In which of the following processes, the bond order increases and paramagnetic character changes to diamagnetic one ?

In the reaction given below

'A' is

The mismatched combinations are

A. Chlorophyll - Co

B. Water hardness - EDTA

C. Photography $-\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{-}$

D. Wilkinson catalyst $-\left[\left(\mathrm{Ph}_{3} \mathrm{P}\right)_{3} \mathrm{RhCl}\right]$

E. Chelating ligand - D-Penicillamine

Choose the correct answer from the options given below :

The energy of an electron in the first Bohr orbit of hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$. Its energy in the third Bohr orbit is ____________.

An organic compound gives $0.220 \mathrm{~g}$ of $\mathrm{CO}_{2}$ and $0.126 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$ on complete combustion. If the $\%$ of carbon is 24 then the $\%$ of hydrogen is __________ $\times 10^{-1}$. ( Nearest integer)

$\mathrm{t}_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $\mathrm{t}_{50}$ is the time required for the reaction to undergo $50 \%$ completion. The relation between $\mathrm{t}_{87.5}$ and $\mathrm{t}_{50}$ for a first order reaction is $\mathrm{t}_{87.5}=x \times \mathrm{t}_{50}$ The value of $x$ is ___________. (Nearest integer)

For the given reaction

The total number of possible products formed by tertiary carbocation of A is ____________.

Solution of $12 \mathrm{~g}$ of non-electrolyte (A) prepared by dissolving it in $1000 \mathrm{~mL}$ of water exerts the same osmotic pressure as that of $0.05 ~\mathrm{M}$ glucose solution at the same temperature. The empirical formula of $\mathrm{A}$ is $\mathrm{CH}_{2} \mathrm{O}$. The molecular mass of $\mathrm{A}$ is __________ g. (Nearest integer)

$\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB} . \Delta H_{f}^{0}=-200 \mathrm{~kJ} \mathrm{~mol}^{-1}$

$\mathrm{AB}, \mathrm{A}_{2}$ and $\mathrm{B}_{2}$ are diatomic molecules. If the bond enthalpies of $\mathrm{A}_{2}, \mathrm{~B}_{2}$ and $\mathrm{AB}$ are in the ratio $1: 0.5: 1$, then the bond enthalpy of $\mathrm{A}_{2}$ is ____________ $\mathrm{kJ} ~\mathrm{mol}^{-1}$ (Nearest integer)

2-Methyl propyl bromide reacts with $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-}$ and gives 'A' whereas on reaction with $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ it gives 'B'. The mechanism followed in these reactions and the products 'A' and 'B' respectively are :

In the above reaction, left hand side and right hand side rings are named as '$\mathrm{A}$' and 'B' respectively. They undergo ring expansion. The correct statement for this process is:

The products formed in the above reaction are

$\mathrm{KMnO}_{4}$ is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute $\mathrm{H}_{2} \mathrm{SO}_{4}$. Number of water molecules produced for 2 molecules of $\mathrm{KMnO}_{4}$ is ___________.

$20 \mathrm{~mL}$ of calcium hydroxide was consumed when it was reacted with $10 \mathrm{~mL}$ of unknown solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. Also $20 \mathrm{~mL}$ standard solution of $0.5 ~\mathrm{M} ~\mathrm{HCl}$ containing 2 drops of phenolphthalein was titrated with calcium hydroxide, the mixture showed pink colour when burette displayed the value of $35.5 \mathrm{~mL}$ whereas the burette showed $25.5 \mathrm{~mL}$ initially. The concentration of $\mathrm{H}_{2} \mathrm{SO}_{4}$ is _____________ M. (Nearest integer)

Which of the following statements are not correct?

A. The electron gain enthalpy of $\mathrm{F}$ is more negative than that of $\mathrm{Cl}$.

B. Ionization enthalpy decreases in a group of periodic table.

C. The electronegativity of an atom depends upon the atoms bonded to it.

D. $\mathrm{Al}_{2} \mathrm{O}_{3}$ and $\mathrm{NO}$ are examples of amphoteric oxides.

Choose the most appropriate answer from the options given below :

