x }{ y } \right) +f(xy) \right] $$ has value

A
-1

B
1/2

C
-2

D
0

Solution
Question 5
1 / -0

Let $$A=\left\{ 1,2,3 \right\} ,\quad B=\left\{ 1,3,5 \right\} .$$ If relation R from A to B is given by $$R=\left\{ \left( 1,3 \right) ,\left( 2,5 \right) ,\left( 3,3 \right) \right\} .\quad Then\quad { R }^{ 1 }\quad is$$

A
$$\left\{ \left( 3,3 \right) ,\left( 3,1 \right) ,\left( 5,2 \right) \right\} $$

B
$$\left\{ \left( 1,2 \right) ,\left( 2,5 \right) ,\left( 3,3 \right) \right\} $$

C
$$\left\{ \left( 1,3 \right) ,\left( 5,2 \right) \right\} $$

D
None of these

Solution
Question 6
1 / -0

If $$2f\left( x \right) - 3f\left( {\frac{1}{x}} \right) = {x^2},x$$ is not equal to zero, then $$f(2)$$ is equal to -

A
$$ - \frac{7}{4}$$

B
$$\frac{5}{2}$$

C
$$-1$$

D
None of these

Solution
Question 7
1 / -0

For each positive integer $$n$$,let $$f\left( n+1 \right)=n{ \left( -1 \right) }^{ n+1 }-2f\left( n \right)$$ and $$f\left( 1 \right)=f\left( 2010 \right)$$. Then $$\sum _{ K=1 }^{ 2009 }{ f\left( K \right) }$$ is equal to

A
$$335$$

B
$$336$$

C
$$331$$

D
$$333$$

Solution
Question 8
1 / -0

Let $$f\left( x \right) = \frac{{\alpha x}}{{x + 1}},\,x \ne - 1$$. then for what value of $$f\left( {f\left( x \right)} \right) = x?$$

A
$$\sqrt 2 $$

B
$$ - \sqrt 2 $$

C
$$1$$

D
$$-1$$

Solution
Question 9
1 / -0

If $$f ( x ) = \cos ( \log x ) ,$$ then the value of $$f ( x ) \cdot f ( y ) - \dfrac { 1 } { 2 } \left\{ f ( x y ) + f \left( \dfrac { x } { y } \right) \right\}$$ equals

A
$$0$$

B
$$1$$

C
$$-1$$

D
Can't be determined

Solution

$$f(x)=\cos \log (x)$$
$$f(x) f(y)-\frac{1}{2}\left\{f(x y)+f\left(\frac{x}{y}\right)\right\}=$$
$$\cos \log (x) \cos \log (y)-\frac{1}{2}\left\{\cos \log (x y)+\cos \log \left(\frac{x}{y}\right)\right\}$$
$$\frac{1}{2}\left\{\cos \log (x y)+\cos \log \left(\frac{x}{y}\right)\right\}-\frac{1}{2}\left\{\cos \log (x y)+\cos \log \left(\frac{x}{y}\right)\right\}$$
$$=0$$
$$\therefore \quad 2 \cos A \cos B=\cos (A+B)+\cos (A-B)$$
Question 10
1 / -0

Let $$f(x)=(1+\sin x)(2+{\sin}^{2}x)....+(n+{\sin}^{n}x)$$, then $$f'(0)$$ is equal to

A
$$1$$

B
$$0$$

C
$$-1$$

D
None of these

Solution