The osmotic pressure of equimolar solutions of $BaCl_2, NaCl$ and glucose at the same temperature follows the order:

The coefficient of $x^5$ in the expansion of $(1 + x)^{21} + (1 + x)^{22} + \dots + (1 + x)^{30}$ is

Four positive point charges $+q$ are kept at the four corners of a square of side $l$. The net electric field at the mid-point of any one side of the square is (Take,$\frac{1}{4 \pi \varepsilon_0}=k$)

If $u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)$,then the value of $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is

The energy levels of a certain atom are $A, B,$ and $C$ in increasing order of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2,$ and $\lambda_3$ are the wavelengths of radiation corresponding to transitions $C \to B, B \to A,$ and $C \to A$ respectively,which of the following relations is correct?

$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\phi_{1}$ to $\phi_{2}$. The induced current in the circuit is: