Identify the incorrect statement from the following.

Which of the following relation is not correct?

Match List - I with List - II.

Choose the correct answer from the options given below:

In which of the following pairs, electron gain enthalpies of constituent elements are nearly the same or identical?

(A) Rb and Cs

(B) Na and K

(C) Ar and Kr

(D) I and At

Choose the correct answer from the options given below :

Match List - I with List - II, match the gas evolved during each reaction.

Choose the correct answer from the options given below :

Which of the following has least tendency to liberate $\mathrm{H}_{2}$ from mineral acids?

Match List - I with List - II.

	List - I		List - II
(A)		(I)	Spiro compound
(B)		(II)	Aromatic compound
(C)		(III)	Non-planar Heterocyclic compound
(D)		(IV)	Bicyclo compound

Choose the correct answer from the options given below :

Choose the correct option for the following reactions.

Among the following marked proton of which compound shows lowest $\mathrm{pK}_{\mathrm{a}}$ value?

Identify the major products A and B for the below given reaction sequence.

Identify the correct statement for the below given transformation.

For the below given cyclic hemiacetal (X), the correct pyranose structure is :

For kinetic study of the reaction of iodide ion with $\mathrm{H}_{2} \mathrm{O}_{2}$ at room temperature :

(A) Always use freshly prepared starch solution.

(B) Always keep the concentration of sodium thiosulphate solution less than that of KI solution.

(C) Record the time immediately after the appearance of blue colour.

(D) Record the time immediately before the appearance of blue colour.

(E) Always keep the concentration of sodium thiosulphate solution more than that of KI solution.

Choose the correct answer from the options given below :

In the given reaction,

$X+Y+3 Z \leftrightarrows X YZ_{3}$

if one mole of each of $X$ and $Y$ with $0.05 \mathrm{~mol}$ of $Z$ gives compound $X Y Z_{3}$. (Given : Atomic masses of $X, Y$ and $Z$ are 10, 20 and 30 amu, respectively.) The yield of $X YZ_{3}$ is _____________ g. (Nearest integer)

The number of paramagnetic species among the following is ___________.

$\mathrm{B}_{2}, \mathrm{Li}_{2}, \mathrm{C}_{2}, \mathrm{C}_{2}^{-}, \mathrm{O}_{2}^{2-}, \mathrm{O}_{2}^{+}$ and $\mathrm{He}_{2}^{+}$

$150 \mathrm{~g}$ of acetic acid was contaminated with $10.2 \mathrm{~g}$ ascorbic acid $\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)$ to lower down its freezing point by $\left(x \times 10^{-1}\right)^{\circ} \mathrm{C}$. The value of $x$ is ___________. (Nearest integer)

[Given $\mathrm{K}_{f}=3.9 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$; molar mass of ascorbic acid $=176 \mathrm{~g} \mathrm{~mol}^{-1}$]

$\mathrm{K}_{\mathrm{a}}$ for butyric acid $\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{COOH}\right)$ is $2 \times 10^{-5}$. The $\mathrm{pH}$ of $0.2 \,\mathrm{M}$ solution of butyric acid is __________ $\times 10^{-1}$. (Nearest integer)

[Given $\log 2=0.30$]

For the given first order reaction

$\mathrm{A} \rightarrow \mathrm{B}$

the half life of the reaction is $0.3010 \mathrm{~min}$. The ratio of the initial concentration of reactant to the concentration of reactant at time $2.0 \mathrm{~min}$ will be equal to ___________. (Nearest integer)

The number of interhalogens from the following having square pyramidal structure is :

$\mathrm{ClF}_{3}, \mathrm{IF}_{7}, \mathrm{BrF}_{5}, \mathrm{BrF}_{3}, \mathrm{I}_{2} \mathrm{Cl}_{6}, \mathrm{IF}_{5}, \mathrm{ClF}, \mathrm{ClF}_{5}$

The disproportionation of $\mathrm{MnO}_{4}^{2-}$ in acidic medium resulted in the formation of two manganese compounds $\mathrm{A}$ and $\mathrm{B}$. If the oxidation state of $\mathrm{Mn}$ in $\mathrm{B}$ is smaller than that of A, then the spin-only magnetic moment $(\mu)$ value of B in BM is __________. (Nearest integer)

Total number of relatively more stable isomer(s) possible for octahedral complex $\left[\mathrm{Cu}(\mathrm{en})_{2}(\mathrm{SCN})_{2}\right]$ will be _________.

