JEE Main 2026 — 21 Jan Shift 2 (3:00 PM - 6:00 PM) (Previous Year

Let $A=\{2, 3, 5, 7, 9\}$. Let R be the relation on A defined by $xRy$ if and only if $2x\le3y$. Let $l$ be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then $l+m$ is equal to :

1. A.23
2. B.21
3. C.25✓
4. D.27

Correct answer: C

Let $z$ be the complex number satisfying $|z-5|\le3$ and having maximum positive principal argument. Then $34\left|\frac{5z-12}{5iz+16}\right|^2$ is equal to :

1. A.12
2. B.16
3. C.26
4. D.20✓

Correct answer: D

The positive integer n, for which the solutions of the equation $x(x+2)+(x+2)(x+4)+\cdots+(x+2n-2)(x+2n)=\frac{8n}{3}$ are two consecutive even integers, is :

1. A.9
2. B.3✓
3. C.12
4. D.6

Correct answer: B

Let $\alpha$ and $\beta$ be the roots of the equation $x^2+2ax+(3a+10)=0$ such that $\alpha<1<\beta$. Then the set of all possible values of a is :

1. A.$\left(-\infty, \frac{-11}{5}\right)\cup(5, \infty)$
2. B.$(-\infty, -3)$
3. C.$(-\infty, -2)\cup(5, \infty)$
4. D.$\left(-\infty, \frac{-11}{5}\right)$✓

Correct answer: D

For the matrices $A=\begin{bmatrix}3 & -4\\ 1 & -1\end{bmatrix}$ and $B=\begin{bmatrix}-29 & 49\\ -13 & 18\end{bmatrix}$, if $(A^{15}+B)\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}0\\ 0\end{bmatrix}$, then among the following which one is **true** ?

1. A.$x=16, y=3$
2. B.$x=18, y=11$
3. C.$x=5, y=7$
4. D.$x=11, y=2$✓

Correct answer: D

If the system of equations $3x+y+4z=3$, $2x+\alpha y-z=-3$, $x+2y+z=4$ has no solution, then the value of $\alpha$ is equal to :

1. A.19✓
2. B.13
3. C.4
4. D.23

Correct answer: A

Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \ldots, \frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. If $a_1+a_2+\ldots+a_{10}=62$, then $a_1$ is equal to :

1. A.$2-\sqrt{2}$
2. B.$2(2-\sqrt{2})$
3. C.$\sqrt{2}-1$
4. D.$2(\sqrt{2}-1)$✓

Correct answer: D

Let $A=\{x: |x^2-10|\le6\}$ and $B=\{x: |x-2|>1\}$. Then

1. A.$A-B=[2, 3)$
2. B.$A\cap B=[-4, -2]\cup[3, 4]$
3. C.$B-A=(-\infty, -4)\cup(-2, 1)\cup(4, \infty)$✓
4. D.$A\cup B=(-\infty, 1]\cup(2, \infty)$

Correct answer: C

The largest $n\in\mathbb{N}$, for which $7^n$ divides $101!$, is :

1. A.15
2. B.19
3. C.16✓
4. D.18

Correct answer: C

A random variable X takes values 0, 1, 2, 3 with probabilities $\frac{2a+1}{30}, \frac{8a-1}{30}, \frac{4a+1}{30}$, b respectively, where $a, b\in\mathbb{R}$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of X such that $\sigma^2+\mu^2=2$. Then $\frac{a}{b}$ is equal to :

1. A.12
2. B.3
3. C.60✓
4. D.30

Correct answer: C

Let one end of a focal chord of the parabola $y^2=16x$ be $(16, 16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio $5:2$, then the minimum value of $\alpha+\beta$ is equal to :

1. A.5
2. B.7✓
3. C.16
4. D.22

Correct answer: B

Let $y^2=12x$ be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the $x$-axis such that $\angle OPA=90^\circ$. Then the locus of the centroid of such triangles OPA is :

1. A.$y^2-4x+8=0$
2. B.$y^2-6x+4=0$
3. C.$y^2-9x+6=0$
4. D.$y^2-2x+8=0$✓

Correct answer: D

If the line $\alpha x+4y=\sqrt{7}$, where $\alpha\in\mathbb{R}$, touches the ellipse $3x^2+4y^2=1$ at the point P in the first quadrant, then one of the focal distances of P is :

