Reaction of \(\mathbf{x}\) g of \(\mathrm{Sn}\) with \(\mathrm{HCl}\) quantitatively produced a salt. Entire amount of the salt reacted with \(\mathbf{y} g\) of nitrobenzene in the presence of required amount of \(\mathrm{HCl}\) to produce \(1.29 \mathrm{~g}\) of an organic salt (quantitatively).
(Use Molar masses (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of \(\mathrm{H}, \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{Cl}\) and \(\mathrm{Sn}\) as \(1,12,14,16,35\) and 119 , respectively).
The value of $\mathrm{y}$ is_________ .

Paragraph I: An organic compound \(\mathrm{P}\) with molecular formula \(\mathrm{C}_5 \mathrm{H}_{18} \mathrm{O}_2\) decolorizes bromine water and also shows positive iodoform test. \(\mathrm{P}\) on ozonolysis followed by treatment with \(\mathrm{H}_2 \mathrm{O}_2\) gives \(\mathrm{Q}\) and \(\mathrm{R}\). While compound \(\mathrm{Q}\) shows positive iodoform test, compound \(\mathrm{R}\) does not give positive iodoform test. \(\mathrm{Q}\) and \(\mathrm{R}\) on oxidation with pyridinium chlorochromate (PCC) followed by heating give \(\mathrm{S}\) and \(\mathrm{T}\), respectively. Both \(\mathrm{S}\) and \(\mathrm{T}\) show positive iodoform test.
Complete copolymerization of 500 moles of \(\mathrm{Q}\) and 500 moles of \(\mathrm{R}\) gives one mole of a single acyclic copolymer \(\mathrm{U}\).
[Given, atomic mass: \(\mathrm{H}=1, \mathrm{C}=12, \mathrm{O}=16\)]
Question: The molecular weight of \(\mathbf{U}\) is

Match the thermodynamic processes given under Column I with the expressions given under Column II.

	Column I		Column II
A.	Freezing of water at 273 K and 1 atm	P.	$\mathrm{q}=0$
B.	Expansion of 1 mol of an ideal gas into a vacuum under isolated conditions	Q.	$\mathrm{w}=0$
C.	Mixing of equal volumes of two ideal gases at constant temperature and pressure in an isolated container	R.	$\mathrm{\Delta }{\mathrm{S}}_{\mathrm{s}\mathrm{y}\mathrm{s}}<0$
D.	Reversible heating of ${\mathrm{H}}_2\left(\mathrm{g}\right)$ at 1 atm from 300 K to 600 K, followed by reversible cooling to 300 K at 1 atm	S.	$\mathrm{\Delta }\mathrm{U}=0$
		T.	$\mathrm{\Delta }\mathrm{G}=0$

One mole of an ideal gas is taken from \(a\) to \(b\) along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is \(W_s\) and that along the dotted line path is \(W_d\), then the integer closest to the ratio \(\frac{W_d}{W_s}\) is

The correct functional group \(X\) and the reagent/reaction conditions \(Y\) in the following schemes are \(\mathrm{X}-\left(\mathrm{CH}_2\right)_4-X\)

LIST-I contains reactions and LIST-II contains major products

List - I	List - II
(A)	(P)
(B)	(Q)
(C)	(R)
(D)	(S)
	(T)

Match each reaction in LIST-I with one or more products in LIST-II and choose the correct option

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
Question:
\(25 \mathrm{~mL}\) of household solution was mixed with \(30 \mathrm{~mL}\) of \(0.50\) M KI and \(10 \mathrm{~mL}\) of \(4 \mathrm{~N}\) acetic acid. In the titration of the liberated iodine, \(48 \mathrm{~mL}\) of \(0.25 \mathrm{~N~} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) was used to reach the end point. The molarity of the household bleach solution is

Let $\mathrm{y}\left(\mathrm{x}\right)$ be a solution of the differential equation $\left(1+{\mathrm{e}}^{\mathrm{x}}\right)\mathrm{ }{\mathrm{y}}^{\mathrm{\prime }}+\mathrm{y}{\mathrm{e}}^{\mathrm{x}}=1.$ If $\mathrm{y}\left(0\right)=2$ , then which of the following statements is (are) true?

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

For any real number \(x\), let \([x]\) denotes the largest integer less than or equal to \(x\). Let \(f\) be a real valued function defined on the interval \([-10,10]\) by \(f(x)=\left\{\begin{array}{cc}x-[x] & \text { if }[x] \text { is odd } \\ 1+[x]-x & \text { if }[x] \text { is even }\end{array}\right.\).
Then the value of \(\frac{\pi^2}{10} \int_{-10}^{10} f(x) \cos \pi x d x\) is

One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

There are three bags ${\mathrm{B}}_1,{\mathrm{B}}_2$ and ${\mathrm{B}}_3.$ The bag ${\mathrm{B}}_1$ contains $5$ red and $5$ green balls, ${\mathrm{B}}_2$ contains $3$ red and $5$ green balls, and ${\mathrm{B}}_3$ contains $5$ red and $3$ green balls, Bags ${\mathrm{B}}_1,{\mathrm{B}}_2$ and ${\mathrm{B}}_3$ have probabilities $\frac{3}{10},\frac{3}{10}$ and $\frac{4}{10}$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

For a radioactive material, its activity $\mathrm{A}$ and rate of change of its activity $\mathrm{R}$ are defined as $\mathrm{A}=-\frac{\mathrm{d}\mathrm{N}}{\mathrm{d}\mathrm{t}}$ and $\mathrm{R}=-\frac{\mathrm{d}\mathrm{A}}{\mathrm{d}\mathrm{t}}$ , where $\mathrm{N}\left(\mathrm{t}\right)$ is the number of nuclei at time $\mathrm{t}$ . Two radioactive sources $\mathrm{P}$ (mean life $\mathrm{\tau }$ ) and $\mathrm{Q}$ (mean life $2\mathrm{\tau }$ ) have the same activity at $\mathrm{t}=0$ . Their rates of change of activities at $\mathrm{t}=2\mathrm{\tau }$ are ${\mathrm{R}}_{\mathrm{P}}$ and ${\mathrm{R}}_{\mathrm{Q}}$ , respectively. If $\frac{{\mathrm{R}}_{\mathrm{P}}}{{\mathrm{R}}_{\mathrm{Q}}}=\frac{\mathrm{n}}{\mathrm{e}}$ , then the value of $\mathrm{n}$ is