In the reaction given below

'B' is

A metal surface of $100 \mathrm{~cm}^{2}$ area has to be coated with nickel layer of thickness $0.001 \mathrm{~mm}$. A current of $2 \mathrm{~A}$ was passed through a solution of $\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}$ for '$\mathrm{x}$' seconds to coat the desired layer. The value of $\mathrm{x}$ is __________. (Nearest integer) ( $\rho_{\mathrm{Ni}}$ (density of Nickel) is $10 \mathrm{~g} \mathrm{~mL}$, Molar mass of Nickel is $60 \mathrm{~g} \mathrm{~mol}^{-1}$ $\left.\mathrm{F}=96500 ~\mathrm{C} ~\mathrm{mol}^{-1}\right)$

In the following reaction 'X' is

Among the following compounds, the one which shows highest dipole moment is

The pair of lanthanides in which both elements have high third - ionization energy is :

$25.0 \mathrm{~mL}$ of $0.050 ~\mathrm{M} ~\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$ is mixed with $25.0 \mathrm{~mL}$ of $0.020 ~\mathrm{M} ~\mathrm{NaF} . \mathrm{K}_{\mathrm{Sp}}$ of $\mathrm{BaF}_{2}$ is $0.5 \times 10^{-6}$ at $298 \mathrm{~K}$. The ratio of $\left[\mathrm{Ba}^{2+}\right]\left[\mathrm{F}^{-}\right]^{2}$ and $\mathrm{K}_{\mathrm{sp}}$ is ___________.

(Nearest integer)

The area of the region enclosed by the curve $f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi$ and the $x$-axis is

Let $\mathrm{PQ}$ be a focal chord of the parabola $y^{2}=36 x$ of length 100 , making an acute angle with the positive $x$-axis. Let the ordinate of $\mathrm{P}$ be positive and $\mathrm{M}$ be the point on the line segment PQ such that PM : MQ = 3 : 1. Then which of the following points does NOT lie on the line passing through M and perpendicular to the line $\mathrm{PQ}$?

Let the mean of the data

be 5. If $m$ and $\sigma^{2}$ are respectively the mean deviation about the mean and the variance of the data, then $\frac{3 \alpha}{m+\sigma^{2}}$ is equal to __________

If $S=\left\{x \in \mathbb{R}: \sin ^{-1}\left(\frac{x+1}{\sqrt{x^{2}+2 x+2}}\right)-\sin ^{-1}\left(\frac{x}{\sqrt{x^{2}+1}}\right)=\frac{\pi}{4}\right\}$, then \sum_\limits{x \in s}\left(\sin \left(\left(x^{2}+x+5\right) \frac{\pi}{2}\right)-\cos \left(\left(x^{2}+x+5\right) \pi\right)\right) is equal to ____________.

Let for $x \in \mathbb{R}, S_{0}(x)=x, S_{k}(x)=C_{k} x+k \int_{0}^{x} S_{k-1}(t) d t$, where

$C_{0}=1, C_{k}=1-\int_{0}^{1} S_{k-1}(x) d x, k=1,2,3, \ldots$ Then $S_{2}(3)+6 C_{3}$ is equal to ____________.

A bullet of $10 \mathrm{~g}$ leaves the barrel of gun with a velocity of $600 \mathrm{~m} / \mathrm{s}$. If the barrel of gun is $50 \mathrm{~cm}$ long and mass of gun is $3 \mathrm{~kg}$, then value of impulse supplied to the gun will be :

A planet having mass $9 \mathrm{Me}$ and radius $4 \mathrm{R}_{\mathrm{e}}$, where $\mathrm{Me}$ and $\mathrm{Re}$ are mass and radius of earth respectively, has escape velocity in $\mathrm{km} / \mathrm{s}$ given by:

(Given escape velocity on earth $\mathrm{V}_{\mathrm{e}}=11.2 \times 10^{3} \mathrm{~m} / \mathrm{s}$ )

The source of time varying magnetic field may be

(A) a permanent magnet

(B) an electric field changing linearly with time

(C) direct current

(D) a decelerating charge particle

(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

A body of mass $(5 \pm 0.5) ~\mathrm{kg}$ is moving with a velocity of $(20 \pm 0.4) ~\mathrm{m} / \mathrm{s}$. Its kinetic energy will be

Let $s_{1}, s_{2}, s_{3}, \ldots, s_{10}$ respectively be the sum to 12 terms of 10 A.P. s whose first terms are $1,2,3, \ldots .10$ and the common differences are $1,3,5, \ldots \ldots, 19$ respectively. Then \sum_\limits{i=1}^{10} s_{i} is equal to :

