In the circuit shown in the given figure,the resistances $R_1$ and $R_2$ are respectively:

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at temperature $T \ K$. The piston of cylinder $A$ is free to move,while that of cylinder $B$ is held fixed. The same amount of heat $dQ$ is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in $B$ is (where $\gamma = \frac{C_{p}}{C_{v}}$):

If $\omega$ is a complex cube root of unity,then $(x+1)(x+\omega)(x-\omega-1)$ is equal to

The properties of $Li$ are similar to those of $Mg$. What is the reason for this?

$A$ beam of monochromatic light is incident at $i = 50^{\circ}$ on one face of an equilateral prism. If the angle of emergence is $e = 40^{\circ}$,then the angle of minimum deviation is:

Let $f: R \rightarrow R$ be a function such that $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+6, x \in R$,then $f(2)$ equals