The reduction potential $\left({\mathrm{E}}^0\right.$, in $\left.\mathrm{V}\right)$ of ${\mathrm{MnO}}_4^{-}\left(\mathrm{aq}\right)/\mathrm{Mn}\left(\mathrm{s}\right)$ is
\(\left[\right.\)Given: \(E _{\left( MnO _4^{-}( aq ) / MnO _2(s)\right)}^{ o }=1.68 V ;\) \( E _{\left( MnO _2(s) / Mn ^{2+}( aq )\right)}^{ o }=\) \(1.21 V ; E _{\left( Mn ^{2+}( aq ) / Mn ( s )\right)}^{ o }\) \(=-1.03 V]\)
Truncate/round-off the value to TWO decimal places.

Statement I Glucose gives a reddish-brown precipitate with Fehling's solution.
Statement II Reaction of glucose with Fehling's solution gives \(\mathrm{CuO}\) and gluconic acid.

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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?

A reversible cyclic process for an ideal gas is shown below. Here, $P,V,\mathrm{a}\mathrm{n}\mathrm{d}T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q,w,H\mathrm{a}\mathrm{n}\mathrm{d}U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)

Ozonolysis of ${\mathrm{ClO}}_2$ produces an oxide of chlorine. The average oxidation state of chlorine in this oxide is ______ .

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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

The work function ( \(\Phi\) ) of some metals is listed below. The number of metals which will show photoelectric effect when light of \(300 \mathrm{~nm}\) wavelength falls on the metal is

The number of distinct solutions of the equation $\frac{5}{4}{\cos }^2\mathrm{ }2\mathrm{x}+{\cos }^4\mathrm{x}+{\sin }^4\mathrm{x}+{\cos }^6\mathrm{x}+{\sin }^6\mathrm{x}=2$ in the interval $[0,\mathrm{ }2\mathrm{\pi }]$ is

Let \(f_{1}:(0, \infty) \rightarrow \mathbb{R}\) and \(f_{2}:(0, \infty) \rightarrow \mathbb{R}\) be defined by

\[

f_{1}(x)=\int_{0}^{x} \prod_{j=1}^{21}(t-j)^{j} d t, \quad x > 0

\(

and

\]

f_{2}(x)=98(x-1)^{50}-600(x-1)^{49}+2450, \quad x > 0

\)

where, for any positive integer \(n\) and real numbers \(a_{1}, a_{2}, \ldots, a_{n}, \prod_{i=1}^{n} a_{i}\) denotes the product of \(a_{1}, a_{2}, \ldots, a_{n} .\) Let \(m_{i}\) and \(n_{i}\), respectively, denote the number of points of local minima and the number of points of local maxima of function \(f_{i}, i=1,2\), in the interval \((0, \infty)\).

The value of $6m_2+4n_2+8m_2{n}_2$ is ____.

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is

Consider the $6\times 6$ square in the figure. Let $A_1,A_2,\dots ,A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_i$ and $A_j$ are friends if they are adjacent along a row or along a column. Assume that each point $A_i$ has an equal chance of being chosen.



(There are two questions based on $\mathrm{PARAGRAPH} "\mathrm{II}"$, the question given below is one of them)

Let $p_i$ be the probability that a randomly chosen point has $i$ many friends, $i=0,1,2,3,4$. Let $X$ be a random variable such that for $i=0,1,2,3,4$, the probability $P(X=i)=p_i$. Then the value of $7 E\left(X\right)$ is

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An aqueous solution of a mixture of two inorganic salts, when treated with dilute \(H C\) ?, gave a precipitate \((\boldsymbol{P})\) and a filtrate \((\boldsymbol{Q})\). The precipitate \(\boldsymbol{P}\) was found to dissolve in hot water. The filtrate \((\boldsymbol{Q})\) remained unchanged, when treated with \(\mathrm{H}_{2} \mathrm{~S}\) in a dilute mineral acid medium. However, it gave a precipitate \((\boldsymbol{R})\) with \(H_{2} S\) in an ammoniacal medium. The precipitate \(\boldsymbol{R}\) gave a coloured solution \((\boldsymbol{S})\), when treated with \(\mathrm{H}_{2} \mathrm{O}_{2}\) in an aqueous \(\mathrm{NaOH}\) medium.

Question:
The precipitate \(\boldsymbol{P}\) contains

A straight line \(L\) through the point \((3,-2)\) is inclined at an angle \(60^{\circ}\) to the line \(\sqrt{3} x+y=1\). If \(L\) also intersects the \(X\)-axis, then the equation of \(L\) is