JEE Main 2026 — 2 Apr Shift 1 (Previous Year Paper)

Let $\alpha, \alpha+2, \alpha \in \mathbb{Z}$, be the roots of the quadratic equation $x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\dots+(x+n-1)(x+n+1)=4n$ for some $n \in \mathbb{N}$. Then $n+\alpha$ is equal to :

1. A.0
2. B.1
3. C.2✓
4. D.3

Correct answer: C

Let $x$ and $y$ be real numbers such that $50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i$, $i=\sqrt{-1}$. Then the value of $10(x-3y)$ is :

1. A.20
2. B.31
3. C.35
4. D.75✓

Correct answer: D

Let $\alpha, \beta \in \mathbb{R}$ be such that the system of linear equations $x+2y+z=5$, $2x+y+\alpha z=5$, $8x+4y+\beta z=18$ has no solution. Then $\frac{\beta}{\alpha}$ is equal to :

1. A.$-4$
2. B.$4$✓
3. C.$8$
4. D.$-8$

Correct answer: B

Let $A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}$. If $A^2-4A+I=O$ and $B^2-5B-6I=O$, then among the two statements : (S1): $[(B-A)(B+A)]^T=\begin{bmatrix}13&15\\7&10\end{bmatrix}$ and (S2): $\det(\operatorname{adj}(A+B))=-5$,

1. A.only (S1) is correct
2. B.only (S2) is correct✓
3. C.both (S1) and (S2) are correct
4. D.both (S1) and (S2) are wrong

Correct answer: B

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in $A \cap B$, which are divisible by 3, is :

1. A.4
2. B.5✓
3. C.6
4. D.7

Correct answer: B

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :

1. A.15400
2. B.17800
3. C.16800✓
4. D.29400

Correct answer: C

The number of elements in the set $S=\left\{(r,k) : k \in \mathbb{Z} \text{ and } {}^{36}C_{r+1}=\frac{6\left({}^{35}C_r\right)}{(k^2-3)}\right\}$, is :

1. A.2
2. B.4✓
3. C.8
4. D.16

Correct answer: B

If the mean of the data (Class : Frequency) 5-10 : 2, 10-15 : $k$, 15-20 : 28, 20-25 : 54, 25-30 : $k+1$, 30-35 : 5 is 21, then $k$ is one of the roots of the equation :

1. A.$2x^2-23x-10=0$
2. B.$4x^2-35x+24=0$
3. C.$2x^2-19x-10=0$✓
4. D.$2x^2-35x+98=0$

Correct answer: C

Let the mid points of the sides of a triangle ABC be $\left(\frac{5}{2},7\right)$, $\left(\frac{5}{2},3\right)$ and $(4,5)$. If its incentre is $(h,k)$, then $3h+k$ is equal to :

1. A.11
2. B.12
3. C.13✓
4. D.14

Correct answer: C

Let an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a<b$, pass through the point $(4,3)$ and have eccentricity $\frac{\sqrt5}{3}$. Then the length of its latus rectum is :

1. A.$\frac{4\sqrt5}{3}$
2. B.$2\sqrt5$
3. C.$\frac{7\sqrt5}{3}$
4. D.$\frac{8\sqrt5}{3}$✓

Correct answer: D

If $\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K$, then the value of $\sin\left(\frac{10K\pi}{3}\right)$ is :

1. A.$\frac{\sqrt3+1}{2\sqrt2}$✓
2. B.$\frac{\sqrt3-1}{\sqrt2}$
3. C.$\frac{\sqrt3}{2}$
4. D.$\frac{1}{2}$

Correct answer: A

Let $S=\{x \in [-\pi,\pi] : \sin x(\sin x+\cos x)=a, a \in \mathbb{Z}\}$. Then $n(S)$ is equal to :

1. A.3
2. B.6
3. C.7
4. D.9✓

Correct answer: D

If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ lies on $xy$-plane, then the value of $a+b$ is :

1. A.2
2. B.5
3. C.7✓
4. D.9

Correct answer: C

If $\vec a$ and $\vec b$ are two vectors such that $|\vec a|=2$ and $|\vec b|=3$, then the maximum value of $3\left|3\vec a+2\vec b\right|+4\left|3\vec a-2\vec b\right|$ is :

1. A.30
2. B.36
3. C.60✓
4. D.72

Correct answer: C

Let a line L passing through the point $(1,1,1)$ be perpendicular to both the vectors $2\hat i+2\hat j+\hat k$ and $\hat i+2\hat j+2\hat k$. If $P(a,b,c)$ is the foot of perpendicular from the origin on the line L, then the value of $34(a+b+c)$ is :

