Match each of the compounds given in Column I with the reaction (s) that they can undergo, given in Column II.

The correct statement(s) about O₃ is(are)

The nitrogen containing compound produced in the reaction of $\mathrm{H}\mathrm{N}{\mathrm{O}}_3$ with ${\mathrm{P}}_4{\mathrm{O}}_{10}$

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Tollen's reagent is used for the detection of aldehyde when a solution of \(\mathrm{AgNO}_3\) is added to glucose with \(\mathrm{NH}_4 \mathrm{OH}\) then gluconic acid is formed
\(\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \)
\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)\) \(+~2 \mathrm{H}^{+}+2 e^{-} ; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \)
\( \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; E_{\mathrm{red}}^{\circ}\) \(=0.337 \mathrm{~V}\)
[Use \(2.303 \times \frac{R T}{F}=0.0592\) and \(\frac{F}{R T}=38.92\) at \(298 \mathrm{~K}\)]
Question:
\(2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Ag}(\mathrm{s})\) \(+~\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_4+2 \mathrm{H}^{+}\). Find \(\ln \mathrm{K}\) of this reaction.

As per IUPAC nomenclature, the name of the complex \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}_{3}\) is :

Choose the correct statement(s) among the following.

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 $\mathrm{He}=4 \mathrm{g}{ \mathrm{mol}}^{-1}$)

In a neutral or faintly alkaline solution, $8$ moles of permanganate anion quantitatively oxidize thiosulphate anions to produce $\mathrm{X}$ moles of a sulphur containing product. The magnitude of $\mathrm{X}$ is:

A particle of mass $m$ is moving in the $xy$-plane such that its velocity at a point $(x, y)$ is given as $\overrightarrow{v}=\alpha \left(y\stackrel{\wedge }{x}+2x\stackrel{\wedge }{y}\right)$ where $\alpha$ is a non-zero constant. What is the force $\overrightarrow{F}$ acting on the particle?

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Read the following passage and answer the questions.
Question:
The value of \(\left[\begin{array}{lll}3 & 2 & 0\end{array}\right]\left[\begin{array}{l}3 \\ 2 \\ 0\end{array}\right]\) is

Among PbS, CuS, HgS, MnS, $\mathrm{A}{\mathrm{g}}_2\mathrm{S}$ , NiS, CoS, $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ and $\mathrm{S}\mathrm{n}{\mathrm{S}}_2$ , the total number of black coloured sulphides is

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If a continuous \(f\) defined on the real line \(R\), assume positive and negative values in \(R\), then the equation \(f(x)=0\) has a root in \(R\). For example, if it is known that a continuous function \(f\) on \(R\) is positive at some point and its minimum values is negative, then the equation \(f(x)=0\) has a root in \(R\).
Consider \(f(x)=k e^x-x\) for all real \(x\), where \(k\) is real constant.Question:
For \(k>0\), the set of all values of \(k\) for which \(k e^x-x=0\) has two distinct roots, 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