$A$ force acts on a $3\, g$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$,where $x$ is in $meters$ and $t$ is in $seconds$. The work done during the first $4\, seconds$ is .............. $mJ$.

Acidity of diprotic acids in aqueous solutions increases in the order

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ \AA}$. The maximum energy of a photon in the radiation in $eV$ is $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$. (in $27,500$)

An oil drop having a mass $4.8 \times 10^{-13} ~kg$ and charge $2.4 \times 10^{-18} ~C$ stands still between two charged horizontal plates separated by a distance of $1 ~cm$. If now the polarity of the plates is changed,the instantaneous acceleration of the drop is: $(g = 10 ~ms^{-2})$ (in $~ms^{-2}$)

$A$ 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:

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively. Their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $r_2/r_1 = ?$