The $1^{\mathrm{st}}$, $2^{\mathrm{nd}}$ and the $3^{\mathrm{rd}}$ ionization enthalpies, ${\mathrm{I}}_1, {\mathrm{I}}_2$ and ${\mathrm{I}}_3$, of four atoms with atomic numbers $\mathrm{n}, \mathrm{n}+1, \mathrm{n}+2,$ and $\mathrm{n}+3,$ where $\mathrm{n}<10,$ are tabulated below. What is the value of $\mathrm{n}$?

Atomic number	Ionization Enthalpy (kJ/mol)
	${\mathrm{I}}_1$	${\mathrm{I}}_2$	${\mathrm{I}}_3$
$\mathrm{n}$	$1681$	$3374$	$6050$
$\mathrm{n}+1$	$2081$	$3952$	$6122$
$\mathrm{n}+2$	$496$	$4562$	$6910$
$\mathrm{n}+3$	$738$	$1451$	$7733$

For the electrochemical cell, $\text{Mg(s)}\left|{\text{Mg}}^{\text{2+}}\left(\text{aq,1}\text{M}\right)\right|\left|{\text{Cu}}^{\text{2+}}\left(\text{aq,1}\text{M}\right)\right|\text{Cu }\left(\text{s}\right)$ the standard emf of the cell is $\text{2}\text{.70 V}$ at $\text{300 K}\text{.}$ When the concentration of ${\text{Mg}}^{\text{2+}}$ is changed to $\text{x M,}$ the cell potential changes to $\text{2}\text{.67 V}$ at $\text{300 K}\text{.}$ The value of $\text{x}$ is ________.
(given, $\frac{\text{F}}{\text{R}}{\text{=11500 K V}}^{-\text{1}}\text{,}$ where $\text{F}$ is the Faraday constant and $\text{R}$ is the gas constants, $\text{ln}\left(\text{10}\right)\text{=}\text{2}\text{.30}$ )

Silver (atomic weight \(=108 \mathrm{~g} \mathrm{~mol}^{-1}\) ) has a density of \(10.5 \mathrm{~g} \mathrm{~cm}^{-3}\). The number of silver atoms on a surface of area \(10^{-12} \mathrm{~m}^2\) can be expressed in scientific notation as \(y \times 10^x\). The value of \(x\) is

Choose the correct option(s) from the following

Match the chemical substance in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

Column I	Column II
A. \(C _6 H _5 CHO\)	p. Gives precipitate with 2, 4-dinitrophenylhydrazine
B. \(CH _3 \equiv CH\)	q. Gives precipitate with \(AgNO _3\)
C. \(CN ^{-}\)	r. Is a nucleophile
D. \(I ^{-}\)	s. Is involved in cyanohydrin formation

A plot of the number of neutrons $(\text{N})$ against the number of protons $(\text{P})$ of the stable nuclei exhibits upwards deviation from linearity for atomic number, $\text{Z}>20$. For an unstable nucleus having $\frac{\text{N}}{\text{P}}$ ratio less than $1$, the possible mode(s) of decay is (are):

Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, \(\mathrm{Na}, \mathrm{Ti}\)

As per IUPAC nomenclature, the name of the complex \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}_{3}\) is :

Let \(\omega=e^{i \pi / 3}\) and \(a, b, c, x, y, z\) be non-zero complex numbers such that \(a+b+c=x, a+b \omega+c \omega^2=y, a+b \omega^2+c \omega=z\).
Then, the value of \(\frac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2}\) is

A cylindrical furnace has height $\left(H\right)$ and diameter $\left(D\right)$ both $1\mathrm{m}$. It is maintained at temperature $360\mathrm{K}$. The air getsheated inside the furnace at constant pressure$P_a$and its temperature becomes $T=360\mathrm{K}$. The hot air with density $\rho$rises up a vertical chimney of diameter $d=0.1\mathrm{m}$ and height $h=9\mathrm{m}$ above the furnace and exits the chimney (seethe figure). As a result, atmospheric air of density${\rho }_a=1.2\mathrm{kg}{\mathrm{m}}^{-3}$,pressure $P_a$and temperature $T_a=300\mathrm{K}$ entersthe furnace. Assume air as an ideal gas, neglect the variations in$\rho$and $T$ inside the chimney and the furnace. Also ignore the viscous effects.
[Given: The acceleration due to gravity$g=10\mathrm{m}{\mathrm{s}}^{-2}$and$\pi =3.14$]


When the chimney is closed using a cap at the top, a pressure difference $∆P$develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of $∆P$is _____ $\mathrm{N}{\mathrm{m}}^{-2}$.

Two large circular discs separated by a distance of $0.01\mathrm{m}$ are connected to a battery via a switch as shown in the figure. Charged oil drops of density $900\mathrm{kg}{\mathrm{m}}^{-3}$ are released through a tiny hole at the centre of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of $200\mathrm{V}$ across the discs. As a result, an oil drop of radius $8\times {10}^{-7}\mathrm{m}$ stops moving vertically and floats between the discs. The number of electrons present in this oil drop is __________. (neglect the buoyancy force, take acceleration due to gravity $=10\mathrm{m}{\mathrm{s}}^{-2}$ and charge on an electron (e) $=1.6\times {10}^{-19}\mathrm{C}$)

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life $\mathrm{T}$ years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5% of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of $\mathrm{n}\mathrm{T}$ years, then the value of $\mathrm{n}$ is

In the following circuit $C_1=12 \mathrm{\mu F},C_2=C_3=4 \mathrm{\mu F}$ and $C_4=C_5=2 \mathrm{\mu F}$. The charge stored in $C_3$ is $\mathrm{\mu C}.$