The edge length of unit cell of a metal having molecular weight \(75 \mathrm{~g} / \mathrm{mol}\) is 5 Å which crystallizes in cubic lattice. If the density is \(2 \mathrm{~g} / \mathrm{cc}\) then find the radius of metal atom, \(\left(N_A=6 \times 10^{23}\right)\). Give the answer in pm.

The correct statement(s) about surface properties is(are)

The boiling point of water in a \(0.1\) molal silver nitrate solution (solution \(\mathbf{A}\) ) is \(\mathbf{x}^{\circ} \mathrm{C}\). To this solution \(\mathbf{A}\), an equal volume of \(0.1\) molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions \(\mathbf{A}\) and \(\mathbf{B}\) is \(\mathbf{y} \times 10^{-2}{ }^{\circ} \mathrm{C}\).
(Assume: Densities of the solutions \(\mathbf{A}\) and \(\mathbf{B}\) are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), \(K_{b}=0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\); Boiling point of pure water as \(100^{\circ} \mathrm{C}\).)
The value of $\left|\mathrm{y}\right|$ is ___.

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If ${\mathrm{\lambda }}_{{\mathrm{X}}^{-}}^0\approx {\mathrm{\lambda }}_{{\mathrm{Y}}^{-}}^0$ , the difference in their $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}$ values, $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}\left(\mathrm{H}\mathrm{X}\right)-\mathrm{p}{\mathrm{K}}_{\mathrm{a}}\left(\mathrm{H}\mathrm{Y}\right)$ , is (Consider degree of ionization of both acids to << 1)

The correct statement about the following disaccharide is

The species having pyramidal shape is

In the following reactions, P, Q, R and S are the major products.

The correct statement(s) about P, Q, R and S is(are)

The value of $\sum _{k=1}^{13}\frac{1}{\sin \left(\frac{\pi }{4}+\frac{\left(k-1\right)\pi }{6}\right)\sin \left(\frac{\pi }{4}+\frac{k\pi }{6}\right)}$ is equal to

Paragraph:

Let \(S=S_{1} \cap S_{2} \cap S_{3}\), where

\(S_{1}=\{z \in \mathbb{C}:|z|<4\}, \quad S_{2}=\left\{z \in \mathbb{C}: \operatorname{Im}\left[\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}\right]>0\right\}\) and \(S_{3}=\{z \in \mathbb{C}: \operatorname{Re} z>0\}\).


Question:

Area of \(S=\)

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

One mole of an ideal gas expands adiabatically from an initial state $(T_A, V_0)$ to final state $(T_f, 5V_0)$. Another mole of the same gas expands isothermally from a different initial state $(T_B, V_0)$ to the same final state $(T_f, 5V_0)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $\frac{T_A}{T_B}$?

Among PbS, CuS, HgS, MnS, $\mathrm{A}{\mathrm{g}}_2\mathrm{S}$ , NiS, CoS, $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ and $\mathrm{S}\mathrm{n}{\mathrm{S}}_2$ , the total number of black coloured sulphides is

Statement I Glucose gives a reddish-brown precipitate with Fehling's solution.
Statement II Reaction of glucose with Fehling's solution gives \(\mathrm{CuO}\) and gluconic acid.