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

Let $\alpha,\beta$ be the roots of the equation $x^2-3x+r=0$, and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2+3x+r=0$. If the roots of the equation $x^2+6x=m$ are $2\alpha+\beta+2r$ and $\alpha-2\beta-\frac{r}{2}$, then $m$ is equal to :

1. A.$-135$
2. B.$-567$
3. C.135
4. D.567✓

Correct answer: D

Let the circles $C_1 : |z|=r$ and $C_2 : |z-3-4i|=5$, $z\in\mathbb{C}$, be such that $C_2$ lies within $C_1$. If $z_1$ moves on $C_1$, $z_2$ moves on $C_2$ and $\min|z_1-z_2|=2$, then $\max|z_1-z_2|$ is equal to :

1. A.12
2. B.17
3. C.22✓
4. D.24

Correct answer: C

If the system of equations $x+5y+6z=4$, $2x+3y+4z=7$, $x+6y+az=b$ has infinitely many solutions, then the point $(a,b)$ lies on the line

1. A.$y-x=3$
2. B.$x-y=3$✓
3. C.$x+y=11$
4. D.$x+y=12$

Correct answer: B

Let $a_1, a_2, a_3, \dots$ be an A.P. and $g_1=a_1, g_2, g_3, \dots$ be an increasing G.P. If $a_1=a_2+g_2=1$ and $a_3+g_3=4$, then $a_{10}+g_5$ is equal to :

1. A.81
2. B.76
3. C.62
4. D.55✓

Correct answer: D

The sum $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots$ up to 8 terms, is :

1. A.70
2. B.71✓
3. C.72
4. D.73

Correct answer: B

If for $3\le r\le30$, $\left({}^{30}C_{30-r}\right)+3\left({}^{30}C_{31-r}\right)+3\left({}^{30}C_{32-r}\right)+\left({}^{30}C_{33-r}\right)={}^{m}C_r$, then $m$ equals :

1. A.31
2. B.32
3. C.33✓
4. D.34

Correct answer: C

Let $p_n$ denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If $p_{n+1}-p_n=66$, then the sum of all distinct prime divisors of $n$ is :

1. A.7
2. B.8
3. C.5✓
4. D.6

Correct answer: C

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $\frac{m}{n}$, $\gcd(m,n)=1$, then $m+n$ is equal to :

1. A.53
2. B.55
3. C.107✓
4. D.105

Correct answer: C

The mean and variance of n observations are 8 and 16, respectively. If the sum of the first $(n-1)$ observations is 48 and the sum of squares of the first $(n-1)$ observations is 496, then the value of n is :

1. A.21
2. B.16
3. C.13
4. D.7✓

Correct answer: D

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x+(k-1)y+3=0$ and $2x+k^2y-4=0$. If the line $x-y+2=0$ intersects the circle at the points A and B, then $(AB)^2$ is equal to :

1. A.10
2. B.27
3. C.18✓
4. D.34

Correct answer: C

Let O be the origin, and P and Q be two points on the rectangular hyperbola $xy=12$ such that the mid point of the line segment PQ is $\left(\frac12,-\frac12\right)$. Then the area of the triangle OPQ equals :

1. A.$\frac32$
2. B.$\frac52$
3. C.$\frac72$✓
4. D.$\frac92$

Correct answer: C

Let the parabola $y=x^2+px+q$ passing through the point $(1,-1)$ be such that the distance between its vertex and the $x$-axis is minimum. Then the value of $p^2+q^2$ is :

1. A.2
2. B.4✓
3. C.5
4. D.8

Correct answer: B

Let $P=\{\theta\in[0,4\pi] : \tan^2\theta\ne1\}$ and $S=\{a\in\mathbb{Z} : 2(\cos^8\theta-\sin^8\theta)\sec2\theta=a^2, \theta\in P\}$. Then $n(S)$ is :

1. A.0✓
2. B.1
3. C.2
4. D.3

Correct answer: A

Let the vectors $\vec a=-\hat i+\hat j+3\hat k$ and $\vec b=\hat i+3\hat j+\hat k$. For some $\lambda,\mu\in\mathbb{R}$, let $\vec c=\lambda\vec a+\mu\vec b$. If $\vec c\cdot\left(3\hat i-6\hat j+2\hat k\right)=10$ and $\vec c\cdot\left(\hat i+\hat j+\hat k\right)=-2$, then $|\vec c|^2$ is equal to :

