Two rods of the same length and material transfer a given amount of heat in $12 \, s$,when they are joined in parallel. But when they are joined in series,then they will transfer the same amount of heat under the same conditions in ......... $s$.

$A$ vessel contains $1$ mole of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing $1$ mole of $He$ gas (molar mass $4$) at a temperature $2T$ has a pressure of:

$x=\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), y=\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right) \Rightarrow \frac{d y}{d x}$ is equal to

The figure shows three similar lamps $L_1, L_2$,and $L_3$ connected across a power supply. If the lamp $L_3$ fuses,how will the light emitted by $L_1$ and $L_2$ change?

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x^2-3x-1=0$,then $\alpha^{-2}+\beta^{-2}+\gamma^{-2}=$