The calculated magnetic moment (in Bohr magnetons) of $Cu^{2+}$ ion is

If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

The value of $x$ for the maximum value of $\sqrt{3} \cos x + \sin x$ is .....$^o$

If $\overrightarrow{a}=-\hat{i}+\hat{j}+2 \hat{k}$,$\overrightarrow{b}=2 \hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{c}=-2 \hat{i}+\hat{j}+3 \hat{k}$,then the angle between $2 \overrightarrow{a}-\overrightarrow{c}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

In a transistor,if $\frac{I_C}{I_E} = \alpha$ and $\frac{I_C}{I_B} = \beta$. If $\alpha$ varies between $\frac{20}{21}$ and $\frac{100}{101}$,then the value of $\beta$ lies between:

The internal energy of a monoatomic gas is $3 \ nRT$. $1$ mole of helium is kept in a cylinder having internal cross section area of $17 \ cm^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling $126 \ J$ heat. If the temperature rises by $4 \ ^\circ C$, then the piston will move $. . . . . . \ cm$.
(atmospheric pressure $= 10^5 \ Pa$)