1. A.50
2. B.80
3. C.100✓
4. D.120

Correct answer: C

If $\lim_{x\to2}\frac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)}=m$, then $a+b+m$ is equal to :

1. A.5
2. B.6✓
3. C.8
4. D.10

Correct answer: B

If the curve $y=f(x)$ passes through the point $(1,e)$ and satisfies the differential equation $dy=y(2+\log_e x)\,dx$, $x>0$, then $f(e)$ is equal to :

1. A.$e^e$
2. B.$e^{e^2}$
3. C.$e^{2e}$✓
4. D.$e^{2^e}$

Correct answer: C

The number of critical points of the function $f(x)=\begin{cases}\left|\frac{\sin x}{x}\right|, & x\ne0\\ 1, & x=0\end{cases}$ in the interval $(-2\pi,2\pi)$ is equal to :

1. A.1
2. B.3
3. C.5✓
4. D.7

Correct answer: C

Let $[\cdot]$ denote the greatest integer function. Then the value of $\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx$ is :

1. A.$e^2+e^3-\frac{1}{e^2}-\frac{1}{e^3}$
2. B.$\frac12\left(e^2+e^3-\frac{1}{e^2}-\frac{1}{e^3}\right)$✓
3. C.$e^2+e^3-\frac{1}{2e^2}-\frac{1}{2e^3}$
4. D.$\frac12\left(e^2+e^3\right)-\frac{1}{e^2}-\frac{1}{e^3}$

Correct answer: B

Let $y=y(x)$ be the solution curve of the differential equation $(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$, $y(0)=0$. If the curve $y=y(x)$ passes through the point $\left(\alpha,\frac{-1}{2}\right)$, then a value of $\alpha$ is :

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

Correct answer: D

If the domain of the function $f(x)=\sqrt{\log_{(0.6)}\left(\left|\frac{2x-5}{x^2-4}\right|\right)}$ is $(-\infty,a]\cup\{b\}\cup[c,d]\cup(e,\infty)$, then the value of $a+b+c+d+e$ is ______.

Correct answer: 4

If $\sum_{k=1}^{n}a_k=6n^3$, then $\sum_{k=1}^{6}\left(\frac{a_{k+1}-a_k}{36}\right)^2$ is equal to ______.

Correct answer: 91

Let $a,b,c \in \{1,2,3,4\}$. If the probability, that $ax^2+2\sqrt2\,bx+c>0$ for all $x\in\mathbb{R}$, is $\frac{m}{n}$, $\gcd(m,n)=1$, then $m+n$ is equal to ______.

Correct answer: 81

Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $x+y=1$ is $\sqrt{14}$, then the square of the radius of C is ______.

Correct answer: 8

If $\alpha=\int_0^{2\sqrt3}\log_2\left(x^2+4\right)dx+\int_2^4\sqrt{2^x-4}\,dx$, then $\alpha^2$ is equal to ______.

Correct answer: 192

The dimensional formula of $\frac12\epsilon_0E^2$ ($\epsilon_0$ = permittivity of vacuum and E = electric field) is $M^aL^bT^c$. The value of $2a-b+c$ = ______.

1. A.0
2. B.1✓
3. C.$-1$
4. D.2

Correct answer: B

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is $\alpha\times10^9\ \mathrm{N/m^2}$. The value of $\alpha$ is ______. (Ignore the contribution of the load to Young's modulus error calculation)

1. A.1.3
2. B.1.65✓
3. C.0.13
4. D.0.25

Correct answer: B

The velocity of a particle is given as $\vec v=-x\hat i+2y\hat j-z\hat k$ m/s. The magnitude of acceleration at point $(1,2,4)$ is ______ $\mathrm{m/s^2}$.

1. A.$\sqrt6$
2. B.9✓
3. C.$\sqrt{33}$
4. D.0

Correct answer: B

The position of an object having mass 0.1 kg as a function of time $t$ is given as $\vec r=\left(10t^2\hat i+5t^3\hat j\right)$ m. At $t=1$ s, which of the following statements are correct? A. The linear momentum $\vec p=\left(2\hat i+1.5\hat j\right)$ kg m/s. B. The force acting on the object $\vec F=\left(2\hat i+3\hat j\right)$ N. C. The angular momentum of the object about its origin $\vec L=15\hat k$ J s. D. The torque acting on the object about its origin $\vec\tau=20\hat k$ N m. Choose the correct answer from the options given below :

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

Correct answer: D

A planet ($P_1$) is moving around the star of mass $2M$ in the orbit of radius $R$. Another planet ($P_2$) is moving around another star of mass $4M$ in a orbit of radius $2R$. Ratio of time periods of revolution of $P_2$ and $P_1$ is ______.

1. A.$\frac12$
2. B.2✓
3. C.4
4. D.$\frac14$

Correct answer: B

A particle is rotating in a circular path and at any instant its motion can be described as $\theta=\frac{5t^4}{40}-\frac{t^3}{3}$. The angular acceleration of the particle after 10 seconds is ______ $\mathrm{rad/s^2}$.

1. A.150
2. B.120
3. C.130✓
4. D.170

Correct answer: C

A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant $K=5$, the percentage increase in the capacitance is ______.

1. A.33.34
2. B.66.67✓
3. C.200
4. D.400

Correct answer: B

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q:\Delta U:\Delta W$ is ______.

1. A.2 : 3 : 5
2. B.5 : 3 : 2
3. C.2 : 5 : 7
4. D.7 : 5 : 2✓

Correct answer: D

Two charged conducting spheres $S_1$ and $S_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ respectively. The value of $\frac{E_{S1}}{E_{S2}}$ is ______.

1. A.$\frac32$
2. B.$\frac23$
3. C.$\frac49$
4. D.$\frac94$✓

Correct answer: D

The equation of a plane progressive wave is given by $y=5\cos\pi\left(200t-\frac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ______ m/s.

1. A.120
2. B.150
3. C.200
4. D.300✓

Correct answer: D

Two short electric dipoles A and B having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $60^\circ$ with the line joining points O and $x$. The ratio of the dipole moments $p_2/p_1$ is ______.

1. A.$\frac{\sqrt3}{2}$
2. B.$2\sqrt3$✓
3. C.$\frac{1}{\sqrt3}$
4. D.$\sqrt3$

Correct answer: B

For the given circuit (shown in part (A)) the time dependent input voltage $v_{in}(t)$ and corresponding output $v_o(t)$ are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y.

1. A.X - resistor - diode - Y
2. B.X - diode - Zener diode - Y (diode and Zener connected back-to-back, opposite orientations)✓
3. C.X - resistor - Zener diode - Y
4. D.X - diode - Zener diode - Y (both in the same orientation)

Correct answer: B

When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number of turns, area of the coil and radius of the coil wire are $N$, $A$ and $r$ respectively. For a second coils number of turns, area of the coil and radius of the coil wire are $2N$, $2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt2\,\alpha P$. The value of $\alpha$ is ______.

1. A.36✓
2. B.$128\sqrt2$
3. C.16
4. D.64

Correct answer: A

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are $B_1$ and $B_2$ respectively, then the ratio $\frac{B_1}{B_2}$ is ______.

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

Correct answer: A

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be ______.

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

Correct answer: B

Refer the figure given below. $\mu_1$ and $\mu_2$ are refractive indices of air and lens material. The height of image will be ______ cm.

1. A.1✓
2. B.0.5
3. C.1.2
4. D.0.25

Correct answer: A

For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3V_0$. When the same metal is illuminated by light of wavelength $2\lambda$, then the stopping potential becomes $V_0$. The threshold wavelength for photoelectric emission for the given metal is $\alpha\lambda$. The value of $\alpha$ is ______.

1. A.1
2. B.4✓
3. C.2
4. D.3

Correct answer: B

An electromagnetic wave travelling in $x$-direction is described by field equation $E_y=300\sin\omega\left(t-\frac{x}{c}\right)$. If the electron is restricted to move in $y$-direction only with speed of $1.5\times10^6$ m/s then ratio of maximum electric and magnetic forces acting on the electron is ______.

1. A.200✓
2. B.150
3. C.400
4. D.300

Correct answer: A

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi}$, then the energy of the electron is ______ eV.

1. A.$-1.51$
2. B.$-0.85$
3. C.$-0.38$✓
4. D.$-0.28$

Correct answer: C

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha\times10^{-6}$ J. The value of $\alpha$ is ______. (Take surface tension of liquid = 0.08 N/m)

1. A.10
2. B.7✓
3. C.8
4. D.11

Correct answer: B

In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is $\alpha\times10^{-2}$ degrees. The value of $\alpha$ is ______.

