'A' and 'B' in the above reactions are:

The complex that dissolves in water is :

Find out the correct statement from the options given below for the above 2 reactions.

For elements $\mathrm{B}, \mathrm{C}, \mathrm{N}, \mathrm{Li}, \mathrm{Be}, \mathrm{O}$ and $\mathrm{F}$, the correct order of first ionization enthalpy is

For compound having the formula $\mathrm{GaAlCl}_{4}$, the correct option from the following is :

Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction

0.004 M K$_2$SO$_4$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of K$_2$SO$_4$ is ___________ (Nearest integer)

$\mathrm{KClO}_{3}+6 \mathrm{FeSO}_{4}+3 \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{KCl}+3 \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+3 \mathrm{H}_{2} \mathrm{O}$

The above reaction was studied at $300 \mathrm{~K}$ by monitoring the concentration of $\mathrm{FeSO}_{4}$ in which initial concentration was $10 \mathrm{M}$ and after half an hour became 8.8 M. The rate of production of $\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}$ is _________ $\times 10^{-6} \mathrm{~mol} \mathrm{~L} \mathrm{~s}^{-1}$ (Nearest integer)

The number of hyperconjugation structures involved to stabilize carbocation formed in the above reaction is _________.

In an electrochemical reaction of lead, at standard temperature, if $\mathrm{E}^{0}\left(\mathrm{~Pb}^{2+} / \mathrm{Pb}\right)=\mathrm{m}$ Volt and $\mathrm{E}^{0}\left(\mathrm{~Pb}^{4+} / \mathrm{Pb}\right)=\mathrm{n}$ Volt, then the value of $\mathrm{E}^{0}\left(\mathrm{~Pb}^{2+} / \mathrm{Pb}^{4+}\right)$ is given by $\mathrm{m-x n}$. The value of $\mathrm{x}$ is ___________. (Nearest integer)

Let R be a rectangle given by the lines $x=0, x=2, y=0$ and $y=5$. Let A$(\alpha,0)$ and B$(0,\beta),\alpha\in[0,2]$ and $\beta\in[0,5]$, be such that the line segment AB divides the area of the rectangle R in the ratio 4 : 1. Then, the mid-point of AB lies on a :

Let $w_{1}$ be the point obtained by the rotation of $z_{1}=5+4 i$ about the origin through a right angle in the anticlockwise direction, and $w_{2}$ be the point obtained by the rotation of $z_{2}=3+5 i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_{1}-w_{2}$ is equal to :

Let $y=y(x)$ be a solution curve of the differential equation.

$\left(1-x^{2} y^{2}\right) d x=y d x+x d y$.

If the line $x=1$ intersects the curve $y=y(x)$ at $y=2$ and the line $x=2$ intersects the curve $y=y(x)$ at $y=\alpha$, then a value of $\alpha$ is :

For any vector $\vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}$, with $10\left|a_{i}\right|<1, i=1,2,3$, consider the following statements :

(A): $\max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\} \leq|\vec{a}|$

(B) : $|\vec{a}| \leq 3 \max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\}$

Consider ellipses $\mathrm{E}_{k}: k x^{2}+k^{2} y^{2}=1, k=1,2, \ldots, 20$. Let $\mathrm{C}_{k}$ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse $\mathrm{E}_{k}$. If $r_{k}$ is the radius of the circle $\mathrm{C}_{k}$, then the value of \sum_\limits{k=1}^{20} \frac{1}{r_{k}^{2}} is :

Let $A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]$, where $a, c \in \mathbb{R}$. If $A^{3}=A$ and the positive value of $a$ belongs to the interval $(n-1, n]$, where $n \in \mathbb{N}$, then $n$ is equal to ___________.

Let $\mathrm{H}_{\mathrm{n}}: \frac{x^{2}}{1+n}-\frac{y^{2}}{3+n}=1, n \in N$. Let $\mathrm{k}$ be the smallest even value of $\mathrm{n}$ such that the eccentricity of $\mathrm{H}_{\mathrm{k}}$ is a rational number. If $l$ is the length of the latus rectum of $\mathrm{H}_{\mathrm{k}}$, then $21 l$ is equal to ____________.

