An inelastic ball is dropped from a height of $100 \ m$. Due to collision with the earth,$20 \%$ of its energy is lost. To what height will the ball rise?

If $\cos x = \tan y$,$\cot y = \tan z$ and $\cot z = \tan x$,then $\sin x$ equals to

Specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_v$ respectively. If $\gamma = \frac{C_p}{C_v}$ and $R$ is the universal gas constant,then $C_v$ is equal to:

Identify the blank spaces $a, b, c$ and $d$ given in the following table and select the correct answer.

Type of microbes	Scientific name	Commercial product
Bacterium	$a$	Clot buster
$b$	Aspergillus niger	Citric acid
Fungus	Trichoderma polysporum	$c$
Bacterium	$d$	Butyric acid

The largest muscle in the human body is

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is: