\(4.0\, L\) of an ideal gas is allowed to expand isothermally into vacuum until the total volume is \(20\, L.\) The amount of heat absorbed in this expansion is \(.....\,L\,atm\)

The correct set of four quantum numbers for the valence electron of rubidium atom \((Z=37)\) is _______.

Consider the following reactions. From these reactions which reaction will give carboxylic acid
as a major product ?
(A) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \mathrm{H}^{+} / \mathrm{H}_2 \mathrm{O}}\)
(B) \(\mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}\)
(C) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}\)
(D) \(\mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}\)
(E)

Choose the correct answer from the options given below:

The maximum number of possible oxidation states of actinoids are shown by

Number of moles of \(AgCl\) formed in the following reaction is \(........\).

\(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_{3}(\mathrm{~g})\) The above reaction is carried out in a vessel starting with partial pressure \(\mathrm{P}_{\mathrm{SO}_{2}}=250\, \mathrm{~m}\) \(bar,\) \(\mathrm{P}_{0_{2}}=750 \,\mathrm{~m}\) \(bar\) and \(\mathrm{P}_{\mathrm{SO}_{3}}=0 \,\mathrm{bar}\). When the reaction is complete, the total pressure in the reaction vessel is \(.....\mathrm{m}\) \(bar.\) (Round off to the Nearest Integer).

For the given reactions \(Sn ^{2+}+2 e ^{-} \rightarrow Sn\) \(Sn ^{4+}+4 e ^{-} \rightarrow Sn\) The electrode potentials are; \(E _{ Sn ^{2+} / Sn }^{\circ}=-0.140\, V\) and \(E _{ Sn ^{4+} / Sn }^{\circ}=0.010\, V\). The magnitude of standard electrode potential for \(Sn ^{4+} / Sn ^{2+}\) i.e. \(E _{ Sn ^{4+} / Sn ^{2+}}^{\circ}\) is \(.....\times 10^{-2}\, V\). (Nearest integer)

In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of sulphur in the compound is ______ \(\times 10^{-1} \%\).
(Molar mass : \(\mathrm{O}=16, \mathrm{~S}=32, \mathrm{Ba}=137\) in \(\mathrm{g} \mathrm{mol}^{-1}\) )

A small ball of mass \(m\) is thrown upward with velocity \(u\) from the ground. The ball experiences a resistive force \(mkv ^{2}\) where \(v\) is its speed. The maximum height attained by the ball is 

If \(y = y ( x )\) is the solution of the differential equation \(2 x^{2} \frac{d y}{d x}-2 x y+3 y^{2}=0 \quad\) such that \(y(e)=\frac{e}{3}\), then \(y(1)\) is equal to

Number of atoms in the following samples of substances is largest in

Two blocks of masses \(m\) and \(M\) are connected by means of a metal wire of cross-sectional area \(A\) passing over a frictionless fixed pulley as shown in the figure. The system is then released. If \(M = 2\, m\), then the stress produced in the wire is

A radio-active material is reduced to \(1 / 8\) of its original amount in \(3\) days. If \(8 \times 10^{-3}\,kg\) of the material is left after \(5\) days. The initial amount of the material is \(.......\,g\)