The number of aldol reaction(s) that occurs in the given transformation is :

Statement 1 Aniline on reaction with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) at \(0^{\circ} \mathrm{C}\) followed by coupling with \(\beta\)-naphthol gives a dark coloured precipitate.
Statement 2 The colour of the compound formed in the reaction of aniline with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) at \(0^{\circ} \mathrm{C}\) followed by coupling with \(\beta\)-naphthol is due to the extended conjugation.

An aqueous solution of hydrazine \(\left(\mathrm{N}_2 \mathrm{H}_4\right)\) is electrochemically oxidized by \(\mathrm{O}_2\), thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is \(\mathrm{N}_2(\mathrm{~g})\).
Choose the correct statement(s) about the above process :

The conductance of $0.0015\mathrm{ }\mathrm{M}$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $\mathrm{Pt}$electrodes. The distance between the electrodes is $120\mathrm{ }\mathrm{cm}$ with an area of cross-section of $1 {\mathrm{cm}}^2$. The conductance of this solution was found to be $5\times {10}^{-7}\mathrm{S}$ . The $\mathrm{pH}$of the solution is $4$. The value of limiting molar conductivity of this weak monobasic acid in aqueous solution is $\mathrm{ }\mathrm{Z}\mathrm{ }\times \mathrm{ }{10}^2\mathrm{S}\mathrm{ }{\mathrm{cm}}^{-1}{\mathrm{mol}}^{-1}.$ The value of $\mathrm{Z}$is.

List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

The cyanide process of gold extraction involves leaching out gold from its ore with ${\mathrm{C}\mathrm{N}}^{-}$ in the presence of $\mathrm{Q}$ in water to form $\mathrm{R}$ . Subsequently, $\mathrm{R}$ is treated with $\mathrm{T}$ to obtain $\mathrm{A}\mathrm{u}$ and $\mathrm{Z}$ . Choose the correct option(s).

Liquids $\mathrm{A}$ and $\mathrm{B}$ form ideal solution for all compositions of $\mathrm{A}$ and $\mathrm{B}$ at ${25}^{\circ }C$. Two such solutions with $0.25$ and $0.50$ mole fractions of $\mathrm{A}$ have the total vapor pressures of $0.3$ and $0.4$ bar, respectively. What is the vapor pressure of pure liquid $\mathrm{B}$ in bar?

A student performed the experiment of determination of focal length of a concave mirror by \(u-v\) method using an optical bench of length \(1.5 \mathrm{~m}\). The focal length of the mirror used is 24 \(\mathrm{cm}\). The maximum error in the location of the image can be \(0.2 \mathrm{~cm}\).
The 5 sets of \((u, v)\) values recorded by the student (in \(\mathrm{cm})\) are : \((42,56),(48\), \(48),(60,40),(66,33),(78,39)\). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is(are)

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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:
When ammonia is added to the solution, \(\mathrm{pH}\) is raised to 11 . Which half-cell reaction is affected by \(\mathrm{pH}\) and by how much?

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There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of \(\mathrm{NH}_3\) and \(\mathrm{PH}_3\). Phosphine is a flammable gas and is prepared from white phosphorus.
Question:
Among the following, the correct statement is

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Let \(O\) be the origin, and \(\overrightarrow{O X}, \overrightarrow{O Y}, \overrightarrow{O Z}\) be three unit vectors in the directions of the sides \(\overrightarrow{Q R}, \overrightarrow{R P}\), \(\overrightarrow{P Q}\), respectively, of a triangle \(P Q R\).


Question:

If the triangle \(P Q R\) varies, then the minimum value of

\(\cos (P+Q)+\cos (Q+R)+\cos (R+P)\) is

Assuming $2\mathrm{s}\mathrm{ }–\mathrm{ }2\mathrm{p}$ mixing is NOT operative, the paramagnetic species among the following is

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Consider an evacuated cylindrical chamber of height \(h\) having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius \(r \ll h\). Now a high voltage source \((HV)\) is connected across the conducting plates such that the bottom plate is at \(+V_{0}\) and the top plate at \(-V_{0} .\) Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)



Question:

The average current in the steady state registered by the ammeter in the circuit will be