$A$ monoatomic gas is suddenly compressed to $(1/8)^{\text{th}}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is (given $\gamma = 5/3$).

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

The proton and neutron are collectively called as

The principal section of a glass prism is an isosceles triangle $ABC$ with $AB=AC$. The face $AC$ is silvered. $A$ ray of light is incident normally on the face $AB$ and after two reflections,it emerges from the base $BC$ perpendicular to the base. Angle $BAC$ of the prism is (in $^{\circ}$)

Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements,and let there be $m$ ordered pairs in $R$. Then