Given that the standard potentials \(\left(\mathrm{E}^{\circ}\right)\) of \(\mathrm{Cu}^{2+}{/ \mathrm{Cu}}\) and \(\mathrm{Cu}^{+}{/ \mathrm{Cu}}\) are \(0.34 \;\mathrm{V}\) and \(0.522 \;\mathrm{V}\) respectively, the \({E}^{\circ}\) of \({C u}^{2+}{/ {C u}^{+}}\) is

\(1\, \mathrm{~kg}\) of \(0.75\) molal aqueous solution of sucrose can be cooled up to \(-4^{\circ} \mathrm{C}\) before freezing. The amount of ice (in \(g\)) that will be separated out is .... . (Nearest integer) \(\left[\right.\) Given \(\left.: \mathrm{K}_{\mathrm{f}}\left(\mathrm{H}_{2} \mathrm{O}\right)=1.86\, \mathrm{~K}\, \mathrm{~kg}\, \mathrm{~mol}^{-1}\right]\)

Choose the correct name for compound given below:

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

In the above conversion of compound \(( X )\) to product \((Y)\), the sequence of reagents to be used will be:

White phosphorus reacts with thionyl chloride to give

For which of the following reactions, \(\Delta H\) is equal to \(\Delta U\) ?

Given a sequence of \(4\) numbers, first three of which are in \(G.P.\) and the last three are in \(A.P\). with common difference six. If first and last terms in this sequence are equal, then the last term is

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with \(3 m / s ^2\). At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is \(5 m / s\). The initial height of the aeroplane is ___________m.
\(\left( g =10 m / s ^2\right)\)

Let \(a_1, a_2, a_3, \ldots\) be in an arithmetic progression of positive terms. Let \(\mathrm{A}_{\mathrm{k}}=\mathrm{a}_1{ }^2-\mathrm{a}_2{ }^2+\mathrm{a}_3{ }^2-\mathrm{a}_4{ }^2+\ldots+\mathrm{a}_{2 \mathrm{k}-1}{ }^2-\mathrm{a}_{2 \mathrm{k}}{ }^2\). If \(\mathrm{A}_3=-153, \mathrm{~A}_5=-435\) and \(\mathrm{a}_1{ }^2+\mathrm{a}_2{ }^2+\mathrm{a}_3{ }^2=66\), then \(\mathrm{a}_{17}-\mathrm{A}_7\) is equal to ....................

The spin-only magnetic moment value of \(M ^{3+}\) ion (in gaseous state) from the pairs \(Cr ^{3+} / Cr ^{2+}\), \(Mn ^{3+} / Mn ^{2}, Fe ^{3+} / Fe ^{2+}\) and \(Co ^{3+} / Co ^{2+}\) that has negative standard electrode potential, is \(B.M...........\) [Nearest integer]

The position vector of a particle changes with time according to the relation \(\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 - 20{t^2}} \right)\hat j\). What is the magnitude of the acceleration at \(t = 1\) ?

Concentrated nitric acid is labelled as \(75 \%\) by mass. The volume in mL of the solution which contains 30 g of nitric acid is _______.
Given : Density of nitric acid solution is \(1.25 \mathrm{~g} / \mathrm{mL}\).