If $\mathrm{Ni}^{2+}$ is replaced by $\mathrm{Pt}^{2+}$ in the complex $\left[\mathrm{NiCl}_{2} \mathrm{Br}_{2}\right]^{2-}$, which of the following properties are expected to get changed ?

A. Geometry

B. Geometrical isomerism

C. Optical isomerism

D. Magnetic properties

What weight of glucose must be dissolved in $100 \mathrm{~g}$ of water to lower the vapour pressure by $0.20 \mathrm{~mm} ~\mathrm{Hg}$ ?

(Assume dilute solution is being formed)

Given : Vapour pressure of pure water is $54.2 \mathrm{~mm} ~\mathrm{Hg}$ at room temperature. Molar mass of glucose is $180 \mathrm{~g} \mathrm{~mol}^{-1}$

Compound 'B' is

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : $\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}$ absorbs at lower wavelength of light with respect to $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}$

Reason R : It is because the wavelength of the light absorbed depends on the oxidation state of the metal ion.

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

Match List I with List II

Choose the correct answer from the options given below :

A solution is prepared by adding $2 \mathrm{~g}$ of "$\mathrm{X}$" to 1 mole of water. Mass percent of "$\mathrm{X}$" in the solution is :

Which one of the following pairs is an example of polar molecular solids?

The major product formed in the following reaction is

Choose the correct answer from the options given below :

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : A solution of the product obtained by heating a mole of glycine with a mole of chlorine in presence of red phosphorous generates chiral carbon atom.

Reason R : A molecule with 2 chiral carbons is always optically active.

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

Product [X] formed in the above reaction is :

The volume of hydrogen liberated at STP by treating $2.4 \mathrm{~g}$ of magnesium with excess of hydrochloric acid is _________ $\times ~10^{-2} \mathrm{~L}$

Given : Molar volume of gas is $22.4 \mathrm{~L}$ at STP.

Molar mass of magnesium is $24 \mathrm{~g} \mathrm{~mol}^{-1}$

The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+\mathrm{x})^{\mathrm{n}+2}$, which are in the ratio $1: 3: 5$, is equal to :

If the $1011^{\text {th }}$ term from the end in the binominal expansion of $\left(\frac{4 x}{5}-\frac{5}{2 x}\right)^{2022}$ is 1024 times $1011^{\text {th }}$R term from the beginning, then $|x|$ is equal to

Let the mean of 6 observations $1,2,4,5, \mathrm{x}$ and $\mathrm{y}$ be 5 and their variance be 10 . Then their mean deviation about the mean is equal to :

The domain of the function $f(x)=\frac{1}{\sqrt{[x]^{2}-3[x]-10}}$ is : ( where $[\mathrm{x}]$ denotes the greatest integer less than or equal to $x$ )

Let $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$. If $\vec{c}$ is a vector such that \vec{a} \cdot \vec{c}=11, \vec{b} \cdot(\vec{a} \times \vec{c})=27\( and \)\vec{b} \cdot \vec{c}=-\sqrt{3}|\vec{b}|\(, then \)|\vec{a} \times \vec{c}|^{2} is equal to _________.

Let $\mathrm{A}=\{1,2,3,4,5\}$ and $\mathrm{B}=\{1,2,3,4,5,6\}$. Then the number of functions $f: \mathrm{A} \rightarrow \mathrm{B}$ satisfying $f(1)+f(2)=f(4)-1$ is equal to __________.

If A is the area in the first quadrant enclosed by the curve $\mathrm{C: 2 x^{2}-y+1=0}$, the tangent to $\mathrm{C}$ at the point $(1,3)$ and the line $\mathrm{x}+\mathrm{y}=1$, then the value of $60 \mathrm{~A}$ is _________.

Let $\mathrm{S}=\left\{z \in \mathbb{C}-\{i, 2 i\}: \frac{z^{2}+8 i z-15}{z^{2}-3 i z-2} \in \mathbb{R}\right\}$. If $\alpha-\frac{13}{11} i \in \mathrm{S}, \alpha \in \mathbb{R}-\{0\}$, then $242 \alpha^{2}$ is equal to _________.

The current flowing through R$_2$ is :

The ratio of the de-Broglie wavelengths of proton and electron having same Kinetic energy :

(Assume $m_{p}=m_{e} \times 1849$ )

When vector $\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$ is subtracted from vector $\overrightarrow{\mathrm{B}}$, it gives a vector equal to $2 \hat{j}$. Then the magnitude of vector $\overrightarrow{\mathrm{B}}$ will be :

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

As shown in the figure, a plane mirror is fixed at a height of $50 \mathrm{~cm}$ from the bottom of tank containing water $\left(\mu=\frac{4}{3}\right)$. The height of water in the tank is $8 \mathrm{~cm}$. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ___________ $\mathrm{cm}$.

