JEE Main 2026 — 22 January, Evening Shift

Let $n$ be the number obtained on rolling a fair die. If the probability that the system $\mathrm{x}-\mathrm{ny}+\mathrm{z}=6$, $\mathrm{x}+(\mathrm{n}-2) \mathrm{y}+(\mathrm{n}+1) \mathrm{z}=8$ ,$(n-1) y+z=1$ Has a unique solution is $\frac{\mathrm{k}}{6}$, then the sum of k and all possible values of $n$ is :

If the mean deviation about the median of the numbers $\mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots, 1000 \mathrm{k}$ is $500$ , then $\mathrm{k}^{2}$ is equal to :

The number of elements in the relation $\mathrm{R}=\{(\mathrm{x}, \mathrm{y})$ : $\left.4 x^{2}+y^{2}<52, x, y \in Z\right\}$ is

Let $\mathrm{S}=\left\{\mathrm{z} \in \mathbb{C}: 4 \mathrm{z}^{2}+\overline{\mathrm{z}}=0\right\}$. Then $\sum_{\mathrm{z} \in \mathrm{S}}|\mathrm{z}|^{2}$ is equal to :

If $\lim _{x \rightarrow 0} \frac{e^{(a-1) x}+2 \cos b x+(c-2) e^{-x}}{x \cos x-\log _{e}(1+x)}=2$, then $a^{2}+ \mathrm{b}^{2}+\mathrm{c}^{2}$ is equal to :

If $y=y(x)$ satisfies the differential equation $16(\sqrt{x+9 \sqrt{x}})(4+\sqrt{9+\sqrt{x}}) \cos y d y=(1+2$ siny)dx, $x>0$ and $y(256)=\frac{\pi}{2}, y(49)=\alpha$, then $2\sin \alpha$ is equal to :

Among the statements

(S1) : If $\mathrm{A}(5,-1)$ and $\mathrm{B}(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$ and

(S2) : If positive numbers $2 \mathrm{a}, \mathrm{b}, \mathrm{c}$ are three consecutive terms of an A.P., then the lines $\mathrm{ax}+$ by $+\mathrm{c}=0$ are concurrent at $(2,-2)$,

Let $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda \hat{j}+2 \hat{k}, \lambda \in Z$ be two vectors, Let $\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{d}}$ be a vector of magnitude 2 in yz-plane. If $|\overrightarrow{\mathrm{c}}|=\sqrt{53}$, then the maximum possible value of $(\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{d}})^{2}$ is equal to :

If $X =\begin{bmatrix}x \\y \\z\end{bmatrix}$ is a solution of the system of equations $AX = B$ where $ \operatorname{adj}(A) =

Let L be the line $\frac{\mathrm{x}+1}{2}=\frac{\mathrm{y}+1}{3}=\frac{\mathrm{z}+3}{6}$ and let S be the set of all points $(\mathrm{a}, \mathrm{b}, \mathrm{c})$ on L , whose distance from the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+9}{0}$ along the line L is 7. Then $\sum_{(\mathrm{a}, \mathrm{b}, \mathrm{c}) \in \mathrm{S}}(\mathrm{a}+\mathrm{b}+\mathrm{c})$ is equal to :

Let $\mathrm{P}(10,2 \sqrt{15})$ be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, whose foci are $S$ and $S^{\prime}$. If the length of its latus rectum is 8 , then the square of the area of $\triangle \mathrm{PSS}^{\prime}$ is equal to :

The area of the region $\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}): 4 \mathrm{x}^{2}+\mathrm{y}^{2} \leq 8\right.$ and $\left.\mathrm{y}^{2} \leq 4 \mathrm{x}\right\}$ is :

Let $\alpha, \beta$ be the roots of the quadratic equation $12 \mathrm{x}^{2}-20 \mathrm{x}+3 \lambda=0, \lambda \in \mathbb{Z}$. If $\frac{1}{2} \leq|\beta-\alpha| \leq \frac{3}{2}$, then the sum of all possible values of $\lambda$ is :

Let the domain of the function $\mathrm{f}(\mathrm{x})=\log _{3} \log _{5}\left(7-\log _{2}\left(\mathrm{x}^{2}-10 \mathrm{x}+85\right)\right)+\sin ^{-1}\left(\left|\frac{3 \mathrm{x}-7}{17-\mathrm{x}}\right|\right)$ be $(\alpha, \beta]$. Then $\alpha+\beta$ is equal to :

