$A$ transformer is used to light a $140 \, W, 24 \, V$ lamp from a $240 \, V \, AC$ mains. The current in the main cable is $0.7 \, A$. The efficiency of the transformer is......$\%$

The product$(s)$ formed when $H_2O_2$ reacts with disodium hydrogen phosphate is

$A$ sinusoidal voltage of peak value $200\, V$ is connected to a diode and resistor $R$ in the circuit shown so that half-wave rectification occurs. If the forward resistance of the diode is negligible compared to $R$,the $rms$ voltage across $R$ is approximately.....$V$.

Identify the order in which the spin-only magnetic moment (in $BM$) increases for the following four ions:
$I. Fe^{2+}$
$II. Ti^{2+}$
$III. Cu^{2+}$
$IV. V^{2+}$

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \ mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $\alpha = 10 \times 10^{-6} \ K^{-1}$)

$A$ class has $15$ boys and $5$ girls. Suppose $3$ students are selected at random from the class. The probability that there are $2$ boys and $1$ girl is