Kjeldahl's method was used for the estimation of nitrogen in an organic compound. The ammonia evolved from \(0.55\, g\) of the compound neutralised \(12.5\, mL\) of \(1\, M \,H _{2} SO _{4}\) solution. The percentage of nitrogen in the compound is \(.....\) (Nearest integer)

For the reaction, \( N_{2}O_{4}\rightleftharpoons 2NO_{2}, \) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is -5.40 kJ mol⁻¹.
B. As \( \Delta G^{\ominus} \) in graph is positive, \( N_{2}O_{4} \) will not dissociate into \( NO_{2} \) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \( N_{2}O_{4} \) changes into equilibrium mixture, value of \( \Delta G^{\ominus}=-0.84 \, kJ \, mol^{-1} \).
E. When 2 mole of \( NO_{2} \) changes into equilibrium mixture, \( \Delta G^{\ominus} \) for equilibrium mixture is -6.24 kJ mol⁻¹.

Choose the correct answer from the options given below:

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)

Given below are two statements:
Statement I: In the oxalic acid vs \(\mathrm{KMnO}_4\) (in the presence of dil \(\mathrm{H}_2 \mathrm{SO}_4\) ) titration the solution needs to be heated initially to \(60^{\circ} \mathrm{C}\), but no heating is required in Ferrous ammonium sulphate (FAS) vs \(\mathrm{KMnO}_4\) titration (in the presence of dil \(\mathrm{H}_2 \mathrm{SO}_4\) )
Statement II: In oxalic acid vs \(\mathrm{KMnO}_4\) titration, the initial formation of \(\mathrm{MnSO}_4\) takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs \(\mathrm{KMnO}_4\), heating oxidizes \(\mathrm{Fe}^{2+}\) into \(\mathrm{Fe}^{3+}\) by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options given below

Two elements \(A\) and \(B\) which form \(0.15\,moles\) of \(A _{2} B\) and \(AB _{3}\) type compounds. If both \(A _{2} B\) and \(A B_{3}\) weigh equally, then the atomic weight of \(A\) is \(....\) times of atomic weight of \(B\).

Fuel cell, using hydrogen and oxygen as fuels, \(A\). has been used in spaceship \(B\). has as efficiency of \(40 \%\) to produce electricity \(C\). uses aluminium as catalysts \(D\). is eco-friendly \(E\). is actually a type of Galvanic cell only

\(\mathrm{FeO}_4^{2-} \xrightarrow{+2.0 \mathrm{v}} \mathrm{Fe}^{3+} \xrightarrow{0.8 \mathrm{v}} \mathrm{Fe}^{2+} \xrightarrow{-0.5 \mathrm{v}} \mathrm{Fe}^0\)
In the above diagram, the standard electrode potentials are given in volts (over the arrow).
The value of \(\mathrm{E}_{\mathrm{FeO}_4^{2-} / \mathrm{Fe}^{2+}}^{\mathrm{O}}\) is _______.

Let \(P\) be the plane passing through the points \((5,3\), \(0),(13,3,-2)\) and \((1,6,2)\). For \(\alpha \in N\), if the distances of the points \(A (3,4, \alpha)\) and \(B (2, \alpha\), a) from the plane \(P\) are \(2\) and \(3\) respectively, then the positive value of a is

The number of elements in the set
\( S=\{x:x\in[0,100] \text{ and } \int_{0}^{x}t^{2}sin(x-t)dt=x^{2}\} \) is:

Let \(\left|z_1-8-2 i\right| \leq 1\) and \(\left|z_2-2+6 i\right| \leq 2, z_1, z_2 \in \mathbf{C}\). Then the minimum value of \(\left|z_1-z_2\right|\) is :

The \(AC\) voltage across a resistance can be measured using a

Let \(X=\{\mathrm{x} \in \mathrm{N}: 1 \leq \mathrm{x} \leq 17\}\) and \(\mathrm{Y}=\{\mathrm{ax}+\mathrm{b}: \mathrm{x} \in \mathrm{X}\) and \(\mathrm{a}, \mathrm{b} \in \mathrm{R}, \mathrm{a}>0\} .\) If mean and variance of elements of \(Y\) are \(17\) and \(216\) respectively then \(a + b\) is equal to 

For some \(\theta \in\left(0, \frac{\pi}{2}\right),\) if the eccentricity of the hyperbola, \(x^{2}-y^{2} \sec ^{2} \theta=10\) is \(\sqrt{5}\) times the eccentricity of the ellipse, \(x^{2} \sec ^{2} \theta+y^{2}=5,\) then the length of the latus rectum of the ellipse is