Let $[\bullet]$ denote the greatest integer function, and let $f(x)=\min \left\{\sqrt{2} x, x^{2}\right\}$. Let $S=\{x \in(-2,2):$ the function $\mathrm{g}(\mathrm{x})=|\mathrm{x}|\left[\mathrm{x}^{2}\right]$ is discontinuous at x$\}$.Then $\sum_{x \in S} f(x)$ equals :

Let S and $\mathrm{S}^{\prime}$ be the foci of the ellipse $\frac{\mathrm{x}^{2}}{25}+\frac{\mathrm{y}^{2}}{9}=1$ and $\mathrm{P}(\alpha, \beta)$ be a point on the ellipse in the first quadrant. If $(\mathrm{SP})^{2}+\left(\mathrm{S}^{\prime} \mathrm{P}\right)^{2}-\mathrm{SP} \bullet \mathrm{S}^{\prime} \mathrm{P}=37$, then $\alpha^{2}+\beta^{2}$ is equal to :

Let the locus of the mid-point of the chord through the origin O of the parabola $\mathrm{y}^{2}=4 \mathrm{x}$ be the curve S . Let P be any point on S . Then the locus of the point, which internally divides OP in the ratio $3: 1$, is :

Let $\mathrm{f}(\mathrm{x})=[\mathrm{x}]^{2}-[\mathrm{x}+3]-3, \mathrm{x} \in \mathbb{R}$ where $[\bullet]$ is the greatest integer function. Then

Let $f$ and $g$ be functions satisfying $f(\mathrm{x}+\mathrm{y})=f(\mathrm{x}) f(\mathrm{y}), \mathrm{f}(\mathrm{l})=7$ and $\mathrm{g}(\mathrm{x}+\mathrm{y})=\mathrm{g}(\mathrm{xy})$, $\mathrm{g}(\mathrm{l})=1$, for all $\mathrm{x}, \mathrm{y} \in \mathbb{N} . \sum_{\mathrm{x}=1}^{\mathrm{n}}\left(\frac{\mathrm{f}(\mathrm{x})}{\mathrm{g}(\mathrm{x})}\right)=19607$, then $n$ is equal to :

Let $\mathrm{C}_{\mathrm{r}}$ denote the coefficient of $\mathrm{x}^{\mathrm{r}}$ in the binomial expansion of $(1+x)^{n}, n \in \mathbb{N}, 0 \leq r \leq n$.

If $\mathrm{P}_{\mathrm{n}}=\mathrm{C}_{0}-\mathrm{C}_{1}+\frac{2^{2}}{3} \mathrm{C}_{2}-\frac{2^{3}}{4} \mathrm{C}_{3}+\ldots . .+\frac{(-2)^{\mathrm{n}}}{\mathrm{n}+1} \mathrm{C}_{\mathrm{n}}$, then the value of $\sum_{n=1}^{25} \frac{1}{\mathrm{P}_{2 n}}$ equals.

Let a vector $\overrightarrow{\mathrm{a}}=\sqrt{2} \hat{\mathrm{i}}-\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \lambda>0$, make an obtuse angle with the vector $\vec{b}=-\lambda^{2} \hat{i}+4 \sqrt{2} \hat{j}+4 \sqrt{2} \hat{k}$ and an angle $\theta, \frac{\pi}{6}<\theta< \frac{\pi}{2}$, with the positive $z$-axis. If the set of all possible values of $\lambda$ is $(\alpha, \beta)-\{\gamma\}$, then $\alpha+\beta+\gamma$ is equal to $\_\_\_\_$ .

Let [•] be the greatest integer function. If $\alpha=\int_{0}^{64}\left(\mathrm{x}^{1 / 3}-\left[\mathrm{x}^{1 / 3}\right]\right) \mathrm{dx}$, then $\frac{1}{\pi} \int_{0}^{\alpha \pi}\left(\frac{\sin ^{2} \theta}{\sin ^{6} \theta+\cos ^{6} \theta}\right) \mathrm{d} \theta$ is equal to $\_\_\_\_$ .

Let $\cos (\alpha+\beta)=-\frac{1}{10}$ and $\sin (\alpha-\beta)=\frac{3}{8}$, where $0<\alpha<\frac{\pi}{3}$ and $0<\beta<\frac{\pi}{4}$.