1. A.8
2. B.12✓
3. C.14
4. D.15

Correct answer: B

Let the point A be the foot of perpendicular drawn from the point $P(a,b,0)$ on the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-\alpha}{3}$. If the midpoint of the line segment PA is $\left(0,\frac34,\frac{-1}{4}\right)$, then the value of $a^2+b^2+\alpha^2$ is equal to :

1. A.1✓
2. B.2
3. C.6
4. D.9

Correct answer: A

Two adjacent sides of a parallelogram PQRS are given by $\vec{PQ}=\hat j+\hat k$ and $\vec{PS}=\hat i-\hat j$. If the side PS is rotated about the point P by an acute angle $\alpha$ in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then $\sin^2\left(\frac{5\alpha}{2}\right)-\sin^2\left(\frac{\alpha}{2}\right)$ is equal to :

1. A.$\frac12$
2. B.$\frac{\sqrt3}{2}$✓
3. C.$\frac{\sqrt3}{4}$
4. D.$\frac{2\sqrt3}{5}$

Correct answer: B

The value of $\int_0^{20\pi}\left(\sin^4x+\cos^4x\right)dx$ is equal to :

1. A.$\frac{15\pi}{2}$
2. B.$25\pi$
3. C.$15\pi$✓
4. D.$\frac{25\pi}{2}$

Correct answer: C

Let $f(x)$ be a polynomial of degree 5, and have extrema at $x=1$ and $x=-1$. If $\lim_{x\to0}\left(\frac{f(x)}{x^3}\right)=-5$, then $f(2)-f(-2)$ is equal to :

1. A.0
2. B.50
3. C.92
4. D.112✓

Correct answer: D

Let $f(x)=\int\left(\frac{16x+24}{x^2+2x-15}\right)dx$. If $f(4)=14\log_e(3)$ and $f(7)=\log_e\left(2^\alpha\cdot3^\beta\right)$, $\alpha,\beta\in\mathbb{N}$, then $\alpha+\beta$ is equal to :

1. A.31
2. B.37
3. C.39✓
4. D.41

Correct answer: C

Let $x=x(y)$ be the solution of the differential equation $2y^2\frac{dx}{dy}-2xy+x^2=0$, $y>1$, $x(e)=e$. Then $x(e^2)$ is equal to :

1. A.$\frac32e^2$
2. B.$\frac23e^2$✓
3. C.$e^2$
4. D.$2e^2$

Correct answer: B

Let $A=\{2,3,4,5,6\}$. Let R be a relation on the set $A\times A$ given by $(x,y)R(z,w)$ if and only if $x$ divides $z$ and $y\le w$. Then the number of elements in R is ______.

Correct answer: 120

Consider the matrices $A=\begin{bmatrix}2&-2\\4&-2\end{bmatrix}$ and $B=\begin{bmatrix}3&9\\1&3\end{bmatrix}$. If matrices P and Q are such that $PA=B$ and $AQ=B$, then the absolute value of the sum of the diagonal elements of $2(P+Q)$ is ______.

Correct answer: 34

Let A be the point $(3,0)$ and circles with variable diameter AB touch the circle $x^2+y^2=36$ internally. Let the curve C be the locus of the point B. If the eccentricity of C is e, then $72e^2$ is equal to ______.

Correct answer: 18

If the area of the region bounded by $16x^2-9y^2=144$ and $8x-3y=24$ is A, then $3\left(A+6\log_e(3)\right)$ is equal to ______.

Correct answer: 24

The number of points in the interval $[2,4]$, at which the function $f(x)=\left[x^2-x-\frac12\right]$, where $[\cdot]$ denotes the greatest integer function, is discontinuous, is ______.

Correct answer: 10

Dimensions of universal gravitational constant ($G$) in terms of Planck's constant ($h$), distance ($L$), mass ($M$) and time ($T$) are ______.

