Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : The energy required to form $\mathrm{Mg}^{2+}$ from $\mathrm{Mg}$ is much higher than that required to produce $\mathrm{Mg}^+$

Reason $\mathbf{R}: \mathrm{Mg}^{2+}$ is small ion and carry more charge than $\mathrm{Mg}^{+}$

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

The number of molecules from the following which contain only two lone pair of electrons is ________

$\mathrm{H}_{2} \mathrm{O}, \mathrm{N}_{2}, \mathrm{CO}, \mathrm{XeF}_{4}, \mathrm{NH}_{3}, \mathrm{NO}, \mathrm{CO}_{2}, \mathrm{~F}_{2}$

For a metal ion, the calculated magnetic moment is $4.90 ~\mathrm{BM}$. This metal ion has ___________ number of unpaired electrons.

The number of incorrect statement/s from the following is ___________

A. The successive half lives of zero order reactions decreases with time.

B. A substance appearing as reactant in the chemical equation may not affect the rate of reaction

C. Order and molecularity of a chemical reaction can be a fractional number

D. The rate constant units of zero and second order reaction are $\mathrm{mol} ~\mathrm{L}^{-1} \mathrm{~s}^{-1}$ and $\mathrm{mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}$ respectively

$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)+\mathrm{C}(g)$

For the given reaction, if the initial pressure is $450 \mathrm{~mm} ~\mathrm{Hg}$ and the pressure at time $\mathrm{t}$ is $720 \mathrm{~mm} ~\mathrm{Hg}$ at a constant temperature $\mathrm{T}$ and constant volume $\mathrm{V}$. The fraction of $\mathrm{A}(\mathrm{g})$ decomposed under these conditions is $x \times 10^{-1}$. The value of $x$ is ___________ (nearest integer)

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :

If the coefficients of $x$ and $x^{2}$ in $(1+x)^{\mathrm{p}}(1-x)^{\mathrm{q}}$ are 4 and $-$5 respectively, then $2 p+3 q$ is equal to :

Let $f$ be a continuous function satisfying \int_\limits{0}^{t^{2}}\left(f(x)+x^{2}\right) d x=\frac{4}{3} t^{3}, \forall t > 0. Then $f\left(\frac{\pi^{2}}{4}\right)$ is equal to :

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution

where $\sum f_{i}=62$. If $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^{2}+\sigma^{2}\right]$ is equal to :

Let $\vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+2 \hat{k}$. Let $\vec{d}$ be a vector which is perpendicular to both $\vec{a}$ and $\vec{b}$, and $\vec{c} \cdot \vec{d}=12$. Then $(-\hat{i}+\hat{j}-\hat{k}) \cdot(\vec{c} \times \vec{d})$ is equal to :

Let A be the point $(1,2)$ and B be any point on the curve $x^{2}+y^{2}=16$. If the centre of the locus of the point P, which divides the line segment $\mathrm{AB}$ in the ratio $3: 2$ is the point C$(\alpha, \beta)$, then the length of the line segment $\mathrm{AC}$ is :

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

For a periodic motion represented by the equation

$y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$

the amplitude of the motion is

The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is $6.0 \times 10^{-7} \mathrm{~T}$. The maximum value of electric field in the electromagnetic wave is

The time period of a satellite, revolving above earth's surface at a height equal to $\mathrm{R}$ will be

(Given $g=\pi^{2} \mathrm{~m} / \mathrm{s}^{2}, \mathrm{R}=$ radius of earth)

Given below are two statements:

Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g)

Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.

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

The major product 'P' formed in the given reaction is:

The decreasing order of hydride affinity for following carbocations is:

Choose the correct answer from the options given below:

In the reaction given below:

The product 'X' is:

The correct order of the number of unpaired electrons in the given complexes is

A. $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$

B. $\left[\mathrm{Fe} \mathrm{F}_{6}\right]^{3-}$

C. $\left[\mathrm{CoF}_{6}\right]^{3-}$

D. $\left.[\mathrm{Cr} \text { (oxalate})_{3}\right]^{3-}$

E. $\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]$

Choose the correct answer from the options given below:

The correct order for acidity of the following hydroxyl compound is :

A. $\mathrm{CH}_{3} \mathrm{OH}$

B. $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}$

C.

D.

E.

Choose the correct answer from the options given below:

An aqueous solution of volume $300 \mathrm{~cm}^{3}$ contains $0.63 \mathrm{~g}$ of protein. The osmotic pressure of the solution at $300 \mathrm{~K}$ is 1.29 mbar. The molar mass of the protein is ___________ $\mathrm{g} ~\mathrm{mol}^{-1}$

Given : R = 0.083 L bar K$^{-1}$ mol$^{-1}$

The number of endothermic process/es from the following is ______________.

