In the reaction,
$\text{P}+\text{Q}\to \text{R}+\text{S}$
the time taken for $75\%$ reaction of $\mathrm{P}$is twice the time taken for$50\%$ reaction of $\mathrm{P}$. The concentration of $\mathrm{Q}$varies with reaction time as shown in the figure.The overall order of the reaction is:

Consider the following reactions (unbalanced)
$\mathrm{Z}\mathrm{n}+H\mathrm{o}\mathrm{t}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4\to \mathrm{G}+\mathrm{R}+\mathrm{X}$
$\mathrm{Z}\mathrm{n}+\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\to \mathrm{T}+\mathrm{Q}$
\(\text G +\text H _2\text S+ \text{NH} _4 \text{OH} \rightarrow\text Z ~(\)a precipitate\()+\text X +\text Y\)
Choose the correct option(s).

The correct statement about the following disaccharide is

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.	$-0.83V$

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 _____.

The freezing point (in \({ }^{\circ} \mathrm{C}\) ) of solution containing \(0.1 \mathrm{~g}\) of \(\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]\) (molecular weight 329\()\) in \(100 \mathrm{~g}\) of water \(\left(K_f=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\) is

A decapeptide (molecular weight 796) on complete hydrolysis gives glycine (molecular weight 75), alanine and phenylalanine. Glycine contributes \(47.0 \%\) to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is

One mole of an ideal monatomic gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100\hspace{0.17em}\mathrm{K}$ and the universal gas constant $R=8.0\mathrm{ J} \mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{ K}}^{-1}$, then how much is the decrease in its internal energy (in $\mathrm{J}$) ?

A series \(R-C\) combination is connected to an \(\mathrm{AC}\) voltage of angular frequency \(\omega=500 \mathrm{rad} / \mathrm{s}\). If the impedance of the \(R-C\) circuit is \(R \sqrt{1.25}\), the time constant (in millisecond) of the circuit is

Consider the cube in the first octant with sides $OP, OQ$ and OR of length $1$, along the x-axis, y-axis and z-axis, respectively, where $O(0,0,0)$ is the origin. Let $S\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ be the centre of the cube and $T$ be the vertex of the cube opposite to the origin $O$ such that $S$ lies on the diagonal $OT$. If $\overrightarrow{p}=\overrightarrow{SP}, \overrightarrow{q}=\overrightarrow{SQ}, \overrightarrow{r}=\overrightarrow{SR}$ and $\overrightarrow{t}=\overrightarrow{ST}$, then the value of $\left|\left(\overrightarrow{p}\times \overrightarrow{q}\right)\times \left(\overrightarrow{r}\times \overrightarrow{t}\right)\right|$ is ______.

An acidified solution of $0.05 \mathrm{M} {\mathrm{Zn}}^{2+}$ is saturated with $0.1 \mathrm{M} {\mathrm{H}}_2\mathrm{S}$. What is the minimum molar concentration $\left(\mathrm{M}\right)$ of ${\mathrm{H}}^{+}$ required to prevent the precipitation of $\mathrm{ZnS}$? Use ${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{ZnS}\right)=1.25\times {10}^{-22}$ and overall dissociation constant of ${\mathrm{H}}_2\mathrm{S}, {\mathrm{K}}_{\mathrm{NET}}={\mathrm{K}}_1{\mathrm{K}}_2=1\times {10}^{-21}$

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air column is the second resonance. Then,

A circle S passes through the point (0, 1) and is orthogonal to the circles ${\left(x-1\right)}^2+y^2=16$ and $x^2+y^2=1$. Then