Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.

	List – I		List – II
A.		P.
B.		Q.
C.		R.
D.		S.

Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists.

	List – I		List – II
A	Pathway P	P.
B.	Pathway Q	Q.
C.	Pathway R	R.
D.	Pathway S	S.

${}_{92}{}^{238}\mathrm{U}$ is known to undergo radioactive decay to form ${}_{82}{}^{206}\mathrm{Pb}$ by emitting alpha and bet a particles. A rock initially contained $68\times {10}^{-6}\mathrm{g}$ of ${}_{92}{}^{238}\mathrm{U}$. If the number of alpha particles that it would emit during its radioactive decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{Pb}$ in three half-lives is $\mathrm{Z}\times {10}^{18}$, then what is the value of $\mathrm{Z}$?

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Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.
A solution \(M\) is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is \(0.9\)
Given Freezing point depression constant of water \(\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\)
Freezing point depression constant of ethanol \(\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of water \(\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of ethanol \(\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Standard freezing point of water \(=273 \mathrm{~K}\)
Standard freezing point of ethanol \(=155.7 \mathrm{~K}\)
Standard boiling point of water \(=373 \mathrm{~K}\)
Standard boiling point of ethanol \(=351.5 \mathrm{~K}\)
Vapour pressure of pure water \(=328 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Vapour pressure of pure ethanol \(=40 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Molecular weight of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\)
Molecular weight of ethanol \(=46 \mathrm{~g} \mathrm{~mol}^{-1}\)
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

Question:
The freezing point of the solution \(M\) is

The treatment of galena with ${\mathrm{HNO}}_3$ produces a gas that is

Consider a reaction \(a G+b H \rightarrow\) products. When concentration of both the reactants \(G\) and \(H\) is doubled, the rate increases by eight times. However, when concentration of \(G\) is doubled keeping the concentration of \(H\) fixed, the rate is doubled. The overall order of the reaction is

The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compounds, is

A series LCR circuit is connected to a $45 \sin \left(\omega t\right)$ Volt source. The resonant angular frequency of the circuit is ${10}^5 \mathrm{rad} {\mathrm{s}}^{-1}$ and current amplitude at resonance is $I_0$. When the angular frequency of the source is $\omega =8\times {10}^4 \mathrm{rad} {\mathrm{s}}^{-1}$, the current amplitude in the circuit is $0.05 I_0$. If $L=50 \mathrm{mH}$, match each entry in List-$\mathrm{I}$ with an appropriate value from List-$\mathrm{II}$ and choose the correct option.

	List-$\mathrm{I}$		List-$\mathrm{II}$
$\mathrm{P}$	$I_0$ in $\mathrm{mA}$	$1$	$44.4$
$\mathrm{Q}$	The quality factor of the circuit	$2$	$18$
$\mathrm{R}$	The bandwidth of the circuit in $\mathrm{rad} {\mathrm{s}}^{-1}$	$3$	$400$
$\mathrm{S}$	The peak power dissipated at resonance in Watt	$4$	$2250$
		$5$	$500$

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In a mixture of \(\mathrm{H}-\mathrm{H}^{+}\)gas \(\left(\mathrm{He}^{+}\right.\)is singly ionised \(\mathrm{He}\) atom), \(\mathrm{H}\) atoms and \(\mathrm{He}^{+}\)ions are excited to their respective first excited states. Subsequently, \(\mathrm{H}\) atoms transfer their total excitation energy to \(\mathrm{He}^{+}\)ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Question:
The wavelength of light emitted in the visible region by \(\mathrm{He}^{+}\)ions after collisions with \(\mathrm{H}\) atoms is

For any integer $k,$ let ${\alpha }_k=\cos \left(\frac{k\pi }{7}\right)+i\sin \left(\frac{k\pi }{7}\right), where i= \sqrt{-1}.$ The value of the expression $\frac{\sum _{k=1}^{12}\left|{\alpha }_{k+1}-{\alpha }_k\right|}{\sum _{k=1}^3\left|{\alpha }_{4k-1}-{\alpha }_{4k-2}\right|}$ is

A rocket is moving in a gravity free space with a constant acceleration of $2\mathrm{}\mathrm{m}{\mathrm{s}}^{-2}$ along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of $0.3\mathrm{}\mathrm{m}{\mathrm{s}}^{-1}$ relative to the rocket. At the same time, another ball is thrown in - x direction with a speed of $0.2\mathrm{}\mathrm{m}{\mathrm{s}}^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other for the first time is

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta ={60}^{\mathrm{o}}$ (see Figure-$1$). The angle of minimum deviation for red light from the same prism is ${\delta }_{\min }={30}^{\mathrm{o}}$ (see Figure-$2$). The refractive index of the prism material for blue light is $\sqrt{3}$. Which of the following statement(s) is(are) correct?

\[
\text { Match the statements of Column I with values of Column II. }
\]