An ideal gas is expanded from $({\mathrm{p}}_1\mathrm{ },\mathrm{ }{\mathrm{V}}_1\mathrm{ },\mathrm{ }{\mathrm{T}}_1)\mathrm{ }\mathrm{to}\mathrm{ }({\mathrm{p}}_2\mathrm{ },\mathrm{ }{\mathrm{V}}_2\mathrm{ },\mathrm{ }{\mathrm{T}}_2)$ under different conditions. The correct statement(s) among the following is(are)

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.
The limiting ionic conductivity \(\left(\Lambda_0\right)\) values (in \(\mathrm{mS} \mathrm{m}^2 \mathrm{~mol}^{-1}\)) for different ions in aqueous solutions are given below:

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus 'volume of titrant' are given in List-II.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

The number of neutrons emitted when \({ }_{92}^{235} \mathrm{U}\) undergoes controlled nuclear fission to \({ }_{54}^{142} \mathrm{Xe}\) and \({ }_{38}^{90} \mathrm{Sr}\) is

Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other.
\(\text { [en } \left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right]\)

The correct statement(s) related to processes involved in the extraction of metals is(are)

If the reaction sequence given below is carried out with $15$ moles of acetylene, the amount of the product $\mathrm{D}$ formed (in $\mathrm{g}$) is The yields of $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ are given in parentheses. [Given: Atomic mass of $\mathrm{H}=1,\mathrm{C}=12,\mathrm{O}=16,\mathrm{Cl}=35$]

Paragraph:
An acylic hydrocarbon \(P\), having molecular formula \(\mathrm{C}_6 \mathrm{H}_{10}\), gave acetone as the only organic product through the following sequence of reactions, in which \(Q\) is an intermediate organic compounds.

Question:
The structure of compound P is

Statement I If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic \(X\)-rays do not change.
Statement II When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

Paragraph :
A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, \(C_{V}=2 R\). Here, \(R\) is the gas constant. Initially, each side has a volume \(V_{0}\) and temperature \(T_{0}\). The left side has an electric heater, which is turned on at very low power to transfer heat \(Q\) to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to \(V_{0} / 2\). Consequently, the gas temperatures on the left and the right sides become \(T_{L}\) and \(T_{R}\), respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.

Question :
The value of $\frac{T_R}{T_0}$ is:

Match each of the reactions given in Column I with the corresponding products(s) given in Column II.

Let \(\alpha\) and \(\beta\) be the roots of \(x^2-6 x-2=0\) with \(\alpha>\beta\). If \(a_n=\alpha^n-\beta^n\) for \(n \geq 1\), then the value of \(\frac{a_{10}-2 a_8}{2 a_9}\) is

The value of \(n\) in the molecular formula \(\mathrm{Be}_n \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18}\) is

The set of values of \(\theta\) satisfying the inequation \(2 \sin ^2 \theta-5 \sin \theta+2>0\), where \(0 < \theta < 2 \pi\), is