If $\tan 2 \alpha=\frac{3(1-r \sqrt{5})}{\sqrt{11}(s+\sqrt{5})}, r, s \in \mathbb{N}$, then $r+s$ is equal to $\_\_\_\_$。

Suppose $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $\mathrm{a}^{2}, 2 \mathrm{~b}^{2}, \mathrm{c}^{2}$ are in G.P. If $\mathrm{a}<\mathrm{b}<\mathrm{c}$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}=1$, then $9\left(\mathrm{a}^{2}+\mathrm{b}^{2}+\right. \mathrm{c}^{2}$ ) is equal to $\_\_\_\_$ .

Let S be the set of the first 11 natural numbers. Then the number of elements in $\mathrm{A}=\{\mathrm{B} \subseteq \mathrm{S}$ : $\mathrm{n}(\mathrm{B}) \geq 2$ and the product of all elements of B is even} is

If $\in, \mathrm{E}$ and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\in E}{t}$ will be :

Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T?

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B . If the collision frequency in gas B is $32 \times 10 \frac{18}{\mathrm{~s}}$ then collision frequency in gas A is $\_\_\_\_$ /s.

A uniform bar of length 12 cm and mass $20 m$ lies on a smooth horizontal table. Two point masses m and $2 m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$. The ratio of v and $\omega$ is :

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

The smallest wavelength of Lyman series is 91 nm . The difference between the largest wavelengths of Paschen and Balmer series is nearly $\_\_\_\_$ nm .

In an open organ pipe $v_{3}$ and $v_{6}$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively.

If $v_{6}-v_{3}=2200 \mathrm{~Hz}$ then length of the pipe is $\_\_\_\_$ mm. (Take velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$.)

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h . If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1 \%$ each, then the height of the liquid in the tube will change by $\_\_\_\_$ %.

An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power of 250 V . The percentage efficiency of transmission line is $\_\_\_\_$。

The wavelength of light, while it is passing through water is 540 nm . The refractive index of water is $\frac{4}{3}$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $\frac{3}{2}$ is $\_\_\_\_$ nm.

Given below are two statements :

Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.

Statement II : The time period of revolution of the satellite is $T=2 \pi \sqrt{\frac{R_{e}}{g}}$ (for satellite very close to the earth surface), where $R_{e}$ radius of earth and $g$ acceleration due to gravity.

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

Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential ( $V$ ) and the electric field ( $\vec{E}$ ) at the center O of the pentagon due to these five positive charges are :

A laser beam has intensity of $4.0 \times 10^{14} \mathrm{~W} / \mathrm{m}^{2}$. The amplitude of magnetic field associated with beam is $\_\_\_\_$ T. ( Take $\epsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}$ and $\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ )

Light is incident on a metallic plate having work function $110 \times 10^{-20} \mathrm{~J}$. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s} .\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)$

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II :

Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.

Statement II : The total kinetic energy can be the sum of kinetic energy of the canter of mass w.r.t. to the origin and the kinetic energy of all the particles w.r.t. the canter of mass as the reference.

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

A conducting circular loop is rotated about its diameter at a constant angular speed of $100 \mathrm{rad} / \mathrm{s}$ in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30^{\circ}$ from the horizontal position, the induced EMF is 15.4 mV . The radius of the loop is $\_\_\_\_$ mm . (Take $\left.\pi=\frac{22}{7}\right)$

Two masses m and 2 m are connected by a light string going over a pulley (disc) of mass 30 m with radius $r=0.1 \mathrm{~m}$. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2 m mass is released from rest and its speed when it has descended through a height of 3.6 m is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$. (Assume string does not slip and $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

A capacitor $P$ with capacitance $10 \times 10^{-6} \mathrm{~F}$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20 \times 10^{-6} \mathrm{~F}$. The charge on capacitor $Q$ when equilibrium is established will be $\alpha \times 10^{-5} \mathrm{C}$ (assume capacitor $Q$ does not have any charge initially), the value of $\alpha$ is $\_\_\_\_$。

A cylindrical conductor of length 2 m and area of cross-section $0.2 \mathrm{~mm}^{2}$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3} \mathrm{~m}^{2} / \mathrm{V}$.s. The value of $\alpha$ is : (electron concentration $=5 \times 10^{28} / \mathrm{m}^{3}$ and electron charge $=1.6 \times 10^{-19} \mathrm{C}$ )

An insulated cylinder of volume $60 \mathrm{~cm}^{3}$ is filled with a gas at $27^{\circ} \mathrm{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 \mathrm{~cm}^{3}$ while allowing the temperature to rise to $77^{\circ} \mathrm{C}$. The final pressure is $\_\_\_\_$ atmospheric pressure.

