Consider a helium $\left(\mathrm{He}\right)$ atom that absorbs a photon of wavelength $330 \mathrm{nm}$. The change in the velocity (in $\mathrm{cm} {\mathrm{s}}^{-1}$) of $\mathrm{He}$ atom after the photon absorption is ______ .
(Assume: Momentum is conserved when photon is absorbed.
Use: Planck constant $=6.6\times {10}^{-34} \mathrm{J} \mathrm{s}$, Avocados number $=6\times {10}^{23}{ \mathrm{mol}}^{-1}$, Molar mass of $\mathrm{He}=4 \mathrm{g}{ \mathrm{mol}}^{-1}$)

\(\mathrm{B}(\mathrm{OH})_3+\mathrm{NaOH} \rightleftharpoons \mathrm{NaBO}_2+\mathrm{Na}[\mathrm{B}\)\((\mathrm{OH})_4]+\mathrm{H}_2 \mathrm{O}\).
How can this reaction is made to proceed in forward direction?

The nitrogen oxide(s) that contain(s) N.N bond(s) is (are)

Paragraph:

The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond Strength. BDE is affected by \(s\)-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. BDEs for some bonds are given below:












Question:
Correct match of the \(\mathbf{C}-\mathbf{H}\) bonds (shown in bold) in Column \(\mathbf{J}\) with their BDE in Column \(\mathbf{K}\) is

On dissolving $0.5\mathrm{ }\mathrm{g}$ of a non-volatile non-ionic solute to $39\mathrm{ }\mathrm{g}$ of benzene, its vapor pressure decreases from $650\mathrm{ }\mathrm{m}\mathrm{m}\mathrm{ }\mathrm{H}\mathrm{g}$ to $640\mathrm{ }\mathrm{m}\mathrm{m}\mathrm{ }\mathrm{H}\mathrm{g}.$ The depression of freezing point of benzene (in $\mathrm{K}$ ) upon addition of the solute is _______
(Given data: Molar mass and the molal freezing point depression constant of benzene are $78\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ and $5.12\mathrm{ }\mathrm{K}\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1},$ respectively)

Dissolving $1.24 \mathrm{g}$ of white phosphorous in boiling $\mathrm{NaOH}$ solution in an inert atmosphere gives a gas $\mathrm{Q}$. The amount of ${\mathrm{CuSO}}_4$ (in $\mathrm{g}$) required to completely consume the gas $\mathrm{Q}$ is____
[Given: Atomic mass of
\(\text H =1,\text O =16, \text{Na} =23,\text P =31,\text S=32,\) \(\text{Cu} =63]\)

Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is

Paragraph :
A special metal \(S\) conducts electricity without any resistance. A closed wire loop, made of \(S\), does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius \(a\), with its center at the origin. A magnetic dipole of moment \(m\) is brought along the axis of this loop from infinity to a point at distance \(r(\gg a)\) from the center of the loop with its north pole always facing the loop, as shown in the figure below.

The magnitude of magnetic field of a dipole \(m\), at a point on its axis at distance \(r\), is \(\frac{\mu_{0}}{2 \pi} \frac{m}{r^{3}}\), where \(\mu_{0}\) is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, \(m_{1}\) and \(m_{2}\), separated by a distance \(r\) on the common axis, with their north poles facing each other, is \(\frac{k m_{1} m_{2}}{r^{4}}\), where \(k\) is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

Question :
The work done in bringing the dipole from infinity to a distance$r$from the centre of the loop by the given process is proportional to:

Which of the following combinations will produce ${\text{H}}_2$ gas?

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

	List-I		List-II
(I)	${10}^{-3} \mathrm{kg}$ of water $100 °\mathrm{C}$ is converted to steam at the same temperature, at a pressure of ${10}^5\mathrm{Pa}$. The volume of the system changes from ${10}^{-6}{\mathrm{m}}^3$ to ${10}^{-3}{\mathrm{m}}^3$ in the process. Latent heat of water $=2250 \mathrm{kJ} {\mathrm{kg}}^{-1}$	(P)	$2 \mathrm{kJ}$
(II)	$0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 \mathrm{K}$ undergoes an isobaric expansion to volume $3 V$. Assume $8.0 \mathrm{J} {\mathrm{mol}}^{–1} {\mathrm{K}}^{–1}$	(Q)	$7 \mathrm{kJ}$
(III)	One mole of a monoatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3}{\mathrm{m}}^3$ and pressure $2 \mathrm{kPa}$ to volume $\frac{V}{8}$.	(R)	$4 \mathrm{kJ}$
(IV)	Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \mathrm{kJ}$ of heat and undergoes isobaric expansion.	(S)	$5 \mathrm{kJ}$
		(T)	$3 \mathrm{kJ}$

Which one of the following options is correct?

Column-II gives certain systems undergoing a process. Column-I suggests changes in some of the parameters related to the system. Match the statements in Column-I to the appropriate process (es) from Column-II.

Reduction of the metal centre in aqueous permanganate ion involves

Let $f\left(x\right)=\frac{\sin \pi x}{x^2}, x>0.$
Let $x_1<x_2<x_3<\dots <x_n<\dots$ be all the points of local maximum of $f$ and $y_1<y_2<y_3<\dots <y_n<\dots$ be all the points of local minimum of $f.$
Then which of the following options is/are correct?