\(31 \mathrm{~g}\) of ethylene glycol \(\left(\mathrm{C}_2 \mathrm{H}_6 \mathrm{O}_2\right)\) is dissolved in \(600 \mathrm{~g}\) of water. The freezing point depression of the solution is \(\left(K_f\right.\) for water is \(\left.1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)

The molar solubility of \(\mathrm{PbI}_2\) in \(0.2 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_3\right)_2\) solution in terms of \(\mathrm{K}_{\mathrm{sp}}\) (solubility product) is

Identify the correct statements from the following
(i) The atomic radius of \(\mathrm{Al}\) is lower than the atomic radius of \(\mathrm{Ga}\).
(ii) Boron exists in many allotropic forms.
(iii) The melting point of \(\mathrm{Ga}\) is lowest among the group 13 elements.

Which of the correct option for the following reaction?
\[
2 \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br} \xrightarrow{2 \mathrm{Na} / \text { Dryether }} \text { ? }
\]

The standard reduction potentials of \(\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Ag}\) are respectively \(-0.76,0.34\) and \(0.8 \mathrm{~V}\). The following cells were constructed :
(1) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}\)
(2) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}\)
(3) \(\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}\)
What is the correct order of \(E_{\text {cell }}^{\circ}\) of these cells?

The radius of the first orbit of \(\mathrm{Li}^{2+}\) is \(\mathrm{X} Å\). The radius of the third orbit of \(\mathrm{He}^{+}\)(in \(Å\) ) is

In the structure of \(\mathrm{B}_2 \mathrm{H}_6\), the number of \(\mathrm{BH}_2\) groups present in one plane, and the number of \(\mathrm{B}-\mathrm{H}\) bonds, \(\mathrm{B}-\mathrm{B}\) bonds, \(\mathrm{B}-\mathrm{H}-\mathrm{B}\) bridge bonds are respectively

In a \(\triangle A B C, A-B=120^{\circ}, R=8 r\), then \(\frac{1+\cos C}{1-\cos C}=\)

The component of a vector \(\mathbf{P}=3 \hat{i}+4 \hat{j}\) alog the direction \((\hat{i}+2 \hat{j})\) is

Which among the following is used as flux in the extraction of iron from oxide ores?

Match the following.


The correct answer is
\(\begin{array}{llll}
A & B & C & D
\end{array}\)

A solid copper cube of \(7 \mathrm{~cm}\) edge is subjected to a hydraulic pressure of \(8000 \mathrm{kPa}\). The volume contraction of the copper cube is (Bulk modulus of copper \(=140 \mathrm{GPa}\) )

If \(\alpha, 2 \alpha, 3 \alpha\) are angles made by a ray with \(\mathrm{OX}, \mathrm{OY}, \mathrm{OZ}\) axes respectively then all the possible values of \(\alpha\) are