$\mathrm{F}{\mathrm{e}}^{3+}$ is reduced to $\mathrm{F}{\mathrm{e}}^{2+}$ by using

For the following reaction scheme, percentage yields are given along the arrow:

\(\mathbf{x} g\) and \(\mathbf{y} g\) are mass of \(\mathbf{R}\) and \(\mathbf{U}\), respectively.
(Use: Molar mass (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of \(\mathrm{H}, \mathrm{C}\) and \(\mathrm{O}\) as 1,12 and 16 , respectively)
The value of$\mathrm{y}$ is ___.

Among the species given below, the total number of diamagnetic species is _____________.
\(H\) atom, \(N O_2\) monomer, \(O_2^{-}\)(superoxide), dimeric sulphur in vapour phase,
\(Mn_3 O_4, \left(NH_4\right)_2\left[FeCl_4\right], \left(NH_4\right)_2\left[NiCl_4\right],\) \(K_2 MnO_4, K_2 CrO_4\)

The option(s) with correct sequence of reagents for the conversion of \(\mathbf{P}\) to \(\mathbf{Q}\) is(are) :

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	$4$	$\mathrm{Aniline} \frac{{\mathrm{NaNO}}_2 /\mathrm{HCl}}{273-278 \mathrm{K}}$
		$5$	$\mathrm{Phenol} \stackrel{\mathrm{Zn},\mathrm{\Delta }}{\to }$

The standard reduction potential data at $25°C$ is given below.
\(E ^o\left( Fe ^{3+}, Fe ^{2+}\right)=+0.77 V ; \)
\( E ^o\left( Fe ^{2+}, Fe \right)=-0 . 44 V \)
\( E ^o\left( Cu ^{2+}, Cu \right)=+0.34 V ; \)
\( E ^o\left( Cu ^{+}, Cu \right)=+0.52 V \)
\( E ^o\left[ O _2(g)+4 H ^{+}+4 e ^{-} \rightarrow 2 H _2 O \right]=\) \(+1.23~V \)
\( E ^o\left[ O _2(g)+2 H _2 O +4 e^{-} \longrightarrow \text { 4OH}^{-}\right]=\) \(+0.40~V \)
\( E ^o\left( Cr ^{3+}, Cr \right)=-0.74 V ; \)
\( E ^o\left( Cr ^{2+}, Cr \right)=-0.91 V\)
Match E^o of the redox pair in List I with the values given in List II and select the correct answer using the code given below the lists :
 

	List I		List II
A.	$E^o\left({\mathit{\text{Fe}}}^{3+},\mathit{\text{Fe}}\right)$	P.	$-0.18V$
B.	$E^o\left(4{\text{H}}_2\text{O}\rightleftharpoons 4H^{+}+4{\mathit{\text{OH}}}^{-}\right)$	Q.	$-0.4V$
C	$E^o\left({\mathit{\text{Cu}}}^{2+}+\mathit{\text{Cu}}\to 2{\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{Cu}}^{+}\right)$	R.	$-0.04V$
D.	$E^o\left({\mathit{\text{Cr}}}^{3+},{\mathit{\text{Cr}}}^{2+}\right)$	S.	$-0.83V$

Paragraph:
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.
A solution \(M\) is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is \(0.9\)
Given Freezing point depression constant of water \(\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\)
Freezing point depression constant of ethanol \(\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of water \(\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of ethanol \(\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Standard freezing point of water \(=273 \mathrm{~K}\)
Standard freezing point of ethanol \(=155.7 \mathrm{~K}\)
Standard boiling point of water \(=373 \mathrm{~K}\)
Standard boiling point of ethanol \(=351.5 \mathrm{~K}\)
Vapour pressure of pure water \(=328 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Vapour pressure of pure ethanol \(=40 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Molecular weight of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\)
Molecular weight of ethanol \(=46 \mathrm{~g} \mathrm{~mol}^{-1}\)
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

Question:
Water is added to the solution \(M\) such that the mole fraction of water in the solution becomes \(0.9\) The boiling point of this solutions is

Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using the code given below the lists :
 

List - I		List - II
(A)		(P)	$\left(\mathrm{i}\right) \mathrm{Hg}{\left(\mathrm{OAc}\right)}_2; \left(\mathrm{ii}\right) {\mathrm{NaBH}}_4$
(B)	​	(Q)	$\mathrm{NaOEt}$
(C)		(R)	$\mathrm{Et}-\mathrm{Br}$
(D)		(S)	$\left(\mathrm{i}\right) {\mathrm{BH}}_3; \left(\mathrm{ii}\right) {\mathrm{H}}_2{\mathrm{O}}_2/\mathrm{NaOH}$

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400\mathrm{ }\mathrm{pm}$ . If the density of the substance in the crystal is $8 \mathrm{g}\mathrm{ }{\mathrm{cm}}^{-3},\mathrm{ }$ then the number of atoms present in $256 \mathrm{g}$ of the crystal $\mathrm{is}\mathrm{ }\mathrm{N}\mathrm{ }\times \mathrm{ }{10}^{24}$ . The value of $\mathrm{N}$is

Let \(a_{n}\) denote the number of all \(n\)-digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let \(b_{n}=\) the number of such \(n\)-digit integers ending with digit 1 and \(c_{n}=\) the number of such \(n\)-digit integers ending with digit 0 .

Question:
The value of \(b_{6}\) is

Two particles, 1 and 2 , each of mass \(m\), are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at \(x_0\), are oscillating with amplitude \(a\) and angular frequency \(\omega\). Thus, their positions at time \(t\) are given by \(x_1(t)=\left(x_0+d\right)+a \sin \omega t\) and \(x_2(t)=\left(x_0-d\right)-a \sin \omega t\), respectively, where \(d>2 a\). Particle 3 of mass \(m\) moves towards this system with speed \(u_0=a \omega / 2\), and undergoes instantaneous elastic collision with particle 2 , at time \(t_0\). Finally, particles 1 and 2 acquire a center of mass speed \(v_{\mathrm{cm}}\) and oscillate with amplitude \(b\) and the same angular frequency \(\omega\).

If the collision occurs at time \(t_0=\pi /(2 \omega)\), then the value of \(4 b^2 / a^2\) will be ________ .

An optical bench has $1.5\mathrm{ }\mathrm{m}$ long scale having four equal divisions in each $\mathrm{c}\mathrm{m}.$ While measuring the focal length of a convex lens, the lens is kept at $75\mathrm{ }\mathrm{c}\mathrm{m}$ mark of the scale and the object pin is kept at $45\mathrm{ }\mathrm{c}\mathrm{m}$ mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at $135\mathrm{ }\mathrm{c}\mathrm{m}$ mark. In this experiment, the percentage error in the measurement of the focal length of the lens is_____

Consider the following reaction,
\(2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)
which follows the mechanism given below:
\(2 \mathrm{NO}(\mathrm{g}) \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})\) \(\quad\) (fast equlibrium)
\(\mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_2} \mathrm{~N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})\) \(\quad\)(slow reaction)
\(\mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_3} \mathrm{~N}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})\) \(\quad\) (fast reaction)
The order of the reaction is_____