On complete combustion of $0.492 \mathrm{~g}$ of an organic compound containing $\mathrm{C}, \mathrm{H}$ and $\mathrm{O}$, $0.7938 \mathrm{~g}$ of $\mathrm{CO}_{2}$ and $0.4428 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$ was produced. The % composition of oxygen in the compound is ___________.

Let the solution curve of the differential equation $x \mathrm{~d} y=\left(\sqrt{x^{2}+y^{2}}+y\right) \mathrm{d} x, x>0$, intersect the line $x=1$ at $y=0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is :

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)$ is :

Let the vectors $\vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k}, \vec{b}=(1-t) \hat{i}+(1+t) \hat{j}+2 \hat{k}$ and $\vec{c}=t \hat{i}-t \hat{j}+\hat{k}, t \in \mathbf{R}$ be such that for $\alpha, \beta, \gamma \in \mathbf{R}, \alpha \vec{a}+\beta \vec{b}+\gamma \vec{c}=\overrightarrow{0} \Rightarrow \alpha=\beta=\gamma=0$. Then, the set of all values of $t$ is :

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to :

Let a vector $\vec{a}$ has magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in \mathbf{R} \times \mathbf{R}-\{(0,0)\}$, the vector $(x \vec{a}+y \vec{b})$ is perpendicular to the vector $(6 y \vec{a}-18 x \vec{b})$. Then the value of $|\vec{a} \times \vec{b}|$ is equal to :

For $\mathrm{t} \in(0,2 \pi)$, if $\mathrm{ABC}$ is an equilateral triangle with vertices $\mathrm{A}(\sin t,-\cos \mathrm{t}), \mathrm{B}(\operatorname{cost}, \sin t)$ and $C(a, b)$ such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $\left(a^{2}-b^{2}\right)$ is equal to :

For $\alpha \in \mathbf{N}$, consider a relation $\mathrm{R}$ on $\mathbf{N}$ given by $\mathrm{R}=\{(x, y): 3 x+\alpha y$ is a multiple of 7$\}$. The relation $R$ is an equivalence relation if and only if :

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :

If $y=y(x), x \in(0, \pi / 2)$ be the solution curve of the differential equation

$\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=2 \mathrm{e}^{-4 x}(2 \sin 2 x+\cos 2 x)$,

with $y(\pi / 4)=\mathrm{e}^{-\pi}$, then $y(\pi / 6)$ is equal to :

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2 y=\frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $\mathrm{C}$, makes an angle of $\frac{\pi}{4}$ with the line $\mathrm{CP}$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $P Q R$ (in unit $^{2}$ ) is :

The remainder when $7^{2022}+3^{2022}$ is divided by 5 is :

Let $S_{1}=\left\{z_{1} \in \mathbf{C}:\left|z_{1}-3\right|=\frac{1}{2}\right\}$ and $S_{2}=\left\{z_{2} \in \mathbf{C}:\left|z_{2}-\right| z_{2}+1||=\left|z_{2}+\right| z_{2}-1||\right\}$. Then, for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$, the least value of $\left|z_{2}-z_{1}\right|$ is :

If the minimum value of $f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0$, is 14 , then the value of $\alpha$ is equal to :

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers. Let $f(x)=\alpha x^{5}+\beta x^{3}+\gamma x, x \in \mathbf{R}$ and $g: \mathbf{R} \rightarrow \mathbf{R}$ be such that $g(f(x))=x$ for all $x \in \mathbf{R}$. If $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots, \mathrm{a}_{\mathrm{n}}$ be in arithmetic progression with mean zero, then the value of $f\left(g\left(\frac{1}{\mathrm{n}} \sum\limits_{i=1}^{\mathrm{n}} f\left(\mathrm{a}_{i}\right)\right)\right)$ is equal to :

The minimum value of the twice differentiable function $f(x)=\int\limits_{0}^{x} \mathrm{e}^{x-\mathrm{t}} f^{\prime}(\mathrm{t}) \mathrm{dt}-\left(x^{2}-x+1\right) \mathrm{e}^{x}$, $x \in \mathbf{R}$, is :

Let $S$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $\{A, B, C, D, E\}$ or a number from $\{1,2,3,4,5\}$ with the repetition of characters allowed. If the number of passwords in $S$ whose at least one character is a number from $\{1,2,3,4,5\}$ is $\alpha \times 5^{6}$, then $\alpha$ is equal to ___________.