Let a line $l$ pass through the origin and be perpendicular to the lines

$l_{1}: \vec{r}=(\hat{\imath}-11 \hat{\jmath}-7 \hat{k})+\lambda(\hat{i}+2 \hat{\jmath}+3 \hat{k}), \lambda \in \mathbb{R}$ and

$l_{2}: \vec{r}=(-\hat{\imath}+\hat{\mathrm{k}})+\mu(2 \hat{\imath}+2 \hat{\jmath}+\hat{\mathrm{k}}), \mu \in \mathbb{R}$.

If $\mathrm{P}$ is the point of intersection of $l$ and $l_{1}$, and $\mathrm{Q}(\propto, \beta, \gamma)$ is the foot of perpendicular from P on $l_{2}$, then $9(\alpha+\beta+\gamma)$ is equal to _____________.

The mean of the coefficients of $x, x^{2}, \ldots, x^{7}$ in the binomial expansion of $(2+x)^{9}$ is ___________.

On a temperature scale '$\mathrm{X}$', the boiling point of water is $65^{\circ} \mathrm{X}$ and the freezing point is $-15^{\circ} \mathrm{X}$. Assume that the $\mathrm{X}$ scale is linear. The equivalent temperature corresponding to $-95^{\circ} \mathrm{X}$ on the Farenheit scale would be:

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $\rho$ and $\rho / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_{A}: g_{B}\right)$ will be:

The logic performed by the circuit shown in figure is equivalent to :

The electric field in an electromagnetic wave is given as

$\overrightarrow{\mathrm{E}}=20 \sin \omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right) \overrightarrow{\mathrm{j}} \mathrm{NC}^{-1}$

where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{-4} \mathrm{~m}^{3}$ will be

(Given $\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}$ )

As per the given graph, choose the correct representation for curve $\mathrm{A}$ and curve B.

Where $\mathrm{X}_{\mathrm{C}}=$ reactance of pure capacitive circuit connected with A.C. source

$\mathrm{X}_{\mathrm{L}}=$ reactance of pure inductive circuit connected with $\mathrm{A} . \mathrm{C}$. source

R = impedance of pure resistive circuit connected with A.C. source.

$\mathrm{Z}=$ Impedance of the LCR series circuit $\}$

The equation of wave is given by

$\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)$

where $x$ and $Y$ are in $\mathrm{m}$ and $\mathrm{t}$ in $s$. The speed of the wave is ________ $\mathrm{km} ~\mathrm{h}^{-1}$.

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

Assertion A : In the photoelectric effect, the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes the surface.

Reason R : When the photon of any energy strikes an electron in the atom, transfer of energy from the photon to the electron takes place.

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

$25 \mathrm{~mL}$ of silver nitrate solution (1M) is added dropwise to $25 \mathrm{~mL}$ of potassium iodide $(1.05 \mathrm{M})$ solution. The ion(s) present in very small quantity in the solution is/are :

When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a dark brown ring was formed whereas on treatment with neutral $\mathrm{FeCl}_{3}$, it gave deep red colour which disppeared on boiling and a brown red ppt was formed. The mixture contains :

Thin layer chromatography of a mixture shows the following observation:

The correct order of elution in the silica gel column chromatography is

'X' is

The set which does not have ambidentate ligand(s) is :

The ratio of spin-only magnetic moment values $\mu_{\text {eff }}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-} / \mu_{\text {eff }}\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ is _________.

The ratio x/y on completion of the above reaction is __________.

Solid fuel used in rocket is a mixture of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ and $\mathrm{Al}$ (in ratio 1 : 2). The heat evolved $(\mathrm{kJ})$ per gram of the mixture is ____________. (Nearest integer)

Given: $\Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)=-1700 \mathrm{~kJ} \mathrm{~mol}^{-1}$

$\Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-840 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Molar mass of Fe, Al and O are 56, 27 and 16 g mol$^{-1}$ respectively.