1. A.$[hTLM^{-2}]$
2. B.$[hT^{-1}LM^{-2}]$✓
3. C.$[hTL^2M^{-2}]$
4. D.$[h^{-1}T^{-1}LM^{-2}]$

Correct answer: B

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is ______. (Take $g=10\ \mathrm{m/s^2}$)

1. A.0.1✓
2. B.0.5
3. C.0.7
4. D.0.3

Correct answer: A

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is ______ m. (Take $g=10\ \mathrm{m/s^2}$)

1. A.3.33
2. B.3.12
3. C.2.22✓
4. D.1.42

Correct answer: C

A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4\hat j$ N/C and $4\times10^{-3}\hat k$ T experiences a force of $\left(4\hat i+2\hat j\right)\times10^{-10}$ N. The velocity of the particle at that instant is ______ m/s.

1. A.$50\hat i+100\hat j$✓
2. B.$100\hat i+50\hat j$
3. C.$-50\hat i+100\hat j$
4. D.$50\hat i-100\hat j$

Correct answer: A

If $X$ and $Y$ are the inputs, the given circuit works as ______.

1. A.OR gate
2. B.AND gate
3. C.NAND gate
4. D.NOR gate✓

Correct answer: D

If a body of mass 1 kg falls on the earth from infinity, it attains velocity ($v$) and kinetic energy ($k$) on reaching the surface of earth. The values of $v$ and $k$ respectively are ______. (Take radius of earth to be 6400 km and $g=9.8\ \mathrm{m/s^2}$)

1. A.11.2 km/s; $6.27\times10^7$ J✓
2. B.11.2 km/s; $12.54\times10^7$ J
3. C.8.8 km/s; $6.27\times10^7$ J
4. D.8.8 km/s; $12.54\times10^7$ J

Correct answer: A

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and $50^{th}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is ______ mm.

1. A.5.045✓
2. B.5.055
3. C.5.450
4. D.5.550

Correct answer: A

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha\pi\times10^{-4}$ J. The value of $\alpha$ is ______. (Take $\pi=3.14$)

1. A.0.86
2. B.0.64
3. C.1.92✓
4. D.7.68

Correct answer: C

A mixture of carbon dioxide and oxygen has volume 8310 $\mathrm{cm^3}$, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ______. (Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol.K]

1. A.0.15 and 0.18
2. B.0.25 and 0.08
3. C.0.21 and 0.12✓
4. D.0.13 and 0.20

Correct answer: C

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 $\mathrm{kg/m^3}$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take $g=10\ \mathrm{m/s^2}$)

1. A.0.88
2. B.8.8✓
3. C.88.8
4. D.0.088

Correct answer: B

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is ______ N. (Take $g=10\ \mathrm{m/s^2}$)

1. A.1980
2. B.2020✓
3. C.2000
4. D.1000

Correct answer: B

An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec B=2\times10^{-7}\hat j$ T is associated with this wave. The value of corresponding electric field $\vec E$ at this point is ______ V/m.

1. A.$60\hat k$
2. B.$-60\hat k$✓
3. C.$30\hat k$
4. D.$-600\hat k$

Correct answer: B

Two resistors of 200 $\Omega$ and 400 $\Omega$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 $\Omega$ resistance. The potential drop across the bulb is ______ V.

1. A.25
2. B.50✓
3. C.66.6
4. D.100

Correct answer: B

Two metal plates (A, B) are kept horizontally with separation of $\left(\frac{12}{\pi}\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 $\mathrm{g/cm^3}$) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials $V_A$ and $V_B$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are ______. (Neglect the air resistance to the droplets and take $g=10\ \mathrm{m/s^2}$)

1. A.100 V and 580 V✓
2. B.580 V and 100 V
3. C.60 V and 400 V
4. D.0 V and $-200$ V

Correct answer: A

Two point charges 8 $\mu$C and $-2$ $\mu$C are located at $x=2$ cm and $x=4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ______.

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

Correct answer: C

One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of prism is 1.6. The minimum value of $n_2$ required for total internal reflection from painted face is ______.

1. A.$3\sqrt3/1.6$
2. B.$\sqrt3$
3. C.$3.2/\sqrt3$
4. D.$4\sqrt3/5$✓

Correct answer: D

The figure given below shows an LCR series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference ($\phi$) between the current and source voltage is 30° and phase difference is 60° when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1-L_2)$ is ______ H.

1. A.$\frac92$
2. B.$\frac29$✓
3. C.$\frac13$
4. D.3

Correct answer: B

A circular current loop of radius $R$ is placed inside square loop of side length $L$ ($L\gg R$) such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between circular loop and square loop is ______.