Correct answer: 36

A vessel contains 0.15 $\mathrm{m^3}$ of a gas at pressure 8 bar and temperature 140 °C with $c_p=3R$ and $c_v=2R$. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ______ kJ. (R is gas constant)

Correct answer: 120

1 $\mu$C charge moving with velocity $\vec v=\left(\hat i-2\hat j+3\hat k\right)$ m/s in the region of magnetic field $\vec B=\left(2\hat i+3\hat j-5\hat k\right)$ T. The magnitude of force acting on it is $\sqrt\alpha\times10^{-6}$ N. The value of $\alpha$ is ______.

Correct answer: 171

A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $\left(\frac{W}{A}+\frac{2}{\gamma}\frac{w}{A}\right)$, where, A is the cross sectional area of the wire. The value of $\gamma$ is ______.

Correct answer: 3

A tub is filled with water and a wooden cube 10 cm $\times$ 10 cm $\times$ 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is ______ gram. (Take water density as 1 $\mathrm{g/cm^3}$ and density of wood as 0.4 $\mathrm{g/cm^3}$)

Correct answer: 387

The mass of iron converted into $\mathrm{Fe_3O_4}$ by the action of 18 g of steam is : (Given : Molar mass of H, O and Fe are 1, 16 and 56 g $\mathrm{mol^{-1}}$ respectively) Assume iron is present in excess :

1. A.2.1 g
2. B.4.2 g
3. C.21 g
4. D.42 g✓

Correct answer: D

What is the energy (in J $\mathrm{atom^{-1}}$) required for the following process? $\mathrm{Li^{2+}(g)\rightarrow Li^{3+}(g)+e^-}$ (Take the ionization energy for the H atom in the ground state as $2.18\times10^{-18}$ J $\mathrm{atom^{-1}}$)

1. A.$8.72\times10^{-18}$
2. B.$1.962\times10^{-18}$
3. C.$1.962\times10^{-17}$✓
4. D.$6.54\times10^{-17}$

Correct answer: C

Given below are two statements : Statement (I) : The correct sequence of bond lengths in the following species is : $\mathrm{O_2^+<O_2<O_2^-<O_2^{2-}}$. Statement (II) : The correct sequence of number of unpaired electrons in the following species is : $\mathrm{O_2>O_2^+>O_2^->O_2^{2-}}$. 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: C

Consider the following data. (i) $\mathrm{2Al(s)+6HCl(aq)\rightarrow Al_2Cl_6(aq)+3H_2(g)}$ + 1200 kJ/mol (ii) $\mathrm{H_2(g)+Cl_2(g)\rightarrow 2HCl(g)}$ + 164 kJ/mol. (iii) $\mathrm{HCl(g)+aq\rightarrow HCl(aq)}$ + 83 kJ/mol. (iv) $\mathrm{Al_2Cl_6(s)+aq\rightarrow Al_2Cl_6(aq)}$ + 663 kJ/mol. The enthalpy of formation of anhydrous solid $\mathrm{Al_2Cl_6}$ is :

1. A.$-648$ kJ $\mathrm{mol^{-1}}$
2. B.$-1350$ kJ $\mathrm{mol^{-1}}$
3. C.$-2002$ kJ $\mathrm{mol^{-1}}$
4. D.$-1527$ kJ $\mathrm{mol^{-1}}$✓

Correct answer: D

19.5 g of fluoro acetic acid (molar mass = 78 g $\mathrm{mol^{-1}}$) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1°C. What is $K_a$ of fluoro acetic acid? (For water, $K_f$ = 1.86 K kg $\mathrm{mol^{-1}}$). Assume molarity and molality to have same values.

1. A.$10^{-6}$
2. B.$4\times10^{-4}$
3. C.$3\times10^{-5}$
4. D.$3\times10^{-3}$✓

Correct answer: D

The solubility product constants of $\mathrm{Ag_2CrO_4}$ and AgBr are $32x$ and $4y$ respectively at 298 K. The value of $\left(\frac{\text{molarity of }\mathrm{Ag_2CrO_4}}{\text{molarity of AgBr}}\right)$ can be expressed as :

1. A.$\frac{2\sqrt[3]{x}}{y}$
2. B.$2\sqrt{\frac{x}{y}}$
3. C.$\sqrt{\frac{x}{y}}$
4. D.$\frac{\sqrt[3]{x}}{\sqrt{y}}$✓

Correct answer: D

An electrochemical cell is constructed using half cells in the direction of spontaneous change : $\mathrm{Fe(OH)_2(s)+2e^-\rightarrow Fe(s)+2OH^-(aq)}$, $E^\theta=-0.88$ V and $\mathrm{AgBr(s)+e^-\rightarrow Ag(s)+Br^-(aq)}$, $E^\theta=+0.07$ V. Which of the following option is correct?