Let $\mathrm{P}(-2,-1,1)$ and $\mathrm{Q}\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)$ be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $\alpha,-1, \beta$, where both $\alpha$ and $\beta$ are integers of minimum absolute values, then $\alpha^{2}+\beta^{2}$ is equal to ____________.

Let $f:[0,1] \rightarrow \mathbf{R}$ be a twice differentiable function in $(0,1)$ such that $f(0)=3$ and $f(1)=5$. If the line $y=2 x+3$ intersects the graph of $f$ at only two distinct points in $(0,1)$, then the least number of points $x \in(0,1)$, at which $f^{\prime \prime}(x)=0$, is ____________.

If $\int\limits_{0}^{\sqrt{3}} \frac{15 x^{3}}{\sqrt{1+x^{2}+\sqrt{\left(1+x^{2}\right)^{3}}}} \mathrm{~d} x=\alpha \sqrt{2}+\beta \sqrt{3}$, where $\alpha, \beta$ are integers, then $\alpha+\beta$ is equal to __________.

Let $A=\left[\begin{array}{cc}1 & -1 \\ 2 & \alpha\end{array}\right]$ and $B=\left[\begin{array}{cc}\beta & 1 \\ 1 & 0\end{array}\right], \alpha, \beta \in \mathbf{R}$. Let $\alpha_{1}$ be the value of $\alpha$ which satisfies $(\mathrm{A}+\mathrm{B})^{2}=\mathrm{A}^{2}+\left[\begin{array}{ll}2 & 2 \\ 2 & 2\end{array}\right]$ and $\alpha_{2}$ be the value of $\alpha$ which satisfies $(\mathrm{A}+\mathrm{B})^{2}=\mathrm{B}^{2}$. Then $\left|\alpha_{1}-\alpha_{2}\right|$ is equal to ___________.

For $\mathrm{p}, \mathrm{q} \in \mathbf{R}$, consider the real valued function $f(x)=(x-\mathrm{p})^{2}-\mathrm{q}, x \in \mathbf{R}$ and $\mathrm{q}>0$. Let $\mathrm{a}_{1}$, $\mathrm{a}_{2^{\prime}}$ $\mathrm{a}_{3}$ and $\mathrm{a}_{4}$ be in an arithmetic progression with mean $\mathrm{p}$ and positive common difference. If $\left|f\left(\mathrm{a}_{i}\right)\right|=500$ for all $i=1,2,3,4$, then the absolute difference between the roots of $f(x)=0$ is ___________.

Let $x_{1}, x_{2}, x_{3}, \ldots, x_{20}$ be in geometric progression with $x_{1}=3$ and the common ratio $\frac{1}{2}$. A new data is constructed replacing each $x_{i}$ by $\left(x_{i}-i\right)^{2}$. If $\bar{x}$ is the mean of new data, then the greatest integer less than or equal to $\bar{x}$ is ____________.

$\lim\limits_{x \rightarrow 0}\left(\frac{(x+2 \cos x)^{3}+2(x+2 \cos x)^{2}+3 \sin (x+2 \cos x)}{(x+2)^{3}+2(x+2)^{2}+3 \sin (x+2)}\right)^{\frac{100}{x}}$ is equal to ___________.

The sum of all real values of $x$ for which $\frac{3 x^{2}-9 x+17}{x^{2}+3 x+10}=\frac{5 x^{2}-7 x+19}{3 x^{2}+5 x+12}$ is equal to __________.

The dimensions of $\left(\frac{\mathrm{B}^{2}}{\mu_{0}}\right)$ will be :

(if $\mu_{0}$ : permeability of free space and $B$ : magnetic field)

A NCC parade is going at a uniform speed of $9 \mathrm{~km} / \mathrm{h}$ under a mango tree on which a monkey is sitting at a height of $19.6 \mathrm{~m}$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )

In two different experiments, an object of mass $5 \mathrm{~kg}$ moving with a speed of $25 \mathrm{~ms}^{-1}$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

A balloon has mass of $10 \mathrm{~g}$ in air. The air escapes from the balloon at a uniform rate with velocity $4.5 \mathrm{~cm} / \mathrm{s}$. If the balloon shrinks in $5 \mathrm{~s}$ completely. Then, the average force acting on that balloon will be (in dyne).

