The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding element \(X\) as shown below. To which group, element \(X\) belongs in the periodic table?

\({ }_{29}^{63} \mathrm{Cu}+{ }_{1}^{1} \mathrm{H} \rightarrow 6_{0}^{1} n+{ }_{2}^{4} \alpha+2{ }_{1}^{1} \mathrm{H}+\mathrm{X}\)

The shape of \(\mathrm{XeO}_{2} \mathrm{~F}_{2}\) molecule is

Among the following, the correct statement(s) is(are)

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is

List$-\mathrm{I}$ includes starting materials and reagents of selected chemical reactions. List$-\mathrm{II}$gives structures of compounds that may be formed as intermediate products and/or final products from the reactions of List$-\mathrm{I}$.

List-I	List-II
(I)	$\left(\mathrm{P}\right)$
(II)	$\left(\mathrm{Q}\right)$
(III)	$\left(\mathrm{R}\right)$
(IV)	$\left(\mathrm{S}\right)$
	$\left(\mathrm{T}\right)$
	$\left(\mathrm{U}\right)$

Which of the following options has the correct combination considering List$-\mathrm{I}$ and List$-\mathrm{II}$?

Among the following complexes, the total number of diamagnetic species is_____
\(\left[\mathrm{Mn}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{FeF}_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\)\(\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]^{3+}\), and \(\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}\)
[Given, atomic number: \(\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27\);
\(\text { en } \left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right]\)

Statement I p-hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.
Statement II o-hydroxybenzoic acid has intramolecular hydrogen bonding.

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$ . The angle of contact between water and the wall of the capillary tube is $\theta$ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

An ideal gas of density $\rho =0.2 \mathrm{kg} {\mathrm{m}}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha =0.8 \mathrm{kg} {\mathrm{s}}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1 {\mathrm{m}}^2$ and the upper end is $A_2=0.4 {\mathrm{m}}^2$. The pressure and the temperature of the gas at the lower end are $600 \mathrm{Pa}$ and $300 \mathrm{K}$, respectively, while its temperature at the upper end is $150 \mathrm{K}$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and the ratio of specific heats of the gas $\gamma =2$. Ignore atmospheric pressure.

Which of the following statement(s) is(are) correct?

Which is correct statement if \(\mathrm{N}_2\) is added at equilibrium condition?

With respect to hypochlorite, chlorate and perchlorate ions, choose the correct statement(s).

Paragraph :
A uniform thin cylindrical disk of mass \(M\) and radius \(R\) is attached to two identical massless springs of spring constant \(k\) which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance \(d\) from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is \(L\). The disk is initially at its equilibrium position with its centre of mass \((C M)\) at a distance Lfrom the wall. The disk rolls without slipping with velocity \(\mathbf{v}_0=v_0 \hat{\mathbf{i}}\) The coefficient of friction is \(\mu\).
Question :
The maximum value of \(v_0\) for which the disk will roll without slipping is

The number of all possible values of \(\theta\), where \(0 < \theta < \pi\), for which the system of equations
\((y+z) \cos 3 \theta=(x y z) \sin 3 \theta \) \( x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z}\) and \((x y z) \sin 3 \theta=(y+2 z) \cos 3 \theta\) \(+y \sin 3 \theta\) have a solution \(\left(x_0, y_0, z_0\right)\) with \(\quad y_0 z_0 \neq 0\), is