1. A.$\frac{1}{\sqrt{3}}+\frac{1}{2\sqrt{5}}$
2. B.$\frac{1}{\sqrt{3}}+\frac{1}{2\sqrt{7}}$✓
3. C.$\frac{1}{\sqrt{3}}-\frac{1}{2\sqrt{5}}$
4. D.$\frac{1}{\sqrt{3}}-\frac{1}{2\sqrt{11}}$

Correct answer: B

Let the line L pass through the point $(-3, 5, 2)$ and make equal angles with the positive coordinate axes. If the distance of L from the point $(-2, r, 1)$ is $\sqrt{\frac{14}{3}}$, then the sum of all possible values of r is :

1. A.16
2. B.12
3. C.10✓
4. D.6

Correct answer: C

Let the line $L_1$ be parallel to the vector $-3\hat{i}+2\hat{j}+4\hat{k}$ and pass through the point $(2, 6, 7)$, and the line $L_2$ be parallel to the vector $2\hat{i}+\hat{j}+3\hat{k}$ and pass through the point $(4, 3, 5)$. If the line $L_3$ is parallel to the vector $-3\hat{i}+5\hat{j}+16\hat{k}$ and intersects the lines $L_1$ and $L_2$ at the points C and D, respectively, then $|\overrightarrow{CD}|^2$ is equal to :

1. A.290✓
2. B.89
3. C.312
4. D.171

Correct answer: A

For a triangle ABC, let $\vec{p}=\overrightarrow{BC}$, $\vec{q}=\overrightarrow{CA}$ and $\vec{r}=\overrightarrow{BA}$. If $|\vec{p}|=2\sqrt{3}$, $|\vec{q}|=2$ and $\cos\theta=\frac{1}{\sqrt{3}}$, where $\theta$ is the angle between $\vec{p}$ and $\vec{q}$, then $|\vec{p}\times(\vec{q}-3\vec{r})|^2+3|\vec{r}|^2$ is equal to :

1. A.340
2. B.220
3. C.200✓
4. D.410

Correct answer: C

Let $f(x)=x^3+x^2f'(1)+2xf''(2)+f'''(3)$, $x\in\mathbb{R}$. Then the value of $f'(5)$ is :

1. A.$\frac{62}{5}$
2. B.$\frac{657}{5}$
3. C.$\frac{2}{5}$
4. D.$\frac{117}{5}$✓

Correct answer: D

Let $f:\mathbb{R}\to\mathbb{R}$ be a twice differentiable function such that $f''(x)>0$ for all $x\in\mathbb{R}$ and $f'(a-1)=0$, where a is a real number. Let $g(x)=f(\tan^2x-2\tan x+a)$, $0<x<\frac{\pi}{2}$. Consider the following two statements : (I) g is increasing in $\left(0, \frac{\pi}{4}\right)$ (II) g is deceasing in $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then,

1. A.Only (II) is True
2. B.Only (I) is True
3. C.Both (I) and (II) are True
4. D.Neither (I) nor (II) is True✓

Correct answer: D

Let $y=y(x)$ be the solution of the differential equation $\sec x\frac{dy}{dx}-2y=2+3\sin x$, $x\in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, $y(0)=-\frac{7}{4}$. Then $y\left(\frac{\pi}{6}\right)$ is equal to :

1. A.$-\frac{5}{2}$✓
2. B.$-\frac{5}{4}$
3. C.$-3\sqrt{2}-7$
4. D.$-3\sqrt{3}-7$

Correct answer: A

If the area of the region $\{(x, y): 1-2x\le y\le4-x^2, x\ge0, y\ge0\}$ is $\frac{\alpha}{\beta}$, $\alpha, \beta\in\mathbb{N}$, $\gcd(\alpha, \beta)=1$, then the value of $(\alpha+\beta)$ is :

1. A.67
2. B.85
3. C.91
4. D.73✓

Correct answer: D

If $\left(\frac{1}{^{15}C_0}+\frac{1}{^{15}C_1}\right)\left(\frac{1}{^{15}C_1}+\frac{1}{^{15}C_2}\right)\cdots\left(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}\right)=\frac{\alpha^{13}}{^{14}C_0\,^{14}C_1\cdots\,^{14}C_{12}}$, then $30\alpha$ is equal to ______.

Correct answer: 32

If P is a point on the circle $x^2+y^2=4$, Q is a point on the straight line $5x+y+2=0$ and $x-y+1=0$ is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such points P is ______.

Correct answer: 2

Let the maximum value of $(\sin^{-1}x)^2+(\cos^{-1}x)^2$ for $x\in\left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\right]$ be $\frac{m}{n}\pi^2$, where $\gcd(m, n)=1$. Then $m+n$ is equal to ______.