If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

The force required to stretch a wire of cross-section $1 \mathrm{~cm}^{2}$ to double its length will be : (Given Yong's modulus of the wire $=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$)

Given below are two statements :

Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2 v$.

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

In the wave equation

$$y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m}$$

the velocity of the wave will be:

Two capacitors, each having capacitance $40 \,\mu \mathrm{F}$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $\mathrm{K}$ such that the equivalence capacitance of the system became $24 \,\mu \mathrm{F}$. The value of $\mathrm{K}$ will be :

A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :

The current sensitivity of a galvanometer can be increased by :

(A) decreasing the number of turns

(B) increasing the magnetic field

(C) decreasing the area of the coil

(D) decreasing the torsional constant of the spring

Choose the most appropriate answer from the options given below :

As shown in the figure, a metallic rod of linear density $0.45 \mathrm{~kg} \mathrm{~m}^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $45^{\circ}$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $0.15 \mathrm{~T}$ magnetic field is acting on it in the vertical upward direction, will be :

{Use $g=10 \mathrm{~m} / \mathrm{s}^{2}$}

The equation of current in a purely inductive circuit is $5 \sin \left(49\, \pi t-30^{\circ}\right)$. If the inductance is $30 \,\mathrm{mH}$ then the equation for the voltage across the inductor, will be :

$\left\{\right.$ Let $\left.\pi=\frac{22}{7}\right\}$

As shown in the figure, after passing through the medium 1 . The speed of light $v_{2}$ in medium 2 will be :

$\left(\right.$ Given $\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}$ )

In normal adujstment, for a refracting telescope, the distance between objective and eye piece is $30 \mathrm{~cm}$. The focal length of the objective, when the angular magnification of the telescope is 2 , will be :

The equation $\lambda=\frac{1.227}{x} \mathrm{~nm}$ can be used to find the de-Brogli wavelength of an electron. In this equation $x$ stands for :

Where

$\mathrm{m}=$ mass of electron

$\mathrm{P}=$ momentum of electron

$\mathrm{K}=$ Kinetic energy of electron

$\mathrm{V}=$ Accelerating potential in volts for electron

Identify the solar cell characteristics from the following options :

If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k}$ on $\hat{i}+2 \hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be ___________.

In a Young's double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes' separation of 7.2 mm. Now another light is used to produce an interference pattern with consecutive bright fringes' separation of 8.1 mm. The wavelength of second light is __________ nm.

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $212\,\mathrm{rad} \,\mathrm{s}^{-1}$ and $232 \,\mathrm{rad} \,\mathrm{s}^{-1}$. The value of resistance in the circuit is $R=5 \,\Omega$. The self inductance in the circuit is __________ $\mathrm{mH}$.

Two electric dipoles of dipole moments $1.2 \times 10^{-30} \,\mathrm{Cm}$ and $2.4 \times 10^{-30} \,\mathrm{Cm}$ are placed in two different uniform electric fields of strengths $5 \times 10^{4} \,\mathrm{NC}^{-1}$ and $15 \times 10^{4} \,\mathrm{NC}^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is __________.

The diameter of an air bubble which was initially $2 \mathrm{~mm}$, rises steadily through a solution of density $1750 \mathrm{~kg} \mathrm{~m}^{-3}$ at the rate of $0.35 \,\mathrm{cms}^{-1}$. The coefficient of viscosity of the solution is _________ poise (in nearest integer). (the density of air is negligible).

A block of mass '$\mathrm{m}$' (as shown in figure) moving with kinetic energy E compresses a spring through a distance $25 \mathrm{~cm}$ when, its speed is halved. The value of spring constant of used spring will be $\mathrm{nE} \,\,\mathrm{Nm}^{-1}$ for $\mathrm{n}=$ _________.

Four identical discs each of mass '$\mathrm{M}$' and diameter '$\mathrm{a}$' are arranged in a small plane as shown in figure. If the moment of inertia of the system about $\mathrm{OO}^{\prime}$ is $\frac{x}{4} \,\mathrm{Ma}^{2}$. Then, the value of $x$ will be ____________.