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of $\mathrm{A}$ and adding 2 to each element of $\mathrm{B}$. Then the sum of the mean and variance of the elements of $\mathrm{C}$ is ___________.

Area of the region $\left\{(x, y): x^{2}+(y-2)^{2} \leq 4, x^{2} \geq 2 y\right\}$ is

The number of triplets $(x, \mathrm{y}, \mathrm{z})$, where $x, \mathrm{y}, \mathrm{z}$ are distinct non negative integers satisfying $x+y+z=15$, is :

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is _________.

If $a$ and $b$ are the roots of the equation $x^{2}-7 x-1=0$, then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to _____________.

The critical angle for a denser-rarer interface is $45^{\circ}$. The speed of light in rarer medium is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. The speed of light in the denser medium is:

A metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V_{0}$. If the same surface is illuminated with radiation of wavelength $2 \lambda$. the stopping potential becomes $\frac{V_{o}}{4}$. The threshold wavelength for this metallic surface will be

From the $\mathrm{v}-t$ graph shown, the ratio of distance to displacement in $25 \mathrm{~s}$ of motion is:

Match List - I with List - II:

Choose the correct answer from the options given below:

L-isomer of tetrose $\mathrm{X}\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{4}\right)$ gives positive Schiff's test and has two chiral carbons. On acetylation, '$\mathrm{X}$' yields triacetate. '$\mathrm{X}$' also undergoes following reactions

'$\mathrm{X}$' is

Which of the following complex has a possibility to exist as meridional isomer?

A mixture of 1 mole of $\mathrm{H}_{2} \mathrm{O}$ and 1 mole of $\mathrm{CO}$ is taken in a 10 litre container and heated to $725 \mathrm{~K}$. At equilibrium $40 \%$ of water by mass reacts with carbon monoxide according to the equation :

$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})$.

The equilibrium constant $\mathrm{K}_{\mathrm{c}} \times 10^{2}$ for the reaction is ____________. (Nearest integer)

Let $S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P(A)$ is equal to :

The value of the integral \int_\limits{-\log _{e} 2}^{\log _{e} 2} e^{x}\left(\log _{e}\left(e^{x}+\sqrt{1+e^{2 x}}\right)\right) d x is equal to :

Let $\mathrm{A}$ be a $2 \times 2$ matrix with real entries such that $\mathrm{A}'=\alpha \mathrm{A}+\mathrm{I}$, where $\alpha \in \mathbb{R}-\{-1,1\}$. If $\operatorname{det}\left(A^{2}-A\right)=4$, then the sum of all possible values of $\alpha$ is equal to :

Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j}, \hat{i}+\hat{k}$ and $\hat{i}-\hat{j}, \hat{j}-\hat{k}$. If $\theta$ is the angle between the vector $\vec{a}$ and the vector $\vec{b}=2 \hat{i}-2 \hat{j}+\hat{k}$ and $\vec{a} \cdot \vec{b}=6$, then the ordered pair $(\theta,|\vec{a} \times \vec{b}|)$ is equal to :

For $m, n > 0$, let \alpha(m, n)=\int_\limits{0}^{2} t^{m}(1+3 t)^{n} d t. If $11 \alpha(10,6)+18 \alpha(11,5)=p(14)^{6}$, then $p$ is equal to ___________.

Given below are two statements :

Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II : $\mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly}$

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

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{\mathrm{rms}}\right)$ and choose the correct answer from the options given below:

A coin placed on a rotating table just slips when it is placed at a distance of $1 \mathrm{~cm}$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of _________ from the centre :

A parallel plate capacitor of capacitance $2 \mathrm{~F}$ is charged to a potential $\mathrm{V}$, The energy stored in the capacitor is $E_{1}$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $\mathrm{E}_{2}$. The ratio $\mathrm{E}_{2} / \mathrm{E}_{1}$ is :

An average force of $125 \mathrm{~N}$ is applied on a machine gun firing bullets each of mass $10 \mathrm{~g}$ at the speed of $250 \mathrm{~m} / \mathrm{s}$ to keep it in position. The number of bullets fired per second by the machine gun is :