A. $\mathrm{I}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{I}(\mathrm{g})$

B. $\mathrm{HCl}(\mathrm{g}) \rightarrow \mathrm{H}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})$

C. $\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$

D. $\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})$

E. Dissolution of ammonium chloride in water

The specific conductance of $0.0025 ~\mathrm{M}$ acetic acid is $5 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}$ at a certain temperature. The dissociation constant of acetic acid is __________ $\times ~10^{-7}$ (Nearest integer)

Consider limiting molar conductivity of $\mathrm{CH}_{3} \mathrm{COOH}$ as $400 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$

Let $S = \left\{ {z = x + iy:{{2z - 3i} \over {4z + 2i}}\,\mathrm{is\,a\,real\,number}} \right\}$. Then which of the following is NOT correct?

If the domain of the function $f(x)=\sec ^{-1}\left(\frac{2 x}{5 x+3}\right)$ is $[\alpha, \beta) \mathrm{U}(\gamma, \delta]$, then $|3 \alpha+10(\beta+\gamma)+21 \delta|$ is equal to _________.

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

Given below are two statements:

Statement I : For diamagnetic substance, $-1 \leq \chi < 0$, where $\chi$ is the magnetic susceptibility.

Statement II : Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field.

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

Young's moduli of the material of wires A and B are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $\mathrm{A}$ and $\mathrm{B}$ will be in the ratio of

[Assume length of wires A and B are same]

The variation of stopping potential $\left(\mathrm{V}_{0}\right)$ as a function of the frequency $(v)$ of the incident light for a metal is shown in figure. The work function of the surface is

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : $3.1500 \mathrm{~g}$ of hydrated oxalic acid dissolved in water to make $250.0 \mathrm{~mL}$ solution will result in $0.1 \mathrm{~M}$ oxalic acid solution.

Reason $\mathbf{R}$ : Molar mass of hydrated oxalic acid is $126 \mathrm{~g} \mathrm{~mol}^{-1}$

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

Incorrect method of preparation for alcohols from the following is:

Match List I with List II

Choose the correct answer from the options given below:

In Carius tube, an organic compound '$\mathrm{X}$' is treated with sodium peroxide to form a mineral acid 'Y'.

The solution of $\mathrm{BaCl}_{2}$ is added to '$\mathrm{Y}$' to form a precipitate 'Z'. 'Z' is used for the quantitative estimation of an extra element. '$\mathrm{X}$' could be

The electron in the $\mathrm{n}^{\text {th }}$ orbit of $\mathrm{Li}^{2+}$ is excited to $(\mathrm{n}+1)$ orbit using the radiation of energy $1.47 \times 10^{-17} \mathrm{~J}$ (as shown in the diagram). The value of $\mathrm{n}$ is ___________

Given: $\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}$

Let $\mathrm{g}(x)=f(x)+f(1-x)$ and $f^{\prime \prime}(x) > 0, x \in(0,1)$. If $\mathrm{g}$ is decreasing in the interval $(0, a)$ and increasing in the interval $(\alpha, 1)$, then $\tan ^{-1}(2 \alpha)+\tan ^{-1}\left(\frac{1}{\alpha}\right)+\tan ^{-1}\left(\frac{\alpha+1}{\alpha}\right)$ is equal to :

If the points $\mathrm{P}$ and $\mathrm{Q}$ are respectively the circumcenter and the orthocentre of a $\triangle \mathrm{ABC}$, then $\overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}+\overrightarrow{\mathrm{PC}}$ is equal to :

Let $\mathrm{A}=\{2,3,4\}$ and $\mathrm{B}=\{8,9,12\}$. Then the number of elements in the relation $\mathrm{R}=\left\{\left(\left(a_{1}, \mathrm{~b}_{1}\right),\left(a_{2}, \mathrm{~b}_{2}\right)\right) \in(A \times B, A \times B): a_{1}\right.$ divides $\mathrm{b}_{2}$ and $\mathrm{a}_{2}$ divides $\left.\mathrm{b}_{1}\right\}$ is :

Let the tangent at any point P on a curve passing through the points (1, 1) and $\left(\frac{1}{10}, 100\right)$, intersect positive $x$-axis and $y$-axis at the points A and B respectively. If $\mathrm{PA}: \mathrm{PB}=1: k$ and $y=y(x)$ is the solution of the differential equation $e^{\frac{d y}{d x}}=k x+\frac{k}{2}, y(0)=k$, then $4 y(1)-6 \log _{\mathrm{e}} 3$ is equal to ____________.

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to __________.

Let $\mathrm{S}$ be the set of values of $\lambda$, for which the system of equations

$6 \lambda x-3 y+3 z=4 \lambda^{2}$,

$2 x+6 \lambda y+4 z=1$,

$3 x+2 y+3 \lambda z=\lambda$ has no solution. Then 12 \sum_\limits{i \in S}|\lambda| is equal to ___________.

A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $\mathrm{v}$, then the relation between $v, v_{1}$ and $v_{2}$ will be.