1. A.$2\sqrt2\frac{\mu_0L^2}{R}$
2. B.$\sqrt2\frac{\mu_0L^2}{R}$
3. C.$\sqrt2\frac{\mu_0R^2}{L}$
4. D.$2\sqrt2\frac{\mu_0R^2}{L}$✓

Correct answer: D

The binding energy per nucleon of ${}^{209}_{83}Bi$ is ______ MeV. [Take $m({}^{209}_{83}Bi)=208.980388$ u, $m_p=1.007825$ u, $m_n=1.008665$ u, 1 u = 931 MeV/$c^2$]

1. A.7.48
2. B.7.84✓
3. C.8.79
4. D.6.94

Correct answer: B

The equation of motion of a particle is given by $x=a\sin\left(50t+\frac{\pi}{3}\right)$ cm. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are ______.

1. A.$\frac{\pi}{300}$ s, $\frac{\pi}{75}$ s✓
2. B.$\frac{\pi}{75}$ s, $\frac{\pi}{300}$ s
3. C.$\frac{\pi}{300}$ s, $\frac{\pi}{25}$ s
4. D.$\frac{\pi}{50}$ s, $\frac{\pi}{100}$ s

Correct answer: A

In a Young's double slit experiment, the intensity at some point on the screen is found to be $\frac34$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $\frac{\lambda}{x}$ where $\lambda$ is wavelength of the incident light. The value of $x$ is ______.

Correct answer: 6

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom ______.

Correct answer: 32

5 moles of unknown gas is heated at constant volume from 10 °C to 20 °C. The molar specific heat of this gas at constant pressure $c_p$ = 8 cal/mol.°C and R = 8.36 J/mol.°C. The change in the internal energy of the gas is ______ calorie.

Correct answer: 300

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is $\frac{\alpha}{10}$. The value of $\alpha$ is ______.

Correct answer: 20

Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius $R$ about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of $R$ is given as $\sqrt{\frac{\alpha}{2}}$. The value of $\alpha$ is ______.

Correct answer: 60

The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g) of $\mathrm{CO_2(g)}$ formed when 3.38 g of this hydrocarbon is completely burnt in oxygen is : (Given : Molar mass in g $\mathrm{mol^{-1}}$ C : 12, H : 1, O : 16)

1. A.5.68
2. B.11.44✓
3. C.22.74
4. D.17.05

Correct answer: B

The first and second ionization constants of a weak dibasic acid $\mathrm{H_2A}$ are $8.1\times10^{-8}$ and $1.0\times10^{-13}$ respectively. 0.1 mol of $\mathrm{H_2A}$ was dissolved in 1L of 0.1 M HCl solution. The concentration of $\mathrm{HA^-}$ in the resultant solution is :

1. A.0.1 M
2. B.$9.53\times10^{-6}$ M
3. C.$8.1\times10^{-8}$ M✓
4. D.$1.0\times10^{-13}$ M

Correct answer: C

$\mathrm{SF_4}$ is isostructural with : A. $\mathrm{BrF_4^-}$ B. $\mathrm{CH_4}$ C. $\mathrm{IF_4^+}$ D. $\mathrm{XeF_4}$ E. $\mathrm{XeO_2F_2}$. Choose the correct answer from the options given below :

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

Correct answer: B

Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is 10 J and 18 J respectively. Now gas is brought back to state 'X' by another process during which 6 J of heat is evolved. In the reverse process of 'Y' to 'X',

1. A.18 J of the work is done by the gas 'A'.
2. B.2 J of the work is done by the gas 'A'.
3. C.12 J of the work is done on the gas 'A' by the surrounding.
4. D.14 J of the work is done on the gas 'A' by the surrounding.✓

Correct answer: D

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g $\mathrm{mol^{-1}}$) in 0.5 L of water at 300 K. Its osmotic pressure is $x$ bar. Solution B is made by dissolving 2 g of same protein in 1 L of water at 300 K. Osmotic pressure of solution B is $y$ bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is $z$ bar. $x$, $y$ and $z$ respectively are : (R = 0.083 L bar $\mathrm{mol^{-1}K^{-1}}$)