1. A.Overall reaction $\mathrm{Fe(s)+2OH^-(aq)+2AgBr(s)\rightleftharpoons Fe(OH)_2(s)+2Ag(s)+2Br^-(aq)}$✓
2. B.$E^\theta_{cell}=-0.95$ V
3. C.Fe is reduced in the electrochemical cell
4. D.$E^\theta_{cell}$ is an extensive property

Correct answer: A

$t_{100\%}$ is the time required for the 100% completion of the reaction while $t_{1/2}$ is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first order reactions respectively?

1. A.$t_{100\%}=(t_{1/2})^2$ and $t_{100\%}=(t_{1/2})^{-\infty}$
2. B.$t_{100\%}=2t_{1/2}$ and $t_{100\%}=(t_{1/2})^{\infty}$✓
3. C.$t_{100\%}=2t_{1/2}$ and $t_{100\%}=(2t_{1/2})^2$
4. D.$t_{100\%}=(t_{1/2})^{\infty}$ and $t_{100\%}=2t_{1/2}$

Correct answer: B

Given below are two statements : Statement (I) : The first ionisation enthalpy of the elements Na, Mg, Cl and Ar follows the order Na > Mg > Cl > Ar. Statement (II) : Among Ca, Al, Fe and B, the third ionisation enthalpy is very high for Ca. 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

Given below are two statements : Statement (I) : Oxidising power of halogens decreases in the order $\mathrm{F_2>Cl_2>Br_2>I_2}$, which is the basis of "Layer test". Statement (II) : "Layer test" to identify $\mathrm{Br_2}$ and $\mathrm{I_2}$ in aqueous solution involves the oxidation of bromide or iodide into $\mathrm{Br_2}$ or $\mathrm{I_2}$ respectively with $\mathrm{Cl_2}$, which is a type of displacement redox reaction. 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: A

Which of the following sets includes all the species that will change the orange colour of $\mathrm{K_2Cr_2O_7}$ in acidic medium?

1. A.$\mathrm{Fe^{2+}, Sn^{2+}, I^-, S^{2-}}$✓
2. B.$\mathrm{S^{2-}, Fe^{3+}, I^-, C_2O_4^{2-}}$
3. C.$\mathrm{Fe^{2+}, NO_2^-, SO_2, Sn^{4+}}$
4. D.$\mathrm{Fe^{3+}, SO_4^{2-}, S^{2-}, Sn^{4+}}$

Correct answer: A

Match List - I with List - II. List - I (Chromium (III) Complexes, en = ethylene diamine) : A. $\mathrm{[Cr(CN)_6]^{3-}}$ B. $\mathrm{[CrF_6]^{3-}}$ C. $\mathrm{[Cr(H_2O)_6]^{3+}}$ D. $\mathrm{[Cr(en)_3]^{3+}}$. List - II ($\Delta_0$ in $\mathrm{cm^{-1}}$) : I. 15,060 II. 17,400 III. 22,300 IV. 26,600. Choose the correct answer from the options given below :

1. A.A-I, B-II, C-III, D-IV
2. B.A-II, B-III, C-IV, D-I
3. C.A-III, B-IV, C-I, D-II
4. D.A-IV, B-I, C-II, D-III✓

Correct answer: D

Given below are two statements : Statement (I) : 1,2,3-Trihydroxypropane can be separated from water by simple distillation. Statement (II) : An azeotropic mixture cannot be separated by fractional distillation. 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

Given below are two statements : Statement (I) : Benzyl chloride reacts faster in $S_N1$ mechanism than ethyl chloride. Statement (II) : Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance. 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: A

In IUPAC nomenclature, the correct order of decreasing priority of functional group is :

1. A.$\mathrm{-CONH_2}$, $\mathrm{>C=O}$, $\mathrm{-CHO}$, $\mathrm{-NH_2}$, $\mathrm{-C\equiv C-}$
2. B.$\mathrm{-CONH_2}$, $\mathrm{-COOCH_3}$, $\mathrm{-CHO}$, $\mathrm{-NH_2}$, $\mathrm{-OH}$
3. C.$\mathrm{-CONH_2}$, $\mathrm{-CHO}$, $\mathrm{>C=O}$, $\mathrm{-NH_2}$, $\mathrm{-C\equiv C-}$✓
4. D.$\mathrm{-CONH_2}$, $\mathrm{-CHO}$, $\mathrm{-CN}$, $\mathrm{-NH_2}$, $\mathrm{-C\equiv C-}$

