With reference to the scheme given below, which of the given statement(s) about \(\mathrm{T}, \mathrm{U}, \mathrm{V}\) and \(\mathrm{W}\) is (are) correct?

\(29.2 \%(\mathrm{w} / \mathrm{w}) \mathrm{HCl}\) stock solution has a density of \(1.25 \mathrm{gmL}^{-1}\). The molecular weight of \(\mathrm{HCl}\) is \(36.5 \mathrm{~g} \mathrm{~mol}^{-1}\). The volume \((\mathrm{mL})\) of stock solution required to prepare a 200 \(\mathrm{mL}\) solution of \(0.4 \mathrm{M} \mathrm{HCl}\) is :

Hydrogen bonding plays a central role in the following phenomena:

For the elementary reaction $\mathrm{M}\to \mathrm{N}$, the rate of disappearance of $\mathrm{M}$ increases by a factor of $8$ upon doubling the concentration of $\mathrm{M}$. The order of the reaction with respect to $\mathrm{M}$ is

Consider an ionic solid $\mathrm{MX}$, with $\mathrm{NaCl}$ structure. Construct a new structure $\left(\mathrm{Z}\right)$, whose unit cell is constructed from the unit cell of $\mathrm{MX}$, following the sequential instructions given below. Neglect the charge balance.
$\left(\mathrm{i}\right)$ Remove all the anions $\left(\mathrm{X}\right)$, except the central one.
$\left(\mathrm{ii}\right)$ Replace all the face centered cations $\left(\mathrm{M}\right)$, by anions $\left(\mathrm{X}\right)$.
$\left(\mathrm{iii}\right)$ Remove all the corner cations $\left(\mathrm{M}\right)$.
$\left(\mathrm{iv}\right)$ Replace the central anion $\left(\mathrm{X}\right)$, with cation $\left(\mathrm{M}\right)$.
The value of $\left(\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}\right)$ in $\mathrm{Z}$ is _____.

Paragraph:
Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately \(6.023 \times 10^{23}\) ) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A \(4.0\) molar aqueous solution of \(\mathrm{NaCl}\) is prepared and \(500 \mathrm{~mL}\) of this solution is electrolysed. This leads to the evolution of chlorine gas at one of electrodes (atomic mass: \(\mathrm{Na}=23, \mathrm{Hg}=200 ; 1\) faraday \(=96500\) coulombs).
Question:
The total number of moles of chlorine gas evolved is

All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $R_3$ has temperature coefficient $0.0004°{\mathrm{C}}^{-1}$. If the temperature of $R_3$ is increased by $100°\mathrm{C},$ the voltage developed between $S$ and $T$ will be __________ volt.

Two transparent media of refractive indices \(\mu_1\) and \(\mu_3\) have a solid lens shaped transparent material of refractive index \(\mu_2\) between them as shown in figures in Column II. A ray traversing these media is also shown in the figures. In Column I different relationships between \(\mu_1, \mu_2\) and \(\mu_3\) are given. Match them to the ray diagram shown in Column II.

For a double strand DNA, one strand is given below:

The amount of energy required to split the double strand DNA into two single strands is _______ kcal \(\mathrm{mol}^{-1}.\)
[Given: Average energy per \(\mathrm{H}\)-bond for A-T base pair \(=1.0 \mathrm{kcal} \mathrm{mol}^{-1}, \mathrm{G}-\mathrm{C}\) base pair \(=1.5 \mathrm{kcal}\) \(\mathrm{mol}^{-1}\), and A-U base pair \(=1.25 \mathrm{kcal} \mathrm{mol}^{-1}.\) Ignore electrostatic repulsion between the phosphate groups.]

The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match List-I with List-II and choose the correct option.

	List I		List II
$\left(\mathrm{P}\right)$	Etard reaction	$1$	$\mathrm{Acetophenone} \stackrel{\mathrm{Zn}-\mathrm{Hg},\mathrm{HCl}}{\to }$
$\left(\mathrm{Q}\right)$	Gattermann reaction	$2$	$\mathrm{Toluene} \underset{\left(\mathrm{ii}\right) {\mathrm{SOCl}}_2 }{\overset{\left(\mathrm{i}\right) {\mathrm{KMnO}}_4, \mathrm{KOH},\mathbf{ }\mathrm{\Delta } }{\to }}$
$\left(\mathrm{R}\right)$	Gattermann-Koch reaction	$3$	$\mathrm{Benzene} \underset{\mathrm{Anhyd}. {\mathrm{AlCl}}_3}{\overset{{\mathrm{CH}}_3\mathrm{Cl}}{\to }}$
$\left(\mathrm{S}\right)$	Rosenmund reduction	$4$	$\mathrm{Aniline} \frac{{\mathrm{NaNO}}_2 /\mathrm{HCl}}{273-278 \mathrm{K}}$
		$5$	$\mathrm{Phenol} \stackrel{\mathrm{Zn},\mathrm{\Delta }}{\to }$

Paragraph :
When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.
We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension \(T\) when the radius of the drop is \(R\). When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
Question :
If the radius of the opening of the dropper is \(r\), the vertical force due to the surface tension on the drop of radius \(R\) (assuming \(r< < R\) ) is

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
 

Column 1	Column 2	Column 3
(I) $x^2+y^2=a^2$	(i) $my=m^{2}x+a$	(P) $\left(\frac{a}{m^2},\frac{2a}{m}\right)$
(II) $x^2+a^2{y}^2=a^2$	(ii) $y=mx+a \sqrt{m^2+1}$	(Q) $\left(\frac{-ma}{\sqrt{m^2+1}},\frac{a}{\sqrt{m^2+1}}\right)$
(III) $y^2=4ax$	(iii) $y=mx+ \sqrt{a^2{m}^2-1}$	(R) $\left(\frac{-a^{2}m}{\sqrt{a^2{m}^2+1}},\frac{1}{\sqrt{a^2{m}^2+1}}\right)$
(IV) $x^2-a^2{y}^2=a^2$	(iv) $y=mx+\sqrt{a^2{m}^2+1}$	(S) $\left(\frac{-a^{2}m}{\sqrt{a^2{m}^2-1}},\frac{-1}{\sqrt{a^2{m}^2-1}}\right)$

For $a=\sqrt{2}$ , if a tangent is drawn to a suitable conic (Column 1) at the point of contact $\left(-1, 1\right)$ , then which of the following options is the only Correct combination for obtaining its equation?