Correct answer: 65

Let $[\cdot]$ denote the greatest integer function and $f(x)=\lim_{n\to\infty}\frac{1}{n^3}\sum_{k=1}^{n}\left[\frac{k^2}{3^x}\right]$. Then $12\sum_{j=1}^{\infty}f(j)$ is equal to ______.

Correct answer: 2

If $\int_0^1 4\cot^{-1}(1-2x+4x^2)\,dx=a\tan^{-1}(2)-b\log_e(5)$, where $a, b\in\mathbb{N}$, then $(2a+b)$ is equal to ______.

Correct answer: 9

Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :

1. A.205.33 m
2. B.205.333 m
3. C.205 m
4. D.205.3 m✓

Correct answer: D

A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $v_0$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with $\sigma$, $\rho$ and $g$, gravitational acceleration)

1. A.$2\left[\frac{\Delta r}{r}-\frac{\Delta v_0}{v_0}\right]$
2. B.$2\left[\frac{\Delta r}{r}+\frac{\Delta v_0}{v_0}\right]$
3. C.$\frac{2\Delta r}{r}+\frac{\Delta v_0}{v_0}$✓
4. D.$2\frac{\Delta r}{r}-\frac{\Delta v_0}{v_0}$

Correct answer: C

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are ______ and ______ respectively.

1. A.20 s and 100 m
2. B.40 s and 100 m
3. C.40 s and 0 m
4. D.40 s and 200 m✓

Correct answer: D

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its center. The magnitudes of the acceleration experienced by the blocks is ______ (assume no slipping of string on pulley).

1. A.$\frac{(M-m)g}{\left[\left(\frac{13}{6}\right)M+m\right]}$
2. B.$\frac{(M-m)g}{\left[\left(\frac{8}{3}\right)M+m\right]}$✓
3. C.$\frac{(M-m)g}{2M+m}$
4. D.$\frac{(M-m)g}{M+m}$

Correct answer: B

Two cars A and B each of mass $10^3$ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is ______ J.s.

1. A.$3\times10^5$
2. B.$10^5$✓
3. C.$3.6\times10^5$
4. D.$2\times10^5$

Correct answer: B

A body of mass 2 kg is moving along $x$-direction such that its displacement as function of time is given by $x(t)=\alpha t^2+\beta t+\gamma$ m, where $\alpha=1$ m/s$^2$, $\beta=1$ m/s and $\gamma=1$ m. The work done on the body during the time interval $t=2$ s to $t=3$ s, is ______ J.

1. A.42
2. B.24✓
3. C.12
4. D.49

Correct answer: B

A large drum having radius R is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M as $\mu$, is :

1. A.$\sqrt{\frac{\mu g}{R}}$
2. B.$\sqrt{\frac{g}{\mu R}}$✓
3. C.$\sqrt{\frac{2g}{\mu R}}$
4. D.$\sqrt{\frac{g}{2\mu R}}$

Correct answer: B

Surface tension of two liquids (having same densities), $T_1$ and $T_2$, are measured using capillary rise method utilizing two tubes with inner radii of $r_1$ and $r_2$ where $r_1>r_2$. The measured liquid heights in these tubes are $h_1$ and $h_2$ respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights $h_1$ and $h_2$ and surfaces tensions $T_1$ and $T_2$ satisfy the relation :

1. A.$h_1>h_2$ and $T_1<T_2$
2. B.$h_1=h_2$ and $T_1=T_2$
3. C.$h_1<h_2$ and $T_1=T_2$✓
4. D.$h_1>h_2$ and $T_1=T_2$

Correct answer: C

The r.m.s. speed of oxygen molecules at $47^\circ$C is equal to that of the hydrogen molecules kept at ______ $^\circ$C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)

1. A.-20
2. B.-253✓
3. C.-235
4. D.-100

Correct answer: B

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator is ______ Hz. [take $\pi=\frac{22}{7}$]

1. A.28
2. B.176
3. C.14✓
4. D.88

Correct answer: C

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is ______ s.

1. A.$\pi\sqrt{\frac{LC}{2}}$
2. B.$\frac{\pi\sqrt{LC}}{6}$✓
3. C.$\frac{\pi\sqrt{LC}}{3}$
4. D.$\frac{\pi\sqrt{LC}}{2}$

Correct answer: B

Two known resistances of $R\ \Omega$ and $2R\ \Omega$ and one unknown resistance $X\ \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $X\ \Omega$, then the value of X is ______ $\Omega$.

