The decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\stackrel{ ∆ }{\to }2{\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$ is started in a closed cylinder under the isothermal isochoric condition at an initial pressure of $1 \mathrm{atm}$. After $\mathrm{Y}\times {10}^3\mathrm{ }\mathrm{s}$ , the pressure inside the cylinder is found to be $1.45\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{m}$ . If the rate constant of the reaction is $5\times {10}^{-4}{\mathrm{s}}^{-1}$, assuming ideal gas behaviour, the value of $\mathrm{Y}$ is

A sample \((5.6 \mathrm{~g})\) containing iron is completely dissolved in cold dilute \(\mathrm{HCl}\) to prepare a \(250 \mathrm{~mL}\) of solution. Titration of \(25.0 \mathrm{~mL}\) of this solution requires \(12.5 \mathrm{~mL}\) of \(0.03 \mathrm{M} \mathrm{KMnO}_{4}\) solution to reach the end point. Number of moles of \(\mathrm{Fe}^{2+}\) present in \(250 \mathrm{~mL}\) solution is \(\mathbf{x} \times 10^{-2}\) (consider complete dissolution of \(\mathrm{FeCl}_{2}\) ). The amount of iron present in the sample is \(\mathbf{y} \%\) by weight.
(Assume: \(\mathrm{KMnO}_{4}\) reacts only with \(\mathrm{Fe}^{2+}\) in the solution Use: Molar mass of iron as \(56 \mathrm{~g} \mathrm{~mol}^{-1}\) )
The value of $\mathrm{x}$ is________ .

The correct stability order for the following species is

The product formed in the reaction of $\mathrm{S}\mathrm{O}\mathrm{C}{\mathrm{l}}_2$ with white phosphorous is

Paragraph:
Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper include chalcanthite \(\left(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\right)\), atacamite \(\left(\mathrm{Cu}_2 \mathrm{Cl}(\mathrm{OH})_3\right)\), cuprite \(\left(\mathrm{Cu}_2 \mathrm{O}\right)\), copper glance \(\left(\mathrm{Cu}_2 \mathrm{~S}\right)\) and malachite \(\left(\mathrm{Cu}_2(\mathrm{OH})_2 \mathrm{CO}_3\right)\). However, 80\% of the world copper production comes from the ore chalcopyrite \(\left(\mathrm{CuFeS}_2\right)\). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.
Question:
In self-reduction, the reducing species is

Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists.

	List – I		List – II
A	Pathway P	P.
B.	Pathway Q	Q.
C.	Pathway R	R.
D.	Pathway S	S.

5.00 mL of 0.10 M oxalic acid solution taken in a conical flask is titrated against NaOH from a burette using phenolphthalein indicator. The volume of NaOH required for the appearance of permanent faint pink color is tabulated below for five experiments. What is the concentration, in molarity, of the NaOH solution?

Exp. No.	Vol. of NaOH (mL)
1	12.5
2	10.5
3	9.0
4	9.0
5	9.0

Paragraph :
Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature \(T_C(0)\). An interesting property of superconductors is that their critical temperature becomes smaller than \(T_C(0)\) if they are placed in a magnetic field i.e., the critical temperature \(T_C(B)\) is a function of the magnetic field strength \(B\). The dependence of \(T_C(B)\) on \(B\) is shown in the figure.

Question :
A superconductor has \(T_C(0)=100 \mathrm{~K}\). When a magnetic field of \(7.5\) Tesla is applied, its \(T_C\) decreases to \(75 \mathrm{~K}\). For this material one can definitely say that when (Note : \(\mathrm{T}\) = Tesla)

The correct acidity order of the following is

The total number of lone pairs of electrons in melamine is 

Which of the following is (are) NOT the square of a $3\times 3$ matrix with real entries?

Statement I The formula connecting \(u, v\) and \(f\) for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Statement II Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

A particle moves in the \(X-Y\) plane under the influence of a force such that its linear momentum is \(\mathbf{p}(t)=A[\hat{\mathbf{i}} \cos k t-\hat{\mathbf{j}} \sin k t]\), where \(A\) and \(k\) are constants. The angle between the force and the momentum is