A wire of density $8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ is stretched between two clamps $0.5 \mathrm{~m}$ apart. The extension developed in the wire is $3.2 \times 10^{-4} \mathrm{~m}$. If $Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$, the fundamental frequency of vibration in the wire will be ___________ $\mathrm{Hz}$.

A block of mass $5 \mathrm{~kg}$ starting from rest pulled up on a smooth incline plane making an angle of $30^{\circ}$ with horizontal with an affective acceleration of $1 \mathrm{~ms}^{-2}$. The power delivered by the pulling force at $t=10 \mathrm{~s}$ from the start is ___________ W.

[use $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ]

(calculate the nearest integer value)

In the given circuit, $\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=0.2 \mu \mathrm{F}, \mathrm{C}_{3}=2 \mu \mathrm{F}, \mathrm{C}_{4}=4 \mu \mathrm{F}, \mathrm{C}_{5}=2 \mu \mathrm{F}, \mathrm{C}_{6}=2 \mu \mathrm{F}$, The charge stored on capacitor $\mathrm{C}_{4}$ is ____________ $\mu \mathrm{C}$.

Compound from the following that will not produce precipitate on reaction with $\mathrm{AgNO}_{3}$ is :

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

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

For a chemical reaction $\mathrm{A}+\mathrm{B} \rightarrow$ Product, the order is 1 with respect to $\mathrm{A}$ and $\mathrm{B}$.

What is the value of $x$ and $y$ ?

The number of possible isomeric products formed when 3-chloro-1-butene reacts with $\mathrm{HCl}$ through carbocation formation is __________.

Let $a, b, c$ and $d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^{5} b^{3} c^{2} d$ is $3750 \beta$, then the value of $\beta$ is

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is :

If $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function satisfying \int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0, then the value of $\alpha$ is :

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+\frac{5}{x\left(x^{5}+1\right)} y=\frac{\left(x^{5}+1\right)^{2}}{x^{7}}, x > 0$. If $y(1)=2$, then $y(2)$ is equal to :

The number of points, where the curve $f(x)=\mathrm{e}^{8 x}-\mathrm{e}^{6 x}-3 \mathrm{e}^{4 x}-\mathrm{e}^{2 x}+1, x \in \mathbb{R}$ cuts $x$-axis, is equal to _________.

The Thermodynamic process, in which internal energy of the system remains constant is

The energy of $\mathrm{He}^{+}$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $-13.6 ~\mathrm{eV})$ :

A capacitor of capacitance $\mathrm{C}$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

Eight equal drops of water are falling through air with a steady speed of $10 \mathrm{~cm} / \mathrm{s}$. If the drops coalesce, the new velocity is:-

The logic operations performed by the given digital circuit is equivalent to:

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be $\frac{E}{x}$. The value of $x$ is

A metallic cube of side $15 \mathrm{~cm}$ moving along $y$-axis at a uniform velocity of $2 \mathrm{~ms}^{-1}$. In a region of uniform magnetic field of magnitude $0.5 \mathrm{~T}$ directed along $z$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

The magnetic moment is measured in Bohr Magneton (BM).

Spin only magnetic moment of $\mathrm{Fe}$ in $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ and $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$ complexes respectively is :

The maximum number of lone pairs of electrons on the central atom from the following species is ____________.

$\mathrm{ClO}_{3}{ }^{-}, \mathrm{XeF}_{4}, \mathrm{SF}_{4}$ and $\mathrm{I}_{3}{ }^{-}$

The number of correct statements from the following is ___________.

A. For $1 \mathrm{s}$ orbital, the probability density is maximum at the nucleus

B. For $2 \mathrm{s}$ orbital, the probability density first increases to maximum and then decreases sharply to zero.

C. Boundary surface diagrams of the orbitals encloses a region of $100 \%$ probability of finding the electron.

D. p and d-orbitals have 1 and 2 angular nodes respectively.

E. probability density of p-orbital is zero at the nucleus

4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of $\mathrm{HI}$ were found. The equilibrium constant for $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})$ is _________.

Let $\mathrm{A}=\{1,3,4,6,9\}$ and $\mathrm{B}=\{2,4,5,8,10\}$. Let $\mathrm{R}$ be a relation defined on $\mathrm{A} \times \mathrm{B}$ such that $\mathrm{R}=\left\{\left(\left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right)\right): a_{1} \leq b_{2}\right.$ and $\left.b_{1} \leq a_{2}\right\}$. Then the number of elements in the set R is :

$\left|\begin{array}{ccc}x+1 & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda^{2}\end{array}\right|=\frac{9}{8}(103 x+81)$, then $\lambda, \frac{\lambda}{3}$ are the roots of the equation :

Let $f$ and $g$ be two functions defined by

$f(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ |x-1|, & x \geq 0\end{array}\right.$ and $\mathrm{g}(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ 1, & x \geq 0\end{array}\right.$

Then $(g \circ f)(x)$ is :

A plane electromagnetic wave of frequency $20 ~\mathrm{MHz}$ propagates in free space along $\mathrm{x}$-direction. At a particular space and time, $\overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}$. What is $\overrightarrow{\mathrm{B}}$ at this point?

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

Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass.

Reason R: For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar.

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

When one light ray is reflected from a plane mirror with $30^{\circ}$ angle of reflection, the angle of deviation of the ray after reflection is :

A projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40 \mathrm{~ms}^{-1}$. The velocity of the projectile at $\mathrm{t}=2 \mathrm{~s}$ from the start will be : (Given $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

A body of mass $500 \mathrm{~g}$ moves along $\mathrm{x}$-axis such that it's velocity varies with displacement $\mathrm{x}$ according to the relation $v=10 \sqrt{x} \mathrm{~m} / \mathrm{s}$ the force acting on the body is:-

A space ship of mass $2 \times 10^{4} \mathrm{~kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $g=10 \mathrm{~m} / \mathrm{s}^{2}$ and radius of earth $=6400 \mathrm{~km}$ ):

If $\mathrm{V}$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

The surface tension of soap solution is $3.5 \times 10^{-2} \mathrm{~Nm}^{-1}$. The amount of work done required to increase the radius of soap bubble from $10 \mathrm{~cm}$ to $20 \mathrm{~cm}$ is _________ $\times ~10^{-4} \mathrm{~J}$.

$(\operatorname{take} \pi=22 / 7)$

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1: 2^{1 / 3}$. Their respective speed have a ratio of $n: 1$. The value of $n$ is __________.

The total number of intensive properties from the following is __________

Volume, Molar heat capacity, Molarity, $\mathrm{E}^{\theta}$ cell, Gibbs free energy change, Molar mass, Mole

Number of compounds from the following which will not produce orange red precipitate with Benedict solution is ___________.

Glucose, maltose, sucrose, ribose, 2-deoxyribose, amylose, lactose

The number of correct statements from the following is __________

A. $\mathrm{E_{\text {cell }}}$ is an intensive parameter

B. A negative $\mathrm{E}^{\ominus}$ means that the redox couple is a stronger reducing agent than the $\mathrm{H}^{+} / \mathrm{H}_{2}$ couple.

C. The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode reaction.

D. The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte.

If the system of linear equations

$$\begin{aligned} & 7 x+11 y+\alpha z=13 \\\\ & 5 x+4 y+7 z=\beta \\\\ & 175 x+194 y+57 z=361 \end{aligned}$$

has infinitely many solutions, then $\alpha+\beta+2$ is equal to :

For $a \in \mathbb{C}$, let $\mathrm{A}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z}) > \operatorname{Im}(\bar{a}+z)\}$ and $\mathrm{B}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})<\operatorname{Im}(\bar{a}+z)\}$. Then among the two statements :

(S1): If $\operatorname{Re}(a), \operatorname{Im}(a) > 0$, then the set A contains all the real numbers

(S2) : If $\operatorname{Re}(a), \operatorname{Im}(a) < 0$, then the set B contains all the real numbers,

Let the function $f:[0,2] \rightarrow \mathbb{R}$ be defined as

$f(x)= \begin{cases}e^{\min \left\{x^{2}, x-[x]\right\},} & x \in[0,1) \\ e^{\left[x-\log _{e} x\right]}, & x \in[1,2]\end{cases}$

where $[t]$ denotes the greatest integer less than or equal to $t$. Then the value of the integral \int_\limits{0}^{2} x f(x) d x is :

Let the probability of getting head for a biased coin be $\frac{1}{4}$. It is tossed repeatedly until a head appears. Let $\mathrm{N}$ be the number of tosses required. If the probability that the equation $64 \mathrm{x}^{2}+5 \mathrm{Nx}+1=0$ has no real root is $\frac{\mathrm{p}}{\mathrm{q}}$, where $\mathrm{p}$ and $\mathrm{q}$ are coprime, then $q-p$ is equal to ________.

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.

A. The electron will experience magnetic force along the axis of the solenoid.

B. The electron will not experience magnetic force.

C. The electron will continue to move along the axis of the solenoid.

D. The electron will be accelerated along the axis of the solenoid.

E. The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C}$ is approximately : (Given mass of a nitrogen molecule $=4.6 \times 10^{-26} \mathrm{~kg}$ and take Boltzmann constant $\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{JK}^{-1}$ )

A coil has an inductance of $2 \mathrm{H}$ and resistance of $4 ~\Omega$. A $10 \mathrm{~V}$ is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ___________ $\times 10^{-2} \mathrm{~J}$.

Two identical cells each of emf $1.5 \mathrm{~V}$ are connected in series across a $10 ~\Omega$ resistance. An ideal voltmeter connected across $10 ~\Omega$ resistance reads $1.5 \mathrm{~V}$. The internal resistance of each cell is __________ $\Omega$.