1. A.R
2. B.$(\sqrt{3}-1)R$✓
3. C.$2(\sqrt{3}-1)R$
4. D.$(\sqrt{3}+1)R$

Correct answer: B

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading then the length AP is ______ cm.

1. A.30✓
2. B.25
3. C.15
4. D.20

Correct answer: A

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre O of the circular loop is :

1. A.$\frac{\mu_0}{2\pi}\frac{I}{r}(\pi-1)\hat{i}$
2. B.$\frac{\mu_0}{2\pi}\frac{I}{r}(\pi+1)\hat{i}$
3. C.$-\frac{\mu_0}{2\pi}\frac{I}{r}(\pi-1)\hat{i}$✓
4. D.$-\frac{\mu_0}{2\pi}\frac{I}{r}(\pi+1)\hat{i}$

Correct answer: C

Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of 4R. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is : (Take $k=\frac{1}{4\pi\epsilon_0}$ and assume $kQ^2>Gm^2$ where G is the Gravitational constant)

1. A.$\sqrt{\frac{kQ^2}{4mR}\left(1-\frac{Gm^2}{kQ^2}\right)}$✓
2. B.$\sqrt{\frac{kQ^2}{2mR}\left(1-\frac{Gm^2}{kQ^2}\right)}$
3. C.$\sqrt{\frac{kQ^2}{2mR}\left(1-\frac{Gm^2}{2kQ^2}\right)}$
4. D.$\sqrt{\frac{kQ^2}{4mR}\left(1+\frac{Gm^2}{kQ^2}\right)}$

Correct answer: A

A battery with EMF E and internal resistance $r$ is connected across a resistance R. The power consumption in R will be maximum when :

1. A.$R=r$✓
2. B.$R=r/2$
3. C.$R=\sqrt{2}r$
4. D.$R=2r$

Correct answer: A

Given below are two statements : Statement I : In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits. Statement II : In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength. In the light of the above statements, choose the **correct answer** from the options given below :

1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true✓

Correct answer: D

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface. If refractive index of the material of prism is $\sqrt{2}$, the angle $\theta$ of prism is.

1. A.$90^\circ$
2. B.$45^\circ$
3. C.$75^\circ$
4. D.$60^\circ$✓

Correct answer: D

The energy of an electron in an orbit of the Bohr's atom is $-0.04E_0$ eV where $E_0$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then $\frac{2\pi L}{h}$ is ______ :

1. A.4
2. B.6
3. C.5✓
4. D.2

Correct answer: C

The charge stored by the capacitor C in the given circuit in the steady state is ______ $\mu$C.

1. A.10✓
2. B.7.5
3. C.5
4. D.12.5

Correct answer: A

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ______ cm/s.

Correct answer: 5

A diatomic gas $(\gamma=1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J.

Correct answer: 350

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma=10$ mho/m. The ratio of maximum conduction current density to maximum displacement current density is ______. [Take $\frac{1}{4\pi\epsilon_0}=9\times10^9$ Nm$^2$/C$^2$]

Correct answer: 1800

In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness 20 $\mu$m is introduced in front of one of the slits then center bright fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is ______.

Correct answer: 14

A particle having electric charge $3\times10^{-19}$ C and mass $6\times10^{-27}$ kg is accelerated by applying an electric potential of 1.21 V. Wavelength of the matter wave associated with the particle is $\alpha\times10^{-12}$ m. The value of $\alpha$ is ______. (Take Planck's constant $=6.6\times10^{-34}$ J.s)

Correct answer: 10

Aqueous HCl reacts with MnO$_2$(s) to form MnCl$_2$(aq), Cl$_2$(g) and H$_2$O($l$). What is the weight (in g) of Cl$_2$ liberated when 8.7 g of MnO$_2$(s) is reacted with excess aqueous HCl solution ? (Given Molar mass in g mol$^{-1}$ Mn = 55, Cl = 35.5, O = 16, H = 1)

1. A.21.3
2. B.71
3. C.14.2
4. D.7.1✓

Correct answer: D

Consider the following spectral lines for atomic hydrogen : A. First line of Paschen series B. Second line of Balmer series C. Third line of Paschen series D. Fourth line of Bracket series. The correct arrangement of the above lines in ascending order of energy is :

1. A.C < D < B < A
2. B.A < B < C < D
3. C.D < C < A < B
4. D.D < A < C < B✓

Correct answer: D

The correct increasing order of C$-$H(A), C$-$O(B), C=O(C) and C$\equiv$N(D) bonds in terms of covalent bond length is :

