For one mole of a van der Waal's gas when \(b=0\) and \(\mathrm{T}=300 \mathrm{~K}\), the PV vs, \(1 / \mathrm{V}\) plot is shown below. The value of the van der Waal's constant \(a\) (atm. liter \({ }^{2} \mathrm{~mol}^{-2}\) ) is :

Match the compounds in Column I with their characteristic test(s)/reactions(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

A gas described by van der Waals' equation

Using the data provided, calculate the multiple bond energy \(\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) of a \(\mathrm{C} \equiv \mathrm{C}\) bond in \(\mathrm{C}_{2} \mathrm{H}_{2}\). That energy is (take the bond energy of a \(\mathrm{C}-\mathrm{H}\) bond as \(350 \mathrm{~kJ} \mathrm{~mol}^{-1}\) ) \(2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HC}=\mathrm{CH}(\mathrm{g}) ; \Delta \mathrm{H}=\) \(225 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

In the given reaction scheme, $\mathbf{P}$ is a phenyl alkyl ether, $\mathbf{Q}$  is an aromatic compound; $\mathbf{R}$ and $\mathbf{S}$ are the major products.

The correct statement about $\mathbf{S}$ is

Among the following complexes \((K-P), \mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right](K)\),
\(\left[\right.\) Co \(\left.\left(\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_3(L), \mathrm{Na}_3\left[\mathrm{Co}(\mathrm{ox})_3\right](M)\),
\(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2(\mathrm{~N}) ; \mathrm{K}_2\left[\mathrm{Pt}(\mathrm{CN})_4\right](\mathrm{O})\) and \(\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]\left(\mathrm{NO}_3\right)_2(P)\)
the diamagnetic complexes are

The total number of compounds having at least one bridging oxo group among the molecules given below is
\(\text N _2\text O _5,\)\(\text P _4\text O _6,\)\(\text P _4\text O _8,\)\(\text H _4\text P _2\text O _5,\)\(\text H _5\text P _3\text O _{10},\) \(\text H _2\text S_2\text O _3,\text H _2\text S_2\text O _5\)

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Two plane harmonic sound waves are expressed by the equations.
\(\begin{aligned}
& y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\
& y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)
\end{aligned}\)
(All parameters are in MKS)
Question:
At \(x=0\) how many times the amplitude of \(y_1+y_2\) is zero in one second at \(x=0\) ?

Statement I In water, orthoboric acid behaves as a weak monobasic acid.
Statement II In water, orthoboric acid acts as proton donor.

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

What is the order of basicity among the following compounds?

A point source \(\mathrm{S}\) emits unpolarized light uniformly in all directions. At two points \(\mathrm{A}\) and \(\mathrm{B}\), the ratio \(r=I_A / I_B\) of the intensities of light is 2. If a set of two polaroids having \(45^{\circ}\) angle between their pass-axes is placed just before point \(\mathrm{B}\), then the new value of \(r\) will be ______

A closed vessel with rigid walls contains 1 mol of ${}_{92}{}^{238}\mathrm{U}$ and 1 mol of air at 298 K. Considering complete decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{P}\mathrm{b}$ , the ratio of the final pressure to the initial pressure of the system at 298 K is