When a ball is freely fallen from a given height,it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

If the bisectors of the pair of lines $x^2-2 m x y-y^2=0$ are represented by $x^2-2 n x y-y^2=0$,then

In a series resonant $LCR$ circuit,the voltage across $R$ is $100\,V$ and $R = 1\,k\Omega$ with $C = 2\,\mu F$. The resonant frequency $\omega$ is $200\,rad/s$. At resonance,the voltage across $L$ is:

Which of the following statements is true for an $N$-type semiconductor?

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is (in $^o$)