The thermal dissociation equilibrium of ${\mathrm{CaCO}}_3\left(\mathrm{s}\right)$ is studied under different conditions.
${\text{CaCO}}_3\left(s\right)\rightleftharpoons \text{CaO}\left(s\right)+{\text{CO}}_2\left(\text{g}\right)$
For this equilibrium, the correct statement(s) is/are

Calamine, malachite, magnetite and cryolite, respectively are:

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

Paragraph:

\(P\) and \(Q\) are isomers of dicarboxylic acid \(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{4}\). Both decolorize \(\mathrm{Br}_{2} / \mathrm{H}_{2} \mathrm{O}\). On heating, \(\boldsymbol{P}\) forms the cyclic anhydride.

Upon treatment with dilute alkaline \(\mathrm{KMnO}_{4}, \boldsymbol{P}\) as well as \(\boldsymbol{Q}\) could produce one or more than one from \(\boldsymbol{S}, \boldsymbol{T}\) and \(\boldsymbol{U}\).




Question:
Compounds formed from \(\boldsymbol{P}\) and \(\boldsymbol{Q}\) are, respectively

Among P, Q, R and S, the aromatic compound(s) is/are

The product formed in the reaction of $\mathrm{S}\mathrm{O}\mathrm{C}{\mathrm{l}}_2$ with white phosphorous is

In a galvanic cell, the salt bridge

The value of  $cot \left(\underset{\text{n}=1}{\overset{23}{\Sigma }}{\text{cot}}^{-1}\left(1+\underset{\text{k}=1}{\overset{\text{n}}{\Sigma }}2\text{k}\right)\right)$  is

Let $\omega$ be a complex cube root of unity with $\omega \ne 1$ and $\text{P}=\left[{\text{p}}_{\text{ij}}\right]$ be a n x n matrix with ${\text{p}}_{\text{ij}}={\omega }^{\text{i}+\text{j}}$. Then ${\text{P}}^2\ne 0$, when n =

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

The value of the integral \(\int_{-\pi / 2}^{\pi / 2}\left(x^{2}+\ln \frac{\pi+x}{\pi-x}\right) \cos x d x\) is

Paragraph:
Let \(p\) be an odd prime number and \(T_p\) be the following set of \(2 \times 2\) matrices
\[
T_p=\left\{A=\left[\begin{array}{ll}
a & b \\
c & a
\end{array}\right] ; a, b, c \in\{0,1,2, \ldots, p-1\}\right\}
\]Question:
The number of \(A\) in \(T_p\) such that the trace of \(A\) is not divisible by \(p\) but det \((A)\) is divisible by \(p\) is
[Note : The trace of a matrix is the sum of its diagonal entries.]

A right-angled prism of refractive index ${\mu }_1$ is placed in a rectangular block of refractive index ${\mu }_2$, which is surrounded by a medium of refractive index ${\mu }_3$, as shown in the figure. A ray of light $e$ enters the rectangular block at normal incidence. Depending upon the relationships between ${\mu }_1\text{, }{\mu }_2$ and ${\mu }_3$, it takes one of the four possible paths $ef, eg, eh$ or $ei$.

Match the paths in List $\mathrm{I}$ with conditions of refractive indices in List $\mathrm{II}$ and select the correct answer using the codes given below the lists:

	List I		List II
A.	$e\to f$	P.	${\mu }_1>\sqrt{2}{\mu }_2$
B.	$e\to g$	Q.	${\mu }_2>{\mu }_1\text{and}{\mu }_2>{\mu }_3$
C.	$e\to h$	R.	${\mu }_1={\mu }_2$
D.	$e\to i$	S.	${\mu }_2<{\mu }_1<\sqrt{2}{\mu }_2\text{and}{\mu }_2>{\mu }_3$