R D Sharma Solutions for Chapter: Continuity, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

Let $f\left(x\right)=\left|x\right|+|x-1|$, then 

Let $f\left(x\right)=\left\{\begin{array}{cl}\frac{x^4-5x^2+4}{\left|\left(x-1\right)\left(x-2\right)\right|},& x\ne 1,2\\ 6,& x=1\\ 12,& x=2\end{array}\right.$. Then, $f\left(x\right)$ is continuous on the set

If $f\left(x\right)=\left\{\begin{array}{l}\begin{array}{cll}\frac{\sin (a+1)x+\sin x}{x}& ,& x<0\\ c& ,& x=0\end{array}\\ \begin{array}{cll}\frac{{\left(x+b{x}^2\right)}^{{\displaystyle \frac{1}{2}}}-x^{\frac{1}{2}}}{b{x}^{{\displaystyle \frac{3}{2}}}}& ,& x>0\end{array}\end{array}\right.$ is continuous at $x=0$, then 

The value of $f\left(0\right)$, so that the function $f\left(x\right)=\frac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a+x}-\sqrt{a-x}}$  becomes continuous for all $x$, given by 

The function $f\left(x\right)=\left\{\begin{array}{l}1,\left|x\right|\ge 1\\ \frac{1}{n^2},\frac{1}{n}<\left|x\right|<\frac{1}{n-1},n=2,3,\dots \\ 0,x=0\end{array}\right.$

The value of $f \left(0\right),$ so that the function $f\left(x\right)=\frac{(27-2x{)}^{{\displaystyle \frac{1}{3}}}-3}{9-3(243+5x{)}^{{\displaystyle \frac{1}{5}}}}\left(x\ne 0\right)$ is continuous, is given by 

The value of $f \left(0\right),$ so that the function $f\left(x\right)=\frac{2-(256-7x{)}^{{\displaystyle \frac{1}{8}}}}{(5x+32{)}^{{\displaystyle \frac{1}{5}}}-2},x\ne 0$ is continuous, is given by 

If $f\left(x\right)=\left\{\begin{array}{ll}\frac{\sqrt{1+px}-\sqrt{1-px}}{x},& -1\le x<0\\ \frac{2x+1}{x-2},& 0\le x\le 1\end{array}\right.$, is continuous in the interval $\left[-1,1\right]$, then $p$ is equal to