Given below are two statements :

Statement (I): On nitration of m-xylene with $\mathrm{HNO}_3, \mathrm{H}_2 \mathrm{SO}_4$ followed by oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product.

Statement (II) : $-\mathrm{CH}_3$ group is o/p-directing while $-\mathrm{NO}_2$ group is m-directing group.

In the light of the above statements, choose the correct answer from the options given below :

Identify the essential amino acids from below:

(A) Valine

(B) Proline

(C) Lysine

(D) Threonine

(E) Tyrosine

Choose the correct answer from the options given below:

Given below are two statements :

Statement (I): NaCl is added to the ice at 0°C, present in the ice cream box to prevent the melting of ice cream.

Statement (II): On addition of NaCl to ice at 0°C, there is a depression in freezing point.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :

Statement (I): In partition chromatography, stationary phase is thin film of liquid present in the inert support.

Statement (II): In paper chromatography, the material of paper acts as a stationary phase.

In the light of the above statements, choose the correct answer from the options given below :

0.1 M solution of KI reacts with excess of $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{KIO}_3$ solutions. According to equation

$$ 5 \mathrm{I}^{-}+\mathrm{IO}_3^{-}+6 \mathrm{H}^{+} \rightarrow 3 \mathrm{I}_2+3 \mathrm{H}_2 \mathrm{O} $$

Identify the correct statements :

(A) 200 mL of KI solution reacts with 0.004 mol of $\mathrm{KIO}_3$

(B) 200 mL of KI solution reacts with 0.006 mol of $\mathrm{H}_2 \mathrm{SO}_4$

(C) 0.5 L of KI solution produced 0.005 mol of $\mathrm{I}_2$

(D) Equivalent weight of $\mathrm{KIO}_3$ is equal to ( $\frac{\text { Molecular weight }}{5}$ )

Choose the correct answer from the options given below :

The type of oxide formed by the element among Li, Na, Be, Mg, B and Al that has the least atomic radius is :

Which one of the following reaction sequences will give an azo dye?

Identify the homoleptic complexes with odd number of $d$ electrons in the central metal :

(A) $\left[\mathrm{FeO}_4\right]^{2-}$

(B) $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$

(C) $\left[\mathrm{Fe}(\mathrm{CN})_5 \mathrm{NO}\right]^{2-}$

(D) $\left[\mathrm{CoCl}_4\right]^{2-}$

(E) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_3 \mathrm{~F}_3\right]$

Choose the correct answer from the options given below :

Match List - I with List - II :

Choose the correct answer from the options given below :

Which one of the following, with HBr will give a phenol?

The calculated spin-only magnetic moments of $K_3[Fe(OH)_6]$ and $K_4[Fe(OH)_6]$ respectively are :

Consider the equilibrium

$$ \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) $$

If the pressure applied over the system increases by two fold at constant temperature then

(A) Concentration of reactants and products increases.

(B) Equilibrium will shift in forward direction.

(C) Equilibrium constant increases since concentration of products increases.

(D) Equilibrium constant remains unchanged as concentration of reactants and products remain same.

Choose the correct answer from the options given below :

First ionisation enthalpy values of first four group 15 elements are given below. Choose the correct value for the element that is a main component of apatite family :

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n?

[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]

If $\quad C$ (diamond $) \rightarrow C$ (graphite) $+X \mathrm{~kJ} \mathrm{~mol}^{-1}$

C (diamond) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{Y} \mathrm{kJ} \mathrm{mol}{ }^{-1}$

C (graphite) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{Z} \mathrm{kJ} \mathrm{mol}^{-1}$

at constant temperature. Then

Given below are two statements :

Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.

Statement (II) : If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is $\geqslant \sqrt{\frac{h}{\pi}} \times \frac{1}{2 m}$.

In the light of the above statements, choose the correct answer from the options given below :

Total number of sigma (σ) _______ and pi(π) ______ bonds respectively present in hex-1-en-4-yne are:

Which among the following halides will generate the most stable carbocation in the nucleophilic substitution reaction?

Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $16 \mathrm{mg} / \mathrm{mL}$ which becomes $4 \mathrm{mg} / \mathrm{mL}$ in 12 months. The expiry time of the drug in months is _________.

Assume that the decomposition of the drug follows first order kinetics.

$\mathrm{O}_2$ gas will be evolved as a product of electrolysis of :

(A) an aqueous solution of $\mathrm{AgNO}_3$ using silver electrodes.