At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $49 \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{w} / \mathrm{w})$ aqueous solution. What is the mole fraction of $\mathrm{H}_{2} \mathrm{SO}_{4}$ in the resultant solution? (Given : Atomic mass $\mathrm{H}=1 \mathrm{u} ; \mathrm{S}=32 \mathrm{u} ; \mathrm{O}=16 \mathrm{u}$ ) (Assume that temperature after mixing remains constant)

For the reaction, $\mathrm{A + 2B \rightarrow AB_2}$. $36.0\,\mathrm{g}$ of $\mathrm{A}$ (molar mass $=60\,\mathrm{g\,mol^{-1}}$) and $56.0\,\mathrm{g}$ of $\mathrm{B}$ (molar mass $=80\,\mathrm{g\,mol^{-1}}$) are allowed to react.

Which of the following statements are correct?

(A) $\mathrm{A}$ is the limiting reagent (B) $77.0\,\mathrm{g}$ of $\mathrm{AB_2}$ is formed (C) Molar mass of $\mathrm{AB_2}$ is $140\,\mathrm{g\,mol^{-1}}$ (D) $15.0\,\mathrm{g}$ of $\mathrm{A}$ is left unreacted

Choose the correct answer from the options given below:

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II :

Statement-I : The first ionization enthalpy of Cr is lower than that of Mn.

Statement-II : The second and third ionization enthalpies of Cr are higher than those of Mn .

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

When 1 g of compound ( X ) is subjected to Kjeldahl's method for estimation of nitrogen, 15 $\mathrm{mL}, 1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ was neutralized by ammonia evolved. The percentage of nitrogen in compound $(\mathrm{X})$ is :

Correct statements regarding Arrhenius equation among the following are :

(A) Factor $\mathrm{e}^{-\mathrm{Ea} / \mathrm{RT}}$ corresponds to fraction of molecules having kinetic energy less than Ea.

(B) At a given temperature, lower the Ea, faster is the reaction.

(C) Increase in temperature by about $10^{\circ} \mathrm{C}$ doubles the rate of reaction.

(D) Plot of $\log \mathrm{k}$ vs $\frac{1}{\mathrm{~T}}$ gives a straight line with slope $=-\frac{\mathrm{Ea}}{\mathrm{R}}$.

Choose the correct answer from the options given below:

The IUPAC name of the following comopound is :

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II :

Statement-I : Element $X$ and $Y$ are the most and least electronegative elements, respectively among $\mathrm{N, As, Sb}$ and $\mathrm{P}$. The nature of the oxides $\mathrm{X_2O_3}$ and $\mathrm{Y_2O_3}$ is acidic and amphoteric, respectively.

Statement-II : $\mathrm{BCl}_{3}$ is covalent in nature and gets hydrolysed in water. It produces $\left[\mathrm{B}(\mathrm{OH})_{4}\right]^{-}$and $\left[\mathrm{B}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ in aqueous medium.

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

Among $\mathrm{H}_{2} \mathrm{~S}, \mathrm{H}_{2} \mathrm{O}, \mathrm{NF}_{3}, \mathrm{NH}_{3}$ and $\mathrm{CHCl}_{3}$, identify the molecule $(\mathrm{X})$ with lowest dipole moment value. The number of lone pairs of electrons present on the central atom of the molecule $(\mathrm{X})$ is :

Given below are two statements, one is labelled as Statement I and the other is labelled as Statement II.

Statement I: $\mathrm{C}<\mathrm{O}<\mathrm{N}<\mathrm{F}$ is the correct order in terms of first ionization enthalpy values.

Statement II: $\mathrm{S}>\mathrm{Se}>\mathrm{Te}>\mathrm{Po}>\mathrm{O}$ is the correct order in terms of the magnitude of electron gain enthalpy values.

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

Which of the following mixture gives a buffer solution with $\mathrm{pH}=9.25$ ? Given : $\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_{4} \mathrm{OH}\right)=4.75$

The energy of the first (lowest) Balmer line of $\mathrm{H}$-atom is $x\,\mathrm{J}$. The energy (in $\mathrm{J}$) of the second Balmer line of $\mathrm{H}$-atom is:

Identify the correct statements :

A. Hydrated salts can be used as primary standard.

B. Primary standard should not undergo any reaction with air.

C. Reactions of primary standard with another substance should be instantaneous and stoichiometric.

D. Primary standard should not be soluble in water.

E. Primary standard should have low relative molar mass.

Choose the correct answer from the options given below :

$\left[\mathrm{Ni}\left(\mathrm{PPh}_{3}\right)_{2} \mathrm{Cl}_{2}\right]$ is a paramagnetic complex. Identify the INCORRECT statements about this complex.

