If $A = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$,then the value of $\alpha$ for which $A^2 = B$ is

The mean and standard deviation of a binomial variate $X$ are $4$ and $\sqrt{3}$ respectively. Then $P(X \geq 1)$ is equal to

$A$ resistor of $2 \Omega$,an inductor of $100 \mu H$,and a capacitor of $400 pF$ are connected in series across a source of $e_{rms} = 0.1 \text{ V}$. At resonance,the voltage drop across the inductor is: (in $\text{ V}$)

$n$-Propyl alcohol and isopropyl alcohol can be chemically distinguished by which of the following reagents?

For the reaction $CH_{4(g)} + 2O_{2(g)} \rightleftharpoons CO_{2(g)} + 2H_2O_{(l)} \, \Delta H_r = -170.8 \, kJ \, mol^{-1}$,which of the following statements is not true?

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is