(B) an aqueous solution of $\mathrm{AgNO}_3$ using platinum electrodes.

(C) a dilute solution of $\mathrm{H}_2 \mathrm{SO}_4$ using platinum electrodes.

(D) a high concentration solution of $\mathrm{H}_2 \mathrm{SO}_4$ using platinum electrodes.

Choose the correct answer from the options given below :

Total number of non-bonded electrons present in NO₂^$-$ ion based on Lewis theory is ______.

Consider the following low-spin complexes

$$ \mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{NO}_2\right)_6\right], \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{Cu}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right] \text { and } \mathrm{Zn}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right] $$

The sum of the spin-only magnetic moment values of complexes having yellow colour is ________ B.M. (answer in nearest integer)

In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of sulphur in the compound is __________ $\times 10^{-1} \%$.

(Molar mass : $\mathrm{O}=16, \mathrm{~S}=32, \mathrm{Ba}=137$ in $\mathrm{g} ~\mathrm{mol}^{-1}$ )

Isomeric hydrocarbons → negative Baeyer’s test

(Molecular formula C₉H₁₂)

The total number of isomers from above with four different non-aliphatic substitution sites is -

Let $\mathrm{S}=\mathbf{N} \cup\{0\}$. Define a relation R from S to $\mathbf{R}$ by :

$$ \mathrm{R}=\left\{(x, y): \log _{\mathrm{e}} y=x \log _{\mathrm{e}}\left(\frac{2}{5}\right), x \in \mathrm{~S}, y \in \mathbf{R}\right\} . $$

Then, the sum of all the elements in the range of $R$ is equal to :

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} \in \{0, 1\}$ for all $i$ and $j$. Let the random variable $X$ denote the possible values of the determinant of the matrix $A$. Then, the variance of $X$ is:

Let a straight line $L$ pass through the point $P(2, -1, 3)$ and be perpendicular to the lines $ \frac{x - 1}{2} = \frac{y + 1}{1} = \frac{z - 3}{-2} $ and $ \frac{x - 3}{1} = \frac{y - 2}{3} = \frac{z + 2}{4} $. If the line $L$ intersects the $yz$-plane at the point $Q$, then the distance between the points $P$ and $Q$ is:

If the domain of the function $ \log_5(18x - x^2 - 77) $ is $ (\alpha, \beta) $ and the domain of the function $ \log_{(x-1)} \left( \frac{2x^2 + 3x - 2}{x^2 - 3x - 4} \right) $ is $(\gamma, \delta)$, then $ \alpha^2 + \beta^2 + \gamma^2 $ is equal to:

Let $ \hat{a} $ be a unit vector perpendicular to the vectors $ \vec{b} = \hat{i} - 2\hat{j} + 3\hat{k} $ and $ \vec{c} = 2\hat{i} + 3\hat{j} - \hat{k} $, and $ \hat{a} $ makes an angle of $ \cos^{-1} \left( -\frac{1}{3} \right) $ with the vector $ \hat{i} + \hat{j} + \hat{k} $. If $ \hat{a} $ makes an angle of $ \frac{\pi}{3} $ with the vector $ \hat{i} + \alpha\hat{j} + \hat{k} $, then the value of $ a $ is:

Let $ \alpha, \beta \ (\alpha \neq \beta) $ be the values of $ m $, for which the equations $ x+y+z=1 $, $ x+2y+4z=m $ and $ x+4y+10z=m^2 $ have infinitely many solutions. Then the value of $ \sum\limits_{n=1}^{10} (n^{\alpha}+n^{\beta}) $ is equal to :

Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of the triangle AMN is $ \frac{4}{9} $ of the area of the triangle OAB and AN : NB = $ \lambda : 1 $, then the sum of all possible value(s) of $ \lambda $ is:

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is $ \frac{29}{45} $, then n is equal to:

The remainder, when $7^{103}$ is divided by 23, is equal to:

If for the solution curve $y=f(x)$ of the differential equation $\frac{d y}{d x}+(\tan x) y=\frac{2+\sec x}{(1+2 \sec x)^2}$, $x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right), f\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{10}$, then $f\left(\frac{\pi}{4}\right)$ is equal to:

Let $\mathrm{A}=\left[a_{i j}\right]$ be a matrix of order $3 \times 3$, with $a_{i j}=(\sqrt{2})^{i+j}$. If the sum of all the elements in the third row of $A^2$ is $\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}$, then $\alpha+\beta$ is equal to :