A. The complex exhibits geometrical isomerism.

B. The complex is white in colour.

C. The calculated spin-only magnetic moment of the complex is 2.84 BM .

D. The calculated CFSE (Crystal Field Stabilization Energy) of Ni in this complex is $-0.8 \Delta_{0}$.

E. The geometrical arrangement of ligands in this complex is similar to that in $\mathrm{Ni}(\mathrm{CO})_{4}$.

Choose the correct answer from the options given below :

Consider the following reduction processes : $\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \rightarrow \mathrm{Al}(\mathrm{s}), \mathrm{E}^{\circ}=-1.66 \mathrm{~V}$ $\mathrm{Fe}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+}, \mathrm{E}^{0}=+0.77 \mathrm{~V}$ $\mathrm{Co}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Co}^{2+}, \mathrm{E}^{\circ}=+1.81 \mathrm{~V}$ $\mathrm{Cr}^{3+}+3 \mathrm{e}^{-} \rightarrow \mathrm{Cr}(\mathrm{s}), \mathrm{E}^{\circ}=-0.74 \mathrm{~V}$ The tendency to act as reducing agent decreases in the order :

The compound A, $\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{2}$ reacts with acetophenone to form a single product via crossAldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as

Consider the following electrochemical cell : $\mathrm{Pt}\left|\mathrm{O}_{2}(\mathrm{~g})(\mathrm{lbar})\right| \mathrm{HCl}(\mathrm{aq}) \| \mathrm{M}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) \mid \mathrm{M}(\mathrm{s})$ The pH above which, oxygen gas would start to evolve at anode is $\_\_\_\_$ (nearest integer). $\left[\begin{array}{ll}\text { Given : } & \left.\begin{array}{l}\mathrm{E}_{\mathrm{M}^{2+} / \mathrm{M}}^{0}=0.994 \mathrm{~V} \mathrm{E}_{\mathrm{O}_{2} / \mathrm{H}_{2} \mathrm{O}}^{0}=1.23 \mathrm{~V}\end{array}\right\} \text { standard \; reduction\; potential } \\& \text { and } \frac{\mathrm{RT}}{\mathrm{F}}(2.303)=0.059 \mathrm{~V} \text { at \;the\; given \;condition }\end{array}\right]$

If the enthalpy of sublimation of Li is $155 \mathrm{~kJ} \mathrm{~mol}^{-1}$, enthalpy of dissociation of $F_{2}$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$, ionization enthalpy of Li is $520 \mathrm{~kJ} \mathrm{~mol}^{-1}$, electron gain enthalpy of $F$ is $-313 \mathrm{~kJ} \mathrm{~mol}^{-1}$, standard enthalpy of formation of LiF is $-594 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The magnitude of lattice enthalpy of LiF is $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$ (Nearest integer).

Among the following oxides of 3d elements, the number of mixed oxides are $\_\_\_\_$ . $\mathrm{Ti}_{2} \mathrm{O}_{3}, \mathrm{~V}_{2} \mathrm{O}_{4}, \mathrm{Cr}_{2} \mathrm{O}_{3}, \mathrm{Mn}_{3} \mathrm{O}_{4}, \mathrm{Fe}_{3} \mathrm{O}_{4}, \mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{Co}_{3} \mathrm{O}_{4}$

The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is $82 \%$, is $\_\_\_\_$ g (nearest integer). (Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}:$

Consider $\mathrm{A} \xrightarrow{\mathrm{k}_{1}} \mathrm{~B}$ and $\mathrm{C} \xrightarrow{\mathrm{k}_{2}} \mathrm{D}$ are two reactions. If the rate constant $\left(k_{1}\right)$ of the $A \rightarrow B$ reaction can be expressed by the following equation $\log _{10} \mathrm{k}=14.34-\frac{1.5 \times 10^{4}}{\mathrm{~T} / \mathrm{K}}$ and activation energy of $\mathrm{C} \rightarrow \mathrm{D}$ reaction $\left(\mathrm{Ea}_{2}\right)$ is $\frac{1}{5}$ th of the $\mathrm{A} \rightarrow \mathrm{B}$ reaction $\left(\mathrm{Ea}_{1}\right)$, then the value of $\left(\mathrm{Ea}_{2}\right)$ is $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest Integer)