Correct answer: C

For the given molecule, "x", the preferred site for the attack of the electrophile is :

1. A.Predominantly at "r"
2. B."r" and "u"
3. C."p" and "s"
4. D.Predominantly at "u"✓

Correct answer: D

Match List - I with List - II. List - I (Mixture of Compounds) : A. Diethyl amine + Ethyl amine B. Acetaldehyde + Acetone C. Ethanol + Phenol D. Benzoic acid + Cinnamic acid. List - II (Reagent used to distinguish) : I. Bromine water II. $\mathrm{CHCl_3}$ + KOH, $\Delta$ III. Neutral $\mathrm{FeCl_3}$ IV. Ammonical silver nitrate. Choose the correct answer from the options given below :

1. A.A-IV, B-II, C-I, D-III
2. B.A-IV, B-II, C-III, D-I
3. C.A-II, B-IV, C-I, D-III
4. D.A-II, B-IV, C-III, D-I✓

Correct answer: D

Consider the three aromatic molecules (P, Q and R) whose structures have been given below. P : N,N-dimethylaniline; Q : N,N-dimethylaniline carrying one methyl group ortho to the $\mathrm{NMe_2}$ group; R : N,N-dimethylaniline carrying methyl groups at both ortho positions. The correct order regarding the reactivity of these compounds with $\mathrm{Ph-\overset{+}{N}\equiv N\,Cl^-}$ under optimum but slightly acidic medium is :

1. A.P > Q > R✓
2. B.R > P > Q
3. C.R > Q > P
4. D.P > R > Q

Correct answer: A

Match List - I with List - II. List - I (Vitamin) : A. Vitamin $\mathrm{B_1}$ B. Vitamin $\mathrm{B_2}$ C. Vitamin $\mathrm{B_6}$ D. Vitamin C. List - II (Name) : I. Pyridoxine II. Ascorbic acid III. Thiamine IV. Riboflavin. Choose the correct answer from the options given below :

1. A.A-II, B-I, C-III, D-IV
2. B.A-IV, B-III, C-II, D-I
3. C.A-III, B-IV, C-I, D-II✓
4. D.A-I, B-III, C-II, D-IV

Correct answer: C

A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with $\mathrm{K_2CrO_4}$ to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. $\mathrm{HNO_3}$ and ammonium molybdate, it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively,

1. A.$\mathrm{Ca^{2+}}$ and $\mathrm{SO_4^{2-}}$
2. B.$\mathrm{Ba^{2+}}$ and $\mathrm{PO_4^{3-}}$✓
3. C.$\mathrm{Mn^{2+}}$ and $\mathrm{PO_4^{3-}}$
4. D.$\mathrm{Ba^{2+}}$ and $\mathrm{SO_4^{2-}}$

Correct answer: B

5.33 g of $\mathrm{CrCl_3\cdot6H_2O}$, which is a 1 : 3 electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with $\mathrm{AgNO_3}$ results in 8.61 g of AgCl. The ratio of moles of complex reacted and moles of AgCl formed is ______ $\times10^{-2}$. (Nearest integer) [Molar mass in g $\mathrm{mol^{-1}}$ Cr : 52, Ag : 108, Cl : 35.5, H : 1, O : 16]

Correct answer: 33

Consider the isomers of hydrocarbon with molecular formula $\mathrm{C_5H_{10}}$. These isomers do not decolourise $\mathrm{KMnO_4}$ solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is ______.

Correct answer: 14

One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is ______.

Correct answer: 17

For reaction A $\rightarrow$ P, rate constant $k=1.5\times10^3\ \mathrm{s^{-1}}$ at 27°C. If activation energy for the above reaction is 60 kJ $\mathrm{mol^{-1}}$, then the temperature (in °C) at which rate constant, $k=4.5\times10^3\ \mathrm{s^{-1}}$ is ______. (Nearest integer) Given : log 2 = 0.30, log 3 = 0.48, R = 8.3 J $\mathrm{K^{-1}\,mol^{-1}}$, ln 10 = 2.3

Correct answer: 41

At the transition temperature T, A $\rightleftharpoons$ B and $\Delta G^0=105-35\log T$ where A and B are two states of substance X. The transition temperature in °C when pressure is 1 atm is ______. (Nearest integer)

Correct answer: 727