Let $B=\left[\begin{array}{lll}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & 4\end{array}\right], \alpha > 2$ be the adjoint of a matrix $A$ and $|A|=2$. Then $\left[\begin{array}{ccc}\alpha & -2 \alpha & \alpha\end{array}\right] B\left[\begin{array}{c}\alpha \\ -2 \alpha \\ \alpha\end{array}\right]$ is equal to :

For $x \in \mathbb{R}$, two real valued functions $f(x)$ and $g(x)$ are such that, $g(x)=\sqrt{x}+1$ and $f \circ g(x)=x+3-\sqrt{x}$. Then $f(0)$ is equal to

For the differentiable function $f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$, let $3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10$, then $\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|$ is equal to

\max _\limits{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}=

A vessel of depth '$d$' is half filled with oil of refractive index $n_{1}$ and the other half is filled with water of refractive index $n_{2}$. The apparent depth of this vessel when viewed from above will be-

The rms speed of oxygen molecule in a vessel at particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$, where $v$ is the average speed of the molecule. The value of $x$ will be:

$\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

Two charges each of magnitude $0.01 ~\mathrm{C}$ and separated by a distance of $0.4 \mathrm{~mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of 10 dyne/C making $30^{\circ}$ angle with $\vec{E}$, the magnitude of torque acting on dipole is:

Under isothermal condition, the pressure of a gas is given by $\mathrm{P}=a \mathrm{~V}^{-3}$, where $a$ is a constant and $\mathrm{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

Two trains 'A' and 'B' of length '$l$' and '$4 l$' are travelling into a tunnel of length '$\mathrm{L}$' in parallel tracks from opposite directions with velocities $108 \mathrm{~km} / \mathrm{h}$ and $72 \mathrm{~km} / \mathrm{h}$, respectively. If train 'A' takes $35 \mathrm{~s}$ less time than train 'B' to cross the tunnel then. length '$L$' of tunnel is :

(Given $\mathrm{L}=60 l$ )

Different combination of 3 resistors of equal resistance $\mathrm{R}$ are shown in the figures. The increasing order for power dissipation is:

The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x}+1}$, that are capable of raising $300 \mathrm{~kg}$ water in 5 minutes and $50 \mathrm{~kg}$ water in 2 minutes respectively from a well of $100 \mathrm{~m}$ deep. The value of $x$ will be

When a resistance of $5 ~\Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $250 \mathrm{~mA}$, however when $1050 ~\Omega$ resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is ____________ $\Omega$.

A potential $\mathrm{V}_{0}$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_{1}$. The wire is then cut into two equal halves and a potential of $V_{0}$ is applied across the length of each half. The total power dissipation across two wires is $P_{2}$. The ratio $P_{2}: \mathrm{P}_{1}$ is $\sqrt{x}: 1$. The value of $x$ is ___________.

At a given point of time the value of displacement of a simple harmonic oscillator is given as $\mathrm{y}=\mathrm{A} \cos \left(30^{\circ}\right)$. If amplitude is $40 \mathrm{~cm}$ and kinetic energy at that time is $200 \mathrm{~J}$, the value of force constant is $1.0 \times 10^{x} ~\mathrm{Nm}^{-1}$. The value of $x$ is ____________.

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5 \mathrm{~m}$ distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi}$ m and $\frac{4}{\pi}$ m perpendicular distances from line charge towards sheet charge, respectively. '$\mathrm{E}_{\mathrm{P}}$' and '$\mathrm{E}_{\mathrm{Q}}$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $\frac{E_{p}}{E_{0}}=\frac{4}{a}$ for $2|\sigma|=|\lambda|$, then the value of $a$ is ___________.

\int_\limits{0}^{\infty} \frac{6}{e^{3 x}+6 e^{2 x}+11 e^{x}+6} d x=

Let $\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}$ and $\vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}$. If a vector $\vec{d}$ satisfies $\vec{d} \times \vec{b}=\vec{c} \times \vec{b}$ and $\vec{d} \cdot \vec{a}=24$, then $|\vec{d}|^{2}$ is equal to :

The number of seven digit positive integers formed using the digits $1,2,3$ and $4$ only and sum of the digits equal to $12$ is ___________.

Let $\alpha$ be the constant term in the binomial expansion of $\left(\sqrt{x}-\frac{6}{x^{\frac{3}{2}}}\right)^{n}, n \leq 15$. If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of $x^{-n}$ is $\lambda \alpha$, then $\lambda$ is equal to _____________.

Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $\mathrm{A}$ is $1.5 \mathrm{~cm}^{2}$, and $\mathrm{B}$ is $25 \mathrm{~mm}^{2}$, if the speed of liquid at $\mathrm{B}$ is $60 \mathrm{~cm} / \mathrm{s}$ then $\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)$ is :

(Given $\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are liquid pressures at $\mathrm{A}$ and $\mathrm{B}$% points.

density $\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$

$\mathrm{A}$ and $\mathrm{B}$ are on the axis of tube

A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$, the top most point on the disc is $\mathrm{A}$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

For the following circuit and given inputs A and B, choose the correct option for output '$Y$'

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

A fish rising vertically upward with a uniform velocity of $8 \mathrm{~ms}^{-1}$, observes that a bird is diving vertically downward towards the fish with the velocity of $12 \mathrm{~ms}^{-1}$. If the refractive index of water is $\frac{4}{3}$, then the actual velocity of the diving bird to pick the fish, will be __________ $\mathrm{ms}^{-1}$.

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $\frac{E^{a}}{2 b} \mathrm{~J} / s$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ will be __________.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi: 22$ then, the value of its angular speed will be ____________ $\mathrm{rad} / \mathrm{s}$.

The elastic potential energy stored in a steel wire of length $20 \mathrm{~m}$ stretched through $2 \mathrm{~cm}$ is $80 \mathrm{~J}$. The cross sectional area of the wire is __________ $\mathrm{mm}^{2}$.

$\left(\right.$ Given, $\left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$

For the system of linear equations

$2 x+4 y+2 a z=b$

$x+2 y+3 z=4$

$2 x-5 y+2 z=8$

which of the following is NOT correct?

Let $y=y_{1}(x)$ and $y=y_{2}(x)$ be the solution curves of the differential equation $\frac{d y}{d x}=y+7$ with initial conditions $y_{1}(0)=0$ and $y_{2}(0)=1$ respectively. Then the curves $y=y_{1}(x)$ and $y=y_{2}(x)$ intersect at

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $\mathrm{X}$ denotes the number of tosses of the coin, then the mean of $\mathrm{X}$ is :

The set of all $a \in \mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root, is :

Fractional part of the number $\frac{4^{2022}}{15}$ is equal to

The number of symmetric matrices of order 3, with all the entries from the set $\{0,1,2,3,4,5,6,7,8,9\}$ is :

Let $w=z \bar{z}+k_{1} z+k_{2} i z+\lambda(1+i), k_{1}, k_{2} \in \mathbb{R}$. Let $\operatorname{Re}(w)=0$ be the circle $\mathrm{C}$ of radius 1 in the first quadrant touching the line $y=1$ and the $y$-axis. If the curve $\operatorname{Im}(w)=0$ intersects $\mathrm{C}$ at $\mathrm{A}$ and $\mathrm{B}$, then $30(A B)^{2}$ is equal to __________

Let $\vec{a}=3 \hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2 \hat{i}-3 \hat{j}+3 \hat{k}$. If $\vec{b}$ is a vector such that $\vec{a}=\vec{b} \times \vec{c}$ and $|\vec{b}|^{2}=50$, then $|72-| \vec{b}+\left.\vec{c}\right|^{2} \mid$ is equal to __________.

The difference between threshold wavelengths for two metal surfaces $\mathrm{A}$ and $\mathrm{B}$ having work function $\phi_{A}=9 ~\mathrm{eV}$ and $\phi_{B}=4 \cdot 5 ~\mathrm{eV}$ in $\mathrm{nm}$ is:

$\{$ Given, hc $=1242 ~\mathrm{eV} \mathrm{nm}\}$

$_{92}^{238}A \to _{90}^{234}B + _2^4D + Q$

In the given nuclear reaction, the approximate amount of energy released will be:

[Given, mass of ${ }_{92}^{238} \mathrm{~A}=238.05079 \times 931.5 ~\mathrm{MeV} / \mathrm{c}^{2},$

mass of ${ }_{90}^{234} B=234 \cdot 04363 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2},$

mass of $\left.{ }_{2}^{4} D=4 \cdot 00260 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}\right]$

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

The radius of $2^{\text {nd }}$ orbit of $\mathrm{He}^{+}$ of Bohr's model is $r_{1}$ and that of fourth orbit of $\mathrm{Be}^{3+}$ is represented as $r_{2}$. Now the ratio $\frac{r_{2}}{r_{1}}$ is $x: 1$. The value of $x$ is ___________.