Match the anionic species given in Column I that are present in the ores(s) given in Column II.

Column I	Column II
A. Carbonate	P. Siderite
B. Sulphide	Q. Malachite
C. Hydroxide	R. Bauxite
D. Oxide	S. Calamine
	T. Argentite

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\(\mathbf{X}\) and \(\mathbf{Y}\) are two volatile liquids with molar weights of \(10 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(40 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Two cotton plugs, one soaked in \(\mathbf{X}\) and the other soaked in \(\mathbf{Y}\), are simultaneously placed at the ends of a tube of length \(L=24 \mathrm{~cm}\), as shown in the figure. The tube is filled with an inert gas at \(1\) atmosphere pressure and a temperature of \(300 \mathrm{~K}\). Vapours of \(\mathbf{X}\) and \(\mathbf{Y}\) react to form a product which is first observed at a distance \(\mathbf{d} \mathrm{~cm}\) from the plug soaked in \(\mathbf{X}\). Take \(\mathbf{X}\) and \(\mathbf{Y}\) to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.



Question:

The value of \(\mathbf{d}\) in \(\mathbf{c m}\) (shown in the figure), as estimated from Graham's law, is

For the identification of $\mathrm{\beta }$ -naphthol using dye test, it is necessary to use

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\mathrm{t}\mathrm{h}}$ orbit of the atom and List-II contains options showing how they depend on $n$ .
 

List - I	List - II
(I) Radius of the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{P}\right)$ $\propto n^{-2}$
(II) Angular momentum of the electron in the $n^{th}$ orbit	$\left(\mathrm{Q}\right)$ $\propto n^{-1}$
(III) Kinetic energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{R}\right)$ $\propto n^0$
(IV) Potential energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{S}\right)$ $\propto n^1$
	$\left(\mathrm{T}\right)$ $\propto n^2$
	$\left(\mathrm{U}\right)$ $\propto n^{1/2}$

Which of the following options has the correct combination considering List-I and List-II?

The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match List-I with List-II and choose the correct option.

	List I		List II
$\left(\mathrm{P}\right)$	Etard reaction	$1$	$\mathrm{Acetophenone} \stackrel{\mathrm{Zn}-\mathrm{Hg},\mathrm{HCl}}{\to }$
$\left(\mathrm{Q}\right)$	Gattermann reaction	$2$	$\mathrm{Toluene} \underset{\left(\mathrm{ii}\right) {\mathrm{SOCl}}_2 }{\overset{\left(\mathrm{i}\right) {\mathrm{KMnO}}_4, \mathrm{KOH},\mathbf{ }\mathrm{\Delta } }{\to }}$
$\left(\mathrm{R}\right)$	Gattermann-Koch reaction	$3$	$\mathrm{Benzene} \underset{\mathrm{Anhyd}. {\mathrm{AlCl}}_3}{\overset{{\mathrm{CH}}_3\mathrm{Cl}}{\to }}$
$\left(\mathrm{S}\right)$	Rosenmund reduction	$4$	$\mathrm{Aniline} \frac{{\mathrm{NaNO}}_2 /\mathrm{HCl}}{273-278 \mathrm{K}}$
		$5$	$\mathrm{Phenol} \stackrel{\mathrm{Zn},\mathrm{\Delta }}{\to }$

LIST-I contains compounds and LIST-II contains reactions

List - I	List - II
(I) \(H _2 O _2\)	(P) \(Mg \left( HCO _3\right)_2+ Ca\) \((OH)_2 \rightarrow\)
(II) \(Mg ( OH )_2\)	(Q) \(BaO _2+ H _2 SO _4 \rightarrow\)
(III) \(BaCl _2\)	(R) \(Ca \left( OH _2\right) 2\) \(+ MgCl _2 \rightarrow\)
(IV) \(CaCO _3\)	(S) \(BaO _2+ HCl \rightarrow\)
	(T) \(Ca \left( HCO _3\right)_2\) \(+ Ca ( OH )_2\)

Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option

Consider the following reactions (unbalanced)
$\mathrm{Z}\mathrm{n}+H\mathrm{o}\mathrm{t}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4\to \mathrm{G}+\mathrm{R}+\mathrm{X}$
$\mathrm{Z}\mathrm{n}+\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\to \mathrm{T}+\mathrm{Q}$
\(\text G +\text H _2\text S+ \text{NH} _4 \text{OH} \rightarrow\text Z ~(\)a precipitate\()+\text X +\text Y\)
Choose the correct option(s).

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Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehydes as depicted below.

Question:
Which one of the following reagents is used the above reaction?

If the distance between the plane \(A x-2 y+z=d\) and the plane containing the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} \quad\) and \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) is \(\sqrt{6}\), then \(|d|\) is

A block of weight $100\mathrm{}\mathrm{N}$ is suspended by copper and steel wires of same cross-sectional area $0.5\mathrm{}\mathrm{c}{\mathrm{m}}^2$ and, length $\sqrt{3}\mathrm{}\mathrm{m}$ and $1\mathrm{}\mathrm{m},$ respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are ${30}^{\mathrm{o}}$ and ${60}^{\mathrm{o}},$ respectively. If elongation in copper wire is $\left(\mathrm{\Delta }{\mathrm{l}}_{\mathrm{C}}\right)$ and elongation in steel wire is $\left(\mathrm{\Delta }{\mathrm{l}}_{\mathrm{S}}\right),$ then the ratio $\frac{\mathrm{\Delta }{\mathrm{l}}_{\mathrm{C}}}{\mathrm{\Delta }{\mathrm{l}}_{\mathrm{S}}}$ is _____.
[Young's modulus for copper and steel are $1\times {10}^{11}\mathrm{N}/{\mathrm{m}}^2$ and $2\times {10}^{11}\mathrm{N}/{\mathrm{m}}^2$ respectively]

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\(RCONH _2\) is converted into \(RNH _2\) by means of Hofmann bromamide degradation.

In this reaction, \(R \mathrm{CONHBr}\) is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.
Question:
Which is the rate determining step in Hofmann bromamide degradation?

Let M be a $2 \times 2$ symmetric matrix with integer entries. Then M is invertible if

Match the following.
 

	List – I		List – II
(A)	The number of polynomials f(x) with non – negative integer coefficients of degree $\le 2,$ satisfying f(0) =0 and $\underset{0}{\overset{1}{\int }}f\left(x\right)dx=1, is$	(P)	8
(B)	The number of point in the interval $\left[- \sqrt{13}, \sqrt{13}\right]$ at which $f\left(x\right)=\sin \left(x^2\right)+\cos \left(x^2\right)$ attains its maximum value, is	(Q)	2
(C)	$\underset{-2}{\overset{2}{\int }}\frac{3x^2}{\left(1+e^x\right)}dx$ equals	(R)	4
(D)	$\frac{\left(\underset{-\frac{1}{2}}{\overset{\frac{1}{2}}{\int }}\cos 2x .\log \left(\frac{1+x}{1-x}\right)dx\right)}{\left(\underset{0}{\overset{\frac{1}{2}}{\int }}\cos 2x .\log \left(\frac{1+x}{1-x}\right)dx\right)}$	(S)	0