The free space inside a current carrying toroid is filled with a material of susceptibility $2 \times 10^{-2}$. The percentage increase in the value of magnetic field inside the toroid will be

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

The current sensitivity of moving coil galvanometer is increased by $25 \%$. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:

A solution of sugar is obtained by mixing $200 \mathrm{~g}$ of its $25 \%$ solution and $500 \mathrm{~g}$ of its $40 \%$ solution (both by mass). The mass percentage of the resulting sugar solution is ___________ (Nearest integer)

Let $x_{1}, x_{2}, \ldots, x_{100}$ be in an arithmetic progression, with $x_{1}=2$ and their mean equal to 200 . If $y_{i}=i\left(x_{i}-i\right), 1 \leq i \leq 100$, then the mean of $y_{1}, y_{2}, \ldots, y_{100}$ is :

Let $f(x)=\left[x^{2}-x\right]+|-x+[x]|$, where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is :

The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :

The number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$ is equal to ___________.

$1 \mathrm{~kg}$ of water at $100^{\circ} \mathrm{C}$ is converted into steam at $100^{\circ} \mathrm{C}$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{-3} \mathrm{~m}^{3}$ as a liquid to $1.671 \mathrm{~m}^{3}$ as steam. The change in internal energy of the system during the process will be

(Given latent heat of vaporisaiton $=2257 \mathrm{~kJ} / \mathrm{kg}$, Atmospheric pressure = $\left.1 \times 10^{5} \mathrm{~Pa}\right)$

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position (A) is given by

In the circuit diagram shown in figure given below, the current flowing through resistance $3 ~\Omega$ is $\frac{x}{3} A$.

The value of $x$ is ___________

The magnetic field B crossing normally a square metallic plate of area $4 \mathrm{~m}^{2}$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $\mathrm{t}=2 s$ to $\mathrm{t}=4 s$, is __________ $\mathrm{mV}$.

As shown in the figure, a configuration of two equal point charges $\left(q_{0}=+2 \mu \mathrm{C}\right)$ is placed on an inclined plane. Mass of each point charge is $20 \mathrm{~g}$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $\mathrm{h}=x \times 10^{-3} \mathrm{~m}$.

The value of $x$ is ____________.

(Take $\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-2}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

A projectile fired at $30^{\circ}$ to the ground is observed to be at same height at time $3 \mathrm{~s}$ and $5 \mathrm{~s}$ after projection, during its flight. The speed of projection of the projectile is ___________ $\mathrm{m} ~\mathrm{s}^{-1}$.

(Given $g=10 \mathrm{~ms}^{-2}$ )

A force $\vec{F}=(2+3 x) \hat{i}$ acts on a particle in the $x$ direction where F is in newton and $x$ is in meter. The work done by this force during a displacement from $x=0$ to $x=4 \mathrm{~m}$, is __________ J.

A solid sphere of mass $500 \mathrm{~g}$ and radius $5 \mathrm{~cm}$ is rotated about one of its diameter with angular speed of $10 ~\mathrm{rad} ~\mathrm{s}^{-1}$. If the moment of inertia of the sphere about its tangent is $x \times 10^{-2}$ times its angular momentum about the diameter. Then the value of $x$ will be ___________.

The length of a wire becomes $l_{1}$ and $l_{2}$ when $100 \mathrm{~N}$ and $120 \mathrm{~N}$ tensions are applied respectively. If $10 ~l_{2}=11~ l_{1}$, the natural length of wire will be $\frac{1}{x} ~l_{1}$. Here the value of $x$ is _____________.

The radius of curvature of each surface of a convex lens having refractive index 1.8 is $20 \mathrm{~cm}$. The lens is now immersed in a liquid of refractive index 1.5 . The ratio of power of lens in air to its power in the liquid will be $x: 1$. The value of $x$ is _________.

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $x \times 10^{15} \mathrm{~Hz}$. The value of $x$ is ____________.

(Given h $=4.25 \times 10^{-15} ~\mathrm{eVs}$ )