Match List \(I\) with List \(II\)

List \(I\) (Spectral Series for Hyddrogen)	List \(II\) (Spectral Region/Higher Energy State)
\(A\). Lyman	\(I\). Infrared region
\(B\). Balmer	\(II\). \(UV\) region
\(C\). Paschen	\(III\). Infrared region
\(D\). Pfund	\(IV\). Visible region

Choose the correct answer from the options given below :-

What is the correct order of acidity of the protons marked \(A-D\) in the given compounds?

The alkane from below having two secondary hydrogens is _______.

\(\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})\) is a first order reaction.
\(\begin{array}{|l|l|l|}\hline \text{Time} & T & \infty \\\hline \mathbf{P}_{\text {system }} & \mathrm{P}_{\mathrm{t}} & \mathrm{P}_{\infty} \\\hline\end{array}\)
The reaction was started with reactant A only. Which of the following expression is correct for rate constant k ?

Match List - \(I\) with List - \(II\):

List - \(I\) (Pair of Compounds)	List - \(II\) (Isomerism)
(\(A\)) n-propanol and Isopropanol	\((I)\) Metamerism
(\(B\)) Methoxypropane and ethoxyethane	\((II)\) Chain Isomerism
(\(C\)) Propanone and propanal	\((III)\) Position Isomerism
(\(D\)) Neopentane and Isopentane	\((IV)\) Functional Isomerism

Choose the correct answer from the options given below:

\(1.22\, \mathrm{~g}\) of an organic acid is separately dissolved in \(100 \,\mathrm{~g}\) of benzene \(\left(\mathrm{K}_{\mathrm{b}}=2.6\, \mathrm{~K}\, \mathrm{~kg} \,\mathrm{~mol}^{-1}\right)\) and \(100\, \mathrm{~g}\) of acetone \(\left(\mathrm{K}_{b}=1.7\, \mathrm{~K} \,\mathrm{~kg} \,\mathrm{~mol}^{-1}\right) .\) The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by \(0.17^{\circ} \mathrm{C}\). The increase in boiling point of solution in benzene in \({ }^{\circ} \mathrm{C}\) is \(\mathrm{x} \times 10^{-2}\). The value of \(\mathrm{x}\) is ..... .(Nearest integer) \([\) Atomic mass : \(\mathrm{C}=12.0, \mathrm{H}=1.0, \mathrm{O}=16.0]\)

The volume \((\text { in } \mathrm{mL})\) of \(0.125\; \mathrm{M}\; \mathrm{AgNO}_{3}\) required to quantitatively precipitate chloride ions in \(0.3\; \mathrm{g}\) of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) is \(^{\mathrm{M}}\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}=267.46 \;\mathrm{g} / \mathrm{mol}\) \(\mathrm{M}_{\mathrm{AgNO}_{3}}=169.87 \;\mathrm{g} / \mathrm{mol}\)

A process will be spontaneous at all temperatures if

The domain of the function \(\operatorname{cosec}^{-1}\left(\frac{1+\mathrm{x}}{\mathrm{x}}\right)\) is :

The distance of the point \((1, 0, 2)\) from the point of intersection of the line \(\frac{{x - 2}}{3} = \frac{{y + 1}}{4} = \frac{{z - 2}}{{12}}\)   and the plane \(x - y + z = 16\) is

Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
(B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
(C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

Choose the correct answer from the options given below :

In a coil of resistance \(8 \Omega\), the magnetic flux due to an external magnetic field varies with time as \(\phi=\frac{2}{3}\left(9- t ^{2}\right)\). The value of total heat produced in the coil, till the flux becomes zero, will be \(....J\)

Let, \(\alpha, \beta\) be the distinct roots of the equation \(\mathrm{x}^2-\left(\mathrm{t}^2-5 \mathrm{t}+6\right) \mathrm{x}+1=0, \mathrm{t} \in \mathrm{R}\) and \(\mathrm{a}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}\). Then the minimum value of \(\frac{\mathrm{a}_{2023}+\mathrm{a}_{2025}}{\mathrm{a}_{2024}}\) is