A P Prabhakaran Solutions for Chapter: Relations and Functions, Exercise 3: OBJECTIVE TYPE QUESTIONS

If $f:R\to R$ is a function with properties $f\left(x+y\right)=f\left(x\right).f\left(y\right)$ for all $x,y\in R$ and $f\left(1\right)=3$ then $f\left(4\right)$ is.

The domain of the function $f\left(x\right)=\sqrt{25-x^2}$ is

The set $B$ is the range of a constant function. Then, $n\left(B\right)$ equals

If $n(\mathrm{A}\cap \mathrm{B})=5$, then $n\left(\right(A\times B)\cap B\times A))$ is equal to

If $A=\left\{a,b,c\right\},B=\{2,3\},C=\{a,b,c,d\}$, then the number of elements in $(A\cup C)\times B$ is

The range of the function $f\left(x\right)=\frac{x}{1+x^2}$ is

 If $f:R\to R$ be defined by $f\left(x\right)=5x-\left|x\right|$, then $f\left(2x\right)-f(-x)-10x$ equals

$A$ and $B$ are two sets having $4$ and $6$ elements respectively and having $3$ elements in common. The number of relations that can be defined from $A$ to $B$ equals to