1. A.$9.96\times10^{-4}$; $9.96\times10^{-4}$; $9.96\times10^{-4}$✓
2. B.$9.96\times10^{-4}$; $9.96\times10^{-4}$; $19.92\times10^{-4}$
3. C.$4.98\times10^{-4}$; $4.98\times10^{-4}$; $9.96\times10^{-4}$
4. D.$4.98\times10^{-4}$; $4.98\times10^{-4}$; $4.98\times10^{-4}$

Correct answer: A

At 25°C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are : Given : $K_a=5\times10^{-4}$, $pK_a=3.3$, $\alpha\ll1$

1. A.(a) 0.7, (b) 2.0
2. B.(a) 2.0, (b) 3.3✓
3. C.(a) 1.1, (b) 2.2
4. D.(a) 3.0, (b) 2.2

Correct answer: B

Consider the reaction aX $\rightarrow$ bY, for which the rate constant at 30°C is $1\times10^{-3}\ \mathrm{mol^{-1}\,L\,s^{-1}}$. Which of the following statements are true? A. When concentration of 'X' is increased to four times, the rate of reaction becomes 16 times. B. The reaction is a second order reaction. C. The half-life period is independent of the concentration of X. D. Decomposition of $\mathrm{N_2O_5}$ is an example of the above reaction. E. A plot of $\ln\frac{[R_0]}{[R]}$ versus time that is a straight line through the origin with positive slope is valid for the above reaction. Choose the correct answer from the options given below :

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

Correct answer: A

The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is :

1. A.$\mathrm{Na_2O, K_2O, Al_2O_3}$ and $\mathrm{As_2O_3}$
2. B.$\mathrm{Al_2O_3, As_2O_3}$, CO and NO
3. C.$\mathrm{K_2O, Cl_2O_7, As_2O_3}$ and NO✓
4. D.$\mathrm{Na_2O, N_2O, Al_2O_3}$ and CO

Correct answer: C

Given below are two statements : Statement I : The second ionization enthalpy of B, Al and Ga is in the order of B > Al > Ga. Statement II : The correct order in terms of first ionization enthalpy is Si < Ge < Pb < Sn. 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: B

Given below are two statements : Statement I : Among Zn, Mn, Sc and Cu, the energy required to remove the third valence electron is highest for Zn and lowest for Sc. Statement II : The correct order of the following complexes in terms of CFSE is $\mathrm{[Co(H_2O)_6]^{2+}<[Co(H_2O)_6]^{3+}<[Co(en)_3]^{3+}}$. 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 complexes will show coordination isomerism? A. $\mathrm{[Ag(NH_3)_2][Ag(CN)_2]}$ B. $\mathrm{[Co(NH_3)_6][Cr(CN)_6]}$ C. $\mathrm{[Co(NH_3)_6][Co(CN)_6]}$ D. $\mathrm{[Fe(NH_3)_6][Co(CN)_6]}$ E. $\mathrm{[Co(NH_3)_6][Fe(CN)_6]}$. Choose the correct answer from the options given below :

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

Correct answer: B

Complete combustion of X g of an organic compound gave 0.25 g of $\mathrm{CO_2}$ and 0.12 g of $\mathrm{H_2O}$. If the % of carbon is 25% and of hydrogen is 4.89%, then X = ______ $\times10^{-3}$ g. (Nearest integer) (Molar mass of C, H and O are 12, 1 and 16 g $\mathrm{mol^{-1}}$ respectively.)

1. A.273✓
2. B.27
3. C.2730
4. D.227

Correct answer: A

Given below are two statements : Statement I : In $\mathrm{O_2N-C_6H_4-\overset{+}{C}H-C_6H_4-OCH_3}$ (both substituents para), the carbocation is stabilised by +R effect of $-\mathrm{OCH_3}$ group. Statement II : In $\mathrm{O_2N-C_6H_4-\overset{-}{C}H-C_6H_4-OCH_3}$ (both substituents para), the carbanion is stabilised by $-$R effect of $-\mathrm{NO_2}$ group. 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

The compound (X) on (i) on heating in the presence of anhydrous $\mathrm{AlCl_3}$ and HCl gas gives 2,4-dimethyl pentane (ii) aromatization gives toulene and (iii) cyclisation gives methyl cyclohexane. The correct name of compound (X) is :

1. A.Hept-2-ene
2. B.Hept-1,3,5-triene
3. C.Heptane✓
4. D.Hept-2,4,6-triene

Correct answer: C

Correct statements regarding alkyl halides (R$-$X) among the following are : