The total number of stereoisomers for the complex $\left[\mathrm{Cr}(o x)_{2} \mathrm{ClBr}\right]^{3-}$ (where $o x=$ oxalate) is :

The naturally occurring amino acid that contains only one basic functional group in its chemical structure is

Given below are two statements :

Statement I : Tropolone is an aromatic compound and has $8 \pi$ electrons.

Statement II : $\pi$ electrons of $> \mathrm{C}=\mathrm{O}$ group in tropolone is involved in aromaticity.

In the light of the above statements, 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 : Order of acidic nature of the following compounds is A > B > C.

Reason R : Fluoro is a stronger electron withdrawing group than Chloro group.

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

The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$, is :

The coefficient of $x^{5}$ in the expansion of $\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}$ is :

Which of the following complexes will exhibit maximum attraction to an applied magnetic field?

The orbital angular momentum of an electron in $3 \mathrm{~s}$ orbital is $\frac{x h}{2 \pi}$. The value of $x$ is ____________ (nearest integer)

At $298 \mathrm{~K}$, the standard reduction potential for $\mathrm{Cu}^{2+} / \mathrm{Cu}$ electrode is $0.34 \mathrm{~V}$.

Given : $\mathrm{K}_{\mathrm{sp}} \mathrm{Cu}(\mathrm{OH})_{2}=1 \times 10^{-20}$

Take $\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}$

The reduction potential at $\mathrm{pH}=14$ for the above couple is $(-) x \times 10^{-2} \mathrm{~V}$. The value of $x$ is ___________

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is :

What happens when methane undergoes combustion in systems A and B respectively?

In the wet tests for detection of various cations by precipitation, $\mathrm{Ba}^{2+}$ cations are detected by obtaining precipitate of

Compound $\mathrm{A}$ from the following reaction sequence is:

The major product for the following reaction is:

The covalency and oxidation state respectively of boron in $\left[\mathrm{BF}_{4}\right]^{-}$, are :

Match List I with List II

1 - Bromopropane is reacted with reagents in List I to give product in List II

Choose the correct answer from the options given below:

A(g) $\to$ 2B(g) + C(g) is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be _________ mm Hg. (Nearest integer)

$0.400 \mathrm{~g}$ of an organic compound $(\mathrm{X})$ gave $0.376 \mathrm{~g}$ of $\mathrm{AgBr}$ in Carius method for estimation of bromine. $\%$ of bromine in the compound $(\mathrm{X})$ is ___________.

(Given: Molar mass $\mathrm{AgBr=188~g~mol^{-1}}$

$\mathrm{Br}=80 \mathrm{~g} \mathrm{~mol}^{-1}$)

See the following chemical reaction:

$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{XH}^{+}+6 \mathrm{~F}_{e}^{2+} \rightarrow \mathrm{YCr}^{3+}+6 \mathrm{~F}_{e}^{3+}+\mathrm{Z} \mathrm{H}_{2} \mathrm{O}$

The sum of $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ is ___________

Let $S=\left\{z \in \mathbb{C}: \bar{z}=i\left(z^{2}+\operatorname{Re}(\bar{z})\right)\right\}$. Then \sum_\limits{z \in \mathrm{S}}|z|^{2} is equal to :

If \lim_\limits{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{cx e^{-c x}}{2}}{1-\cos (2 x)}=17, then $5 a^{2}+b^{2}$ is equal to

Given below are two statements :

Statement I : $\mathrm{SO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ both possess V-shaped structure.

Statement II : The bond angle of $\mathrm{SO}_{2}$ is less than that of $\mathrm{H}_{2} \mathrm{O}$.

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

$1 \mathrm{~g}$ of a carbonate $\left(\mathrm{M}_{2} \mathrm{CO}_{3}\right)$ on treatment with excess $\mathrm{HCl}$ produces $0.01 \mathrm{~mol}$ of $\mathrm{CO}_{2}$. The molar mass of $\mathrm{M}_{2} \mathrm{CO}_{3}$ is __________ $\mathrm{g} ~\mathrm{mol}^{-1}$. (Nearest integer)

Sea water contains $29.25 \% ~\mathrm{NaCl}$ and $19 \% ~\mathrm{MgCl}_{2}$ by weight of solution. The normal boiling point of the sea water is _____________ ${ }^{\circ} \mathrm{C}$ (Nearest integer)

Assume $100 \%$ ionization for both $\mathrm{NaCl}$ and $\mathrm{MgCl}_{2}$

Given : $\mathrm{K}_{\mathrm{b}}\left(\mathrm{H}_{2} \mathrm{O}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

Molar mass of $\mathrm{NaCl}$ and $\mathrm{MgCl}_{2}$ is 58.5 and 95 $\mathrm{g} \mathrm{~mol}^{-1}$ respectively.

20 mL of $0.1 ~\mathrm{M} ~\mathrm{NaOH}$ is added to $50 \mathrm{~mL}$ of $0.1 ~\mathrm{M}$ acetic acid solution. The $\mathrm{pH}$ of the resulting solution is ___________ $\times 10^{-2}$ (Nearest integer)

Given : $\mathrm{pKa}\left(\mathrm{CH}_{3} \mathrm{COOH}\right)=4.76$

$\log 2=0.30$

$\log 3=0.48$

Let a$_1$, a$_2$, a$_3$, .... be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3^rd and 5^th terms be $\frac{1}{9}$. Then $6(a_2+a_4)(a_4+a_6)$ is equal to

Let $|\vec{a}|=2,|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi}{4}$. Then $|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^{2}$ is equal to :

Let $\alpha, \beta$ be the roots of the equation $x^{2}-\sqrt{2} x+2=0$. Then $\alpha^{14}+\beta^{14}$ is equal to

Let $(\alpha, \beta)$ be the centroid of the triangle formed by the lines $15 x-y=82,6 x-5 y=-4$ and $9 x+4 y=17$. Then $\alpha+2 \beta$ and $2 \alpha-\beta$ are the roots of the equation :

If the system of equations

$2 x+y-z=5$

$2 x-5 y+\lambda z=\mu$

$x+2 y-5 z=7$

has infinitely many solutions, then $(\lambda+\mu)^{2}+(\lambda-\mu)^{2}$ is equal to

Let for a triangle $\mathrm{ABC}$,

$\overrightarrow{\mathrm{AB}}=-2 \hat{i}+\hat{j}+3 \hat{k}$

$\overrightarrow{\mathrm{CB}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$

$\overrightarrow{\mathrm{CA}}=4 \hat{i}+3 \hat{j}+\delta \hat{k}$

If $\delta > 0$ and the area of the triangle $\mathrm{ABC}$ is $5 \sqrt{6}$, then $\overrightarrow{C B} \cdot \overrightarrow{C A}$ is equal to

Let $[\alpha]$ denote the greatest integer $\leq \alpha$. Then $[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots+[\sqrt{120}]$ is equal to __________

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits $1,2,3,4,5$ with repetition, is _________.

In the equation $\left[X+\frac{a}{Y^{2}}\right][Y-b]=\mathrm{R} T, X$ is pressure, $Y$ is volume, $\mathrm{R}$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:

In the network shown below, the charge accumulated in the capacitor in steady state will be:

In a Young's double slits experiment, the ratio of amplitude of light coming from slits is $2: 1$. The ratio of the maximum to minimum intensity in the interference pattern is:

Given below are two statements:

Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.

Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.

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

Given below are two statements:

Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.

Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.

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

An electron is moving along the positive $\mathrm{x}$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then

A. The electron will experience magnetic force along positive y-axis

B. The electron will experience magnetic force along negative y-axis

C. The electron will not experience any force in magnetic field

D. The electron will continue to move along the positive $\mathrm{x}$-axis

E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

Let $\mathrm{A}=\{-4,-3,-2,0,1,3,4\}$ and $\mathrm{R}=\left\{(a, b) \in \mathrm{A} \times \mathrm{A}: b=|a|\right.$ or $\left.b^{2}=a+1\right\}$ be a relation on $\mathrm{A}$. Then the minimum number of elements, that must be added to the relation $\mathrm{R}$ so that it becomes reflexive and symmetric, is __________

The remainder, when $7^{103}$ is divided by 17, is __________

Let f(x)=\sum_\limits{k=1}^{10} k x^{k}, x \in \mathbb{R}. If $2 f(2)+f^{\prime}(2)=119(2)^{\mathrm{n}}+1$ then $\mathrm{n}$ is equal to ___________

For $x \in(-1,1]$, the number of solutions of the equation $\sin ^{-1} x=2 \tan ^{-1} x$ is equal to __________.

If $y=y(x)$ is the solution of the differential equation

$\frac{d y}{d x}+\frac{4 x}{\left(x^{2}-1\right)} y=\frac{x+2}{\left(x^{2}-1\right)^{\frac{5}{2}}}, x > 1$ such that

$y(2)=\frac{2}{9} \log _{e}(2+\sqrt{3}) \text { and } y(\sqrt{2})=\alpha \log _{e}(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}, \alpha, \beta, \gamma \in \mathbb{N} \text {, then } \alpha \beta \gamma \text { is equal to }$ :

A vehicle of mass $200 \mathrm{~kg}$ is moving along a levelled curved road of radius $70 \mathrm{~m}$ with angular velocity of $0.2 ~\mathrm{rad} / \mathrm{s}$. The centripetal force acting on the vehicle is:

Two planets A and B of radii $\mathrm{R}$ and 1.5 R have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $\mathrm{B}$ to $\mathrm{A}$ is:

The mean free path of molecules of a certain gas at STP is $1500 \mathrm{~d}$, where $\mathrm{d}$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373 \mathrm{~K}$ is approximately:

The output from NAND gate having inputs A and B given below will be,

A passenger sitting in a train A moving at $90 \mathrm{~km} / \mathrm{h}$ observes another train $\mathrm{B}$ moving in the opposite direction for $8 \mathrm{~s}$. If the velocity of the train B is $54 \mathrm{~km} / \mathrm{h}$, then length of train B is:

Three point charges $\mathrm{q},-2 \mathrm{q}$ and $2 \mathrm{q}$ are placed on $x$-axis at a distance $x=0, x=\frac{3}{4} R$ and $x=R$ respectively from origin as shown. If $\mathrm{q}=2 \times 10^{-6} \mathrm{C}$ and $\mathrm{R}=2 \mathrm{~cm}$, the magnitude of net force experienced by the charge $-2 q$ is ___________ N.

An atom absorbs a photon of wavelength $500 \mathrm{~nm}$ and emits another photon of wavelength $600 \mathrm{~nm}$. The net energy absorbed by the atom in this process is $n \times 10^{-4} ~\mathrm{eV}$. The value of n is __________. [Assume the atom to be stationary during the absorption and emission process] (Take $\mathrm{h}=6.6 \times 10^{-34} ~\mathrm{Js}$ and $\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ )

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$^{-2}$.

A straight wire $\mathrm{AB}$ of mass $40 \mathrm{~g}$ and length $50 \mathrm{~cm}$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $0.40 \mathrm{~T}$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ___________ A.

$\left(\right.$ Take $g=10 \mathrm{~ms}^{-2}$ ).

Two plates $\mathrm{A}$ and $\mathrm{B}$ have thermal conductivities $84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and $126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $\mathrm{A}$ and $\mathrm{B}$ are kept at $100^{\circ} \mathrm{C}$ and $0{ }^{\circ} \mathrm{C}$ respectively, then the temperature of the surface of contact in steady state is _____________ ${ }^{\circ} \mathrm{C}$.

In an experiment with sonometer when a mass of $180 \mathrm{~g}$ is attached to the string, it vibrates with fundamental frequency of $30 \mathrm{~Hz}$. When a mass $\mathrm{m}$ is attached, the string vibrates with fundamental frequency of $50 \mathrm{~Hz}$. The value of $\mathrm{m}$ is ___________ g.

In the circuit shown, the energy stored in the capacitor is $n ~\mu \mathrm{J}$. The value of $n$ is __________

A car accelerates from rest to $u \mathrm{~m} / \mathrm{s}$. The energy spent in this process is E J. The energy required to accelerate the car from $u \mathrm{~m} / \mathrm{s}$ to $2 \mathrm{u} \mathrm{m} / \mathrm{s}$ is $\mathrm{nE~J}$. The value of $\mathrm{n}$ is ____________.

The range of $f(x)=4 \sin ^{-1}\left(\frac{x^{2}}{x^{2}+1}\right)$ is

The area of the region $\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\}$ is

Let f_{n}=\int_\limits{0}^{\frac{\pi}{2}}\left(\sum_\limits{k=1}^{n} \sin ^{k-1} x\right)\left(\sum_\limits{k=1}^{n}(2 k-1) \sin ^{k-1} x\right) \cos x d x, n \in \mathbb{N}. Then $f_{21}-f_{20}$ is equal to _________

The distance travelled by an object in time $t$ is given by $s=(2.5) t^{2}$. The instantaneous speed of the object at $\mathrm{t}=5 \mathrm{~s}$ will be:

The initial pressure and volume of an ideal gas are P$_0$ and V$_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be :

(Given $\gamma$ = ratio of specific heats at constant pressure and at constant volume)

In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $z$-axis and magnetic field is along the positive $x$-axis. Then the direction of propagation of electromagnetic wave is:

A $10 ~\mu \mathrm{C}$ charge is divided into two parts and placed at $1 \mathrm{~cm}$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

The value of ${{{e^{ - {\pi \over 4}}} + \int\limits_0^{{\pi \over 4}} {{e^{ - x}}{{\tan }^{50}}xdx} } \over {\int\limits_0^{{\pi \over 4}} {{e^{ - x}}({{\tan }^{49}}x + {{\tan }^{51}}x)dx} }}$ is

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is _________

Given below are two statements:

Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.

Statement II : Escape velocity is independent of the radius of the planet.

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

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

Assertion A : A spherical body of radius $(5 \pm 0.1) \mathrm{mm}$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4 \%$.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

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

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $24 \mathrm{~cm}^{2}$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12 ~\Omega$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5 \mathrm{~T}$ in one direction to $1.5 ~\mathrm{T}$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $\mathrm{mC}$.

A bi convex lens of focal length $10 \mathrm{~cm}$ is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ____________ D.