If ${}^n C_{r-1}=330$,${}^n C_r=462$,and ${}^n C_{r+1}=462$,then $r$ is equal to

The angle of elevation of a stationary cloud from a point $2500 \ m$ above a lake is $15^{\circ}$ and from the same point the angle of depression of its reflection in the lake is $45^{\circ}$. The height (in metres) of the cloud above the lake,given that $\cot 15^{\circ}=2+\sqrt{3}$,is

$CO_2$ $(O-C-O)$ is a triatomic gas. The mean kinetic energy of one gram of the gas will be (where $N$ is Avogadro's number,$k$ is Boltzmann's constant,and the molecular weight of $CO_2 = 44$).

The specific resistance (resistivity) of material $B$ is twice that of material $A$. The diameter of a circular wire made of $B$ is twice that of a wire made of $A$. If the resistances of both wires are equal,then the ratio of their lengths $l_B/l_A$ will be .......

$A$ Carnot engine whose low temperature reservoir is at $7^{\circ} C$ has an efficiency of $50 \%$. It is desired to increase the efficiency to $70 \%$. By how many degrees should the temperature of the high temperature reservoir be increased? (in $K$)

The equations of motion of a projectile are given by $x = 36 t$ metre and $2 y = 96 t - 9.8 t^2$ metre. The angle of projection is: