Match List \(I\) with List \(II\).

List \(I\)	List \(II\)
\(A\) van't Hoff factor, \(i\)	\(I\) Cryoscopic constant
\(B\) \(k _{ f }\)	\(II\) Isotonic solutions
\(C\) Solutions with same osmotic pressure	\(III\) \(\frac{Normal\,molar\,mass}{Abnormal\,molar\,mass}\)
\(D\) Azeotropes	\(IV\) Solutions with same composition of vapour above it

Choose the correct answer from the options given below :

\(\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{A} \xrightarrow{{4\,KO{H_1}{O_2}}}\mathop {2\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{B} }\limits_{(Green)}  + 2{H_2}O\) \(3\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{B} \xrightarrow{{4\,HCl}}\mathop {2C}\limits_{(Purple)}  + Mn{O_2} + 2{H_2}O\) \(3\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{C} \xrightarrow{{{H_2}O,KI}}2\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{A}  + 2KOH + \underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{D} \) In the above sequence of reactions, \(\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{A}\) and \(\underset{\raise0.3em\hbox{\)\smash{\scriptscriptstyle-}\(}}{D} \) ,  respectively are

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. \(\mathrm{A}+\mathrm{B} \underset{\text { Step } 3}{\text { Step } 1} \mathrm{C} \xrightarrow{\text { Step } 2} \mathrm{P}\) Some details of the above reaction are listed below.

Step	Rate constant\(\left(\sec ^{-1}\right)\)	Activation energy\(\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\)
\(1\)	\({k}_1\)	\(300\)
\(2\)	\({k}_2\)	\(200\)
\(3\)	\({k}_3\)	\(\mathrm{Ea}_3\)

If the overall rate constant of the above transformation (k) is given as \(\mathrm{k}=\frac{\mathrm{k}_1 \mathrm{k}_2}{\mathrm{k}_3}\) and the overall activation energy \(\left(E_2\right)\) is \(400 \mathrm{~kJ} \mathrm{~mol}^{-1}\), then the value of \(\mathrm{Ea}_3\) is _______ \(\mathrm{kJ} \mathrm{mol}^{-1}\). (nearest integer)

The most suitable reagent for the given conversion is

The correct order of stability of following carbocations is :

If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _______ nm. (Nearest integer)

The decreasing order of reactivity of the following compounds towards nucleophilic substitution \(\left( S _{ N }{ }^{2}\right)\) is :

The line \(12 x \,\cos \theta+5 y \,\sin \theta=60\) is tangent to which of the following curves?

Let \(\alpha, \beta\) be the roots of the equation \(x^2-\sqrt{2} x+2=0\). Then \(\alpha^{14}+\beta^{14}\) is equal to

Let a line \(L\) pass through the point \(P (2,3,1)\) and be parallel to the line \(x+3 y-2 z-2=0=x-y+2 z\). If the distance of \(L\) from the point \((5,3,8)\) is \(\alpha\), then \(3 \alpha^2\) is equal to \(......\).

The total change in the oxidation state of manganese involved in the reaction of \(KMnO _4\) and potassium iodide in the acidic medium is \(..........\).

An antenna is placed in a dielectric medium of dielectric constant \(6.25\). If the maximum size of that antenna is \(5.0\, mm\). it can radiate a signal of minimum frequency of \(GHz .\) (Given \(\mu_{ r }=1\) for dielectric medium)

A metal wire of resistance \(3\,\Omega \) is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle \(60^o\) at the centre, the equivalent resistance between these two points will be