If $\sin x + \sin^2 x = 1$, $x \in \left(0, \frac{\pi}{2}\right)$, then

$(\cos^{12} x + \tan^{12} x) + 3(\cos^{10} x + \tan^{10} x + \cos^8 x + \tan^8 x) + (\cos^6 x + \tan^6 x)$ is equal to:

Let the area enclosed between the curves $|y| = 1 - x^2$ and $x^2 + y^2 = 1$ be $\alpha$. If $9\alpha = \beta \pi + \gamma; \beta, \gamma$ are integers, then the value of $|\beta - \gamma|$ equals:

Let P be the foot of the perpendicular from the point $(1,2,2)$ on the line $\mathrm{L}: \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z-2}{2}$.
Let the line $\vec{r}=(-\hat{i}+\hat{j}-2 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}), \lambda \in \mathbf{R}$, intersect the line L at Q . Then $2(\mathrm{PQ})^2$ is equal to :

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is :

If $ 24 \int\limits_0^{\frac{\pi}{4}} \bigg[\sin \left| 4x - \frac{\pi}{12} \right| + [2 \sin x] \bigg] dx = 2\pi + \alpha $, where $[\cdot]$ denotes the greatest integer function, then $\alpha$ is equal to ________.

Let $y^2=12 x$ be the parabola and $S$ be its focus. Let $P Q$ be a focal chord of the parabola such that $(S P)(S Q)=\frac{147}{4}$. Let $C$ be the circle described taking $P Q$ as a diameter. If the equation of a circle $C$ is $64 x^2+64 y^2-\alpha x-64 \sqrt{3} y=\beta$, then $\beta-\alpha$ is equal to $\qquad$ .

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1+\left(a_5+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to _________.

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side a in free space. At $t=0$, they are given an initial velocity $\overrightarrow{V_A}=V_0 \overrightarrow{A C}, \overrightarrow{V_B}=V_0 \overrightarrow{B A}$ and $\overrightarrow{V_C}=V_0 \overrightarrow{C B}$. Here, $\overrightarrow{A C}, \overrightarrow{C B}$ and $\overrightarrow{B A}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

In an experiment with photoelectric effect, the stopping potential,

The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R) : In isothermal process, PV = constant, while in adiabatic process $PV^{\gamma}$ = constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below:

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{dm}{dt} \propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

A plane electromagnetic wave propagates along the + x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are

A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k₁ and k₂, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

Match List - I with List - II.

Choose the correct answer from the options given below :

Match List - I with List - II.

Choose the correct answer from the options given below:

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is :

The truth table for the circuit given below is:

A poly-atomic molecule $\left(C_V=3 R, C_P=4 R\right.$, where $R$ is gas constant) goes from phase space point $\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.$ $\mathrm{Pa}, \mathrm{V}_C=8 \times 10^{-6} \mathrm{~m}^3$ ). A to $B$ is an adiabatic path and $B$ to $C$ is an isothermal path.

The net heat absorbed per unit mole by the system is :

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L₁, L₂ by AB plane and L₃, L₄ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L₁ and L₃ is

A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :

(Given $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

A capacitor, $C_1 = 6 \mu F$ is charged to a potential difference of $V_0 = 5V$ using a 5V battery. The battery is removed and another capacitor, $C_2 = 12 \mu F$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached.

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_{\mathrm{o}}$. Choose the correct option from the following.

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, v_{\mathrm{C}}=4 \mathrm{~m} / \mathrm{s}$. If we wait sufficiently long for elastic collision to happen, then $v_{\mathrm{A}}=4 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}$, $v_{\mathrm{C}}=5 \mathrm{~m} / \mathrm{s}$ will be the final velocities.

Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.

In the light of the above statements, choose the correct answer from the options given below:

$\text { A physical quantity } Q \text { is related to four observables } a, b, c, d \text { as follows : }$

$Q = \frac{ab^4}{cd}$

where, $\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2}$ and $\mathrm{d}=(50 \pm 0.1) \mathrm{m}$, then the percentage error in Q is $\frac{x}{1000}$, where $x=$ _________ .

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.

Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2 R_A$. The planet $B$ is $4 \sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{L}_{\mathrm{A}}}\right)$ of angular momentum $\left(L_B\right)$ of planet $B$ to that of planet $A\left(L_A\right)$ is closest to integer ________.

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is $7 \times 10^8 \mathrm{~V} / \mathrm{s}$ then the integer value of the distance between the parallel plates is