Which of the following compounds will exhibit geometrical isomerism ?

A substance ' X ' \((1.5 g)\) dissolved in 150 g of a solvent ' Y ' (molar mass \(=300 g mol ^{-1}\) ) led to an elevation of the boiling point by 0.5 K . The relative lowering in the vapour pressure of the solvent ' Y ' is __________ \(\times 10^{-2}\). (Nearest integer) [Given : \(K _{ b }\) of the solvent \(=5.0 K kg mol ^{-1}\) ] Assume the solution to be dilute and no association or dissociation of X takes place in solution.

Choose the correct tests with respective observations.
(A) \(\mathrm{CuSO}_4\) (acidified with acetic acid) \(+ \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Chocolate brown precipitate.
(B) \(\mathrm{FeCl}_3+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Prussian blue precipitate.
(C) \(\mathrm{ZnCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with \(\mathrm{NH}_4 \mathrm{OH}\) \(\rightarrow\) White or bluish white precipitate.
(D) \(\mathrm{MgCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Blue precipitate.
(E) \(\mathrm{BaCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with NaOH \(\rightarrow\) White precipitate.
Choose the correct answer from the options given below :

The electrode potential of the following half cell at \(298\,K\) \(X \left| X ^{2+}(0.001 M ) \| Y ^{2+}(0.01 M )\right| Y\) is \(.......\times 10^{-2} V\) (Nearest integer). Given: \(E _{ x ^{2+} \mid x }^0=-2.36\,V\) \(E _{ Y ^{3+} \mid Y }^0=+0.36\,V\) \(\frac{2.303\,RT }{ F }=0.06\,V\)

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). Assertion \((A)\) : Haloalkanes react with \(\mathrm{KCN}\) to form alkyl cyanides as a main product while with \(\mathrm{AgCN}\) form isocyanide as the main product. Reason \((R)\) : \(\mathrm{KCN}\) and \(\mathrm{AgCN}\) both are highly ionic compounds. In the light of the above statement, choose the most appropriate answer from the options given below:

\(A ( g ) \rightarrow 2 B ( g )+ C ( g )\) is a first order reaction. The initial pressure of the system was found to be \(800\,mm\,Hg\) which increased to \(1600\,mm\,Hg\) after \(10\,min\). The total pressure of the system after \(30\,min\) will be \(.........\,mm\,Hg\). (Nearest integer)

The vapour pressures of \(A\) and \(B\) at \(25^{\circ} \mathrm{C}\) are \(90\, \mathrm{~mm}\, \mathrm{Hg}\) and \(15\, \mathrm{~mm} \,\mathrm{Hg}\) respectively. If \(\mathrm{A}\) and \(\mathrm{B}\) are mixed such that the mole fraction of \(A\) in the mixture is \(0.6\), then the mole fraction of \(B\) in the vapour phase is \(x \times 10^{-1}\). The value of \(x\) is \(.....\) (Nearest integer)

At \(1990\, K\) and \(1\, atm\) pressure, there are equal number of \(Cl _{2}\) molecules and \(Cl\) atoms in the reaction mixture. The value \(K _{ P }\) for the reaction \(Cl _{2( g )} \rightleftharpoons 2 \,Cl _{( g )}\) under the above conditions is \(x \times 10^{-1}\) The value of \(x\) is .......... (Rounded of to the nearest integer)

An inductor of \(10\, {mH}\) is connected to a \(20\, {V}\) battery through a resistor of \(10\, {k}\, \Omega\) and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after \(1\, \mu\, {s}\) is \(\frac{{x}}{100}\, {mA}\). Then \({x}\) is equal to ...... . (Take \(\left.{e}^{-1}=0.37\right)\)

Given below are two statements:
Statement I: Due to increase in van der Waals forces, the order of boiling points is CH\(_3\)CH\(_2\)CH\(_2\)I > CH\(_3\)CH\(_2\)I > CH\(_3\)I.
Statement II: As para-dichlorobenzene is more symmetric, its melting point is higher than ortho-dichlorobenzene, however its boiling point is lower than ortho-dichlorobenzene.
In the light of the above statements, choose the correct answer from the options given below:

If the area of the region bounded by the curves \(y=4-\frac{x^2}{4}\) and \(y=\frac{x-4}{2}\) is equal to \(\alpha\), then \(6 \alpha\) equals

The number of optical isomers possible for \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) is ..... .

If the point \(\left(\alpha, \frac{7 \sqrt{3}}{3}\right)\) lies on the curve traced by the mid-points of the line segments of the lines \(x\) \(\cos \theta+ y \sin \theta=7, \theta \in\left(0, \frac{\pi}{2}\right)\) between the coordinates axes, then \(\alpha\) is equal to