Consider the following sequence of reactions.

Total number of \(\mathrm{sp}^3\) hybridised carbon atoms in the major product C formed is ________.

Given below are two statements :
1 M aqueous solution of each of \(\mathrm{Cu}\left(\mathrm{NO}_3\right)_2, \mathrm{AgNO}_3\), \(\mathrm{Hg}_2\left(\mathrm{NO}_3\right)_2 ; \mathrm{Mg}\left(\mathrm{NO}_3\right)_2\) are electrolysed using inert electrodes,
\(\begin{aligned} & \text { Given : } \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^\theta=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Hg}_2^{2+} / \mathrm{Hg}}^\theta=0.79 \mathrm{~V}, \\ & \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^\theta=0.24 \mathrm{~V} \text { and } \mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^\theta=-2.37 \mathrm{~V}\end{aligned}\)
Statement (I) : With increasing voltage, the sequence of deposition of metals on the cathode will be \(\mathrm{Ag}, \mathrm{Hg}\) and Cu
Statement (II) : Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statement, choose the most appropriate answer from the options given below

\(2\) molal solution of a weak acid \(HA\) has a freezing point of \(3.885^{\circ} C\). The degree of dissociation of this acid is ........ \(\times 10^{-3} .\) (Round off to the Nearest Integer). [Given : Molal depression constant of water = \(1.85 \,K \,kg \,mol ^{-1}\) Freezing point of pure water \(\left.=0^{\circ} C \right]\)

Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with \(\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\) is _____.
\(\mathrm{Cu}^{2+}, \mathrm{Fe}^{3+}, \mathrm{Ba}^{2+}, \mathrm{Ca}^{2+}, \mathrm{NH}_4^{+}, \mathrm{Mg}^{2+}, \mathrm{Zn}^{2+}\)

Among the following, the energy of \(2s\) orbital is lowest in

The percentage dissociation of a salt \(\left(\mathrm{MX}_3\right)\) solution at given temperature (van't Hoff factor \(\mathrm{i}=\) 2) is ______ % (Nearest integer)

A variable, opposite external potential \((E_{ext})\) is applied to the cell \(Zn\,|\,Z{n^{2 + }}\,(1\,M)\,\,||\,\,C{u^{2 + }}\,(1\,M)\,|\,Cu,\) of potential \(1.1\,V.\) When \(E_{ext} < 1.1\,V\) and \(E_{ext} > 1.1\,V,\) respectively electrons flow from

\(A + 2B \to C\), the rate equation for this reaction is given as Rate \(= K[A][B]\) . If the concentration of \(A\) is kept the same but that of \(B\) is doubled what will happen to the rate it self ?

Two \(4\) bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output \((Y)\) will be:

If the mirror image of the point \(\mathrm{P}(3,4,9)\) in the line \(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((\alpha, \beta, \gamma)\), then \(14(\alpha+\beta+\gamma)\) is :

If \(\{ p \}\) denotes the fractional part of the number \(p\), then \(\left\{\frac{3^{200}}{8}\right\},\) is equal to

If the image of the point \((4,4,3)\) in the line \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}\) is \((\alpha, \beta, \gamma)\), then \(\alpha+\beta+\gamma\) is equal to

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is \(\frac{1}{4} .\) If the probability that at most two machines will be out of service on the same day is \(\left(\frac{3}{4}\right)^{3} \mathrm{k},\) then \(\mathrm{k}\) is equal to