Match List I with List II

Choose the correct answer from the options given below:

In alkaline medium, the reduction of permanganate anion involves a gain of __________ electrons.

Let the number $(22)^{2022}+(2022)^{22}$ leave the remainder $\alpha$ when divided by 3 and $\beta$ when divided by 7. Then $\left(\alpha^{2}+\beta^{2}\right)$ is equal to :

For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _{e} x d x=\frac{1}{\alpha}\left(\frac{x}{e}\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{e}{x}\right)^{\delta x}+C$ , where e=\sum_\limits{n=0}^{\infty} \frac{1}{n !} and $\mathrm{C}$ is constant of integration, then $\alpha+2 \beta+3 \gamma-4 \delta$ is equal to :

If the area of the region $\left\{(x, \mathrm{y}):\left|x^{2}-2\right| \leq y \leq x\right\}$ is $\mathrm{A}$, then $6 \mathrm{A}+16 \sqrt{2}$ is equal to __________.

Let the equations of two adjacent sides of a parallelogram $\mathrm{ABCD}$ be $2 x-3 y=-23$ and $5 x+4 y=23$. If the equation of its one diagonal $\mathrm{AC}$ is $3 x+7 y=23$ and the distance of A from the other diagonal is $\mathrm{d}$, then $50 \mathrm{~d}^{2}$ is equal to ____________.

If each diode has a forward bias resistance of $25 ~\Omega$ in the below circuit,

Which of the following options is correct :

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : An electric fan continues to rotate for some time after the current is switched off.

Reason R : Fan continues to rotate due to inertia of motion.

In the light of above statements, choose the most appropriate answer from the options given below.

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

A gas is compressed adiabatically, which one of the following statement is NOT true.

The ratio of intensities at two points $\mathrm{P}$ and $\mathrm{Q}$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $\pi / 3$ and $\pi / 2$, respectively are

In an experiment with vernier callipers of least count $0.1 \mathrm{~mm}$, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between $3.2 \mathrm{~cm}$ and $3.3 \mathrm{~cm}$ marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as

The distance between two plates of a capacitor is $\mathrm{d}$ and its capacitance is $\mathrm{C}_{1}$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2 d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $\mathrm{C}_{2}$. The ratio $\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}$ is

A force of $-\mathrm{P} \hat{\mathrm{k}}$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is $\mathrm{P}(a \hat{i}+b \hat{j})$, The ratio of $\frac{a}{b}$ is $\frac{x}{2}$. The value of $x$ is -

A square loop of side $2.0 \mathrm{~cm}$ is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude $2.5 \mathrm{~A}$ and angular frequency $700 ~\mathrm{rad} ~\mathrm{s}^{-1}$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x \times 10^{-4} \mathrm{~V}$. The value of $x$ is __________.

$$\text { (Take, } \pi=\frac{22}{7} \text { ) }$$

If the maximum load carried by an elevator is $1400 \mathrm{~kg}$ ( $600 \mathrm{~kg}$ - Passengers + 800 $\mathrm{kg}$ - elevator), which is moving up with a uniform speed of $3 \mathrm{~m} \mathrm{~s}^{-1}$ and the frictional force acting on it is $2000 \mathrm{~N}$, then the maximum power used by the motor is __________ $\mathrm{kW}\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$ with focal length $24 \mathrm{~cm}$ and $9 \mathrm{~cm}$ respectively. The distance between two lenses is $10 \mathrm{~cm}$ and the object is placed $6 \mathrm{~cm}$ away from lens $\mathrm{L}_{1}$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is __________ $\mathrm{cm}$.

An electron revolves around an infinite cylindrical wire having uniform linear charge density $2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ $\times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}$. Given mass of electron $=9 \times 10^{-31} \mathrm{~kg}$

If 917 $\mathop A\limits^o$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ $\mathop A\limits^o$.

A straight wire carrying a current of $14 \mathrm{~A}$ is bent into a semi-circular arc of radius $2.2 \mathrm{~cm}$ as shown in the figure. The magnetic field produced by the current at the centre $(\mathrm{O})$ of the arc. is ____________ $\times ~10^{-4} \mathrm{~T}$

A rectangular block of mass $5 \mathrm{~kg}$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1 \mathrm{~m}$ and time period $3.14 \mathrm{~s}$. The maximum force exerted by spring on block is _________ N

A rectangular parallelopiped is measured as $1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 100 \mathrm{~cm}$. If its specific resistance is $3 \times 10^{-7} ~\Omega \mathrm{m}$, then the resistance between its two opposite rectangular faces will be ___________ $\times 10^{-7} ~\Omega$.

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0 \mathrm{~cm}^{2}$. The area of cross section at the outlet is $10 \mathrm{~mm}^{2}$. If the piston is pushed at a speed of $4 \mathrm{~cm} \mathrm{~s}^{-1}$, the speed of outgoing fluid is __________ $\mathrm{cm} \mathrm{s}^{-1}$