1. A.A < D < C < B✓
2. B.A < B < C < D
3. C.D < C < B < A
4. D.D < C < A < B

Correct answer: A

Consider the following data : $\Delta_fH^\ominus$ (methane, g) $=-X$ kJ mol$^{-1}$; Enthalpy of sublimation of graphite $=Y$ kJ mol$^{-1}$; Dissociation enthalpy of H$_2$ $=Z$ kJ mol$^{-1}$. The bond enthalpy of C$-$H bond is given by :

1. A.$\frac{X+Y+4Z}{2}$
2. B.$\frac{X+Y+2Z}{4}$✓
3. C.$\frac{-X+Y+Z}{4}$
4. D.$X+Y+Z$

Correct answer: B

For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature ?

1. A.$E_{cell}$ increases linearly with time
2. B.$E_{cell}$ constant with time (horizontal line)✓
3. C.$E_{cell}$ decreases with time (falling line)
4. D.Vertical line at a fixed time

Correct answer: B

Decomposition of A is a first order reaction at T(K) and is given by A(g) $\to$ B(g) + C(g). In a closed 1 L vessel, 1 bar A(g) is allowed to decompose at T(K). After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in min$^{-1}$) of the reaction ? (log 2 = 0.3)

1. A.$6.9\times10^{-4}$
2. B.$6.9\times10^{-1}$
3. C.$6.9\times10^{-2}$
4. D.$6.9\times10^{-3}$✓

Correct answer: D

Given below are two statements : Statement I : The correct order in terms of atomic/ionic radii is Al > Mg > Mg$^{2+}$ > Al$^{3+}$. Statement II : The correct order in terms of the magnitude of electron gain enthalpy is Cl > Br > S > O. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are false
2. B.Both Statement I and Statement II are true
3. C.Statement I is false but Statement II is true✓
4. D.Statement I is true but Statement II is false

Correct answer: C

Given below are two statements : Statement I : The correct order in terms of bond dissociation enthalpy is Cl$_2$ > Br$_2$ > F$_2$ > I$_2$. Statement II : The correct trend in the covalent character of the metal halides is [SnCl$_4$ > SnCl$_2$], [PbCl$_4$ > PbCl$_2$] and [UF$_4$ > UF$_6$]. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are true
2. B.Statement I is false but Statement II is true
3. C.Statement I is true but Statement II is false✓
4. D.Both Statement I and Statement II are false

Correct answer: C

Given below are some of the statements about Mn and Mn$_2$O$_7$. Identify the correct statements. A. Mn forms the oxide Mn$_2$O$_7$, in which Mn is in its highest oxidation state. B. Oxygen stabilizes the Mn in higher oxidation states by forming multiple bonds with Mn. C. Mn$_2$O$_7$ is an ionic oxide. D. The structure of Mn$_2$O$_7$ consists of one bridged oxygen. Choose the correct answer from the options given below :

1. A.A, B and D Only✓
2. B.A, C and D Only
3. C.A, B and C Only
4. D.A, B, C and D

Correct answer: A

Given below are two statements : Statement I : Crystal Field Stabilization Energy (CFSE) of [Cr(H$_2$O)$_6$]$^{2+}$ is greater than that of [Mn(H$_2$O)$_6$]$^{2+}$. Statement II : Potassium ferricyanide has a greater spin-only magnetic moment than sodium ferrocyanide. In the light of the above statements, choose the correct answer from the options given below :

1. A.Statement I is true but Statement II is false
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are true✓
4. D.Both Statement I and Statement II are false

Correct answer: C

By usual analysis, 1.00 g of compound (X) gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is : (nearest integer) (Given, molar mass in g mol$^{-1}$ : O = 16, Mg = 24, P = 31)

1. A.20
2. B.40
3. C.30
4. D.50✓

Correct answer: D

The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is : CH$_3$Br + Nu$^\ominus$ $\to$ CH$_3$Nu + Br$^\ominus$

1. A.CH$_3$COO$^-$ > PhO$^-$ > $^-$OH > ClO$_4^-$
2. B.ClO$_4^-$ > CH$_3$COO$^-$ > $^-$OH > PhO$^-$
3. C.$^-$OH > PhO$^-$ > CH$_3$COO$^-$ > ClO$_4^-$✓
4. D.PhO$^-$ > $^-$OH > CH$_3$COO$^-$ > ClO$_4^-$