Relations and Functions Test

Result

Relations and Functions Test - 61

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Weekly Quiz Competition

Question 1
1 / -0

If $ A $ is a finite set containing n distinct elements, then the number of relations on A is equal to

A
$$ 2^{n} $$

B
$$ 2^{n^{2}} $$

C
$$ 2^{2} $$

D
none of these

Solution
Question 2
1 / -0

Let $$f\left( n \right) =1+\frac { 1 }{ 2 } +\frac { 1 }{ 3 } +....+\frac { 1 }{ n } .\quad Then\quad f\left( 1 \right) +f\left( 2 \right) +f\left( 3 \right) +......+f\left( n \right) \quad is\quad equal\quad to$$

A
$$nf\left( n \right) -1$$

B
$$\left( n+1 \right) f\left( n \right) -n$$

C
$$\left( n+1 \right) f\left( n \right) +n$$

D
$$nf\left( n \right) +n$$

Solution
Question 3
1 / -0

If $$f(x + \frac 1 2) + f(x - \frac 1 2) = f(x)$$,$$\forall\ x\ \epsilon\ R$$, then $$f(x-3) + f(x + 3)$$ is equal to

A
$$f(x)$$

B
$$2f(x)$$

C
$$0$$

D
$$6f(x)$$

Solution
Question 4
1 / -0

If $$f(x)=\cfrac { 1 }{ \sqrt { x+2\sqrt { 2x-4 } } } +\cfrac { 1 }{ \sqrt { x-2\sqrt { 2x-4 } } } $$ for x > 2, then $$f(11)=$$

A
7/6

B
5/6

C
6/7

D
5/7
Question 5
1 / -0

If n(A)=5 then number of relation on 'A' is:

A
$${ 2 }^{ 5 }$$

B
$${ 2 }^{ 25 }$$

C
$${ 5 }^{ 2 }$$

D
none
Question 6
1 / -0

If $$p,q$$ be non-zero real numbers and $$f\left(x\right)\neq 0$$ in $$\left[0,2\right]$$ and $${\int}_{0}^{1}f\left(x\right).\left(x^{2}+px+q\right)dx={\int}_{0}^{2}f\left(x\right).\left(x^{2}+px+q\right)dx=0$$ then equation $$x^{2}+px+q=0$$ has

A
Two imaginary roots

B
No root in $$\left(0,2\right)$$

C
One root in $$\left(0,1\right)$$ and other in $$\left(1,2\right)$$

D
One root in $$\left(-\infty,0\right)$$ and other in $$\left( 2,\infty\right)$$

Solution
Question 7
1 / -0

Let $$f(n)=2cosnx\forall n\epsilon N$$, then $$f(1)f(n+1)-f(n)$$ is equal to

A
$$f(n+3)$$

B
$$f(n+2)$$

C
$$f(n+1)f(2)$$

D
$$f(n+2)f(2)$$

Solution
Question 8
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 9
1 / -0

A non-zero function $$f (x)$$ is symmetrical about the line $$y = x$$ then the value of $$\lambda$$ such that:
$${ f }^{ 2 }(x)=({ f }^{ -1 }x))^{ 2 }-\lambda xf(x){ f }^{ -1 }(x)+3{ x }^{ 2 }f(x)\forall x\in R$$ is

A
1

B
2

C
3

D
4

Solution
Question 10
1 / -0

Let $$f:(0, \infty) \rightarrow R $$ and $$\int^{2x}_0 (1+t)f(t) dt =-2x^3-\dfrac{x^2}{2} +2x+K$$, where K is constant , then $$\Sigma^8_{r=1} f(r)$$ is equal to

A
$$43$$

B
$$57$$

C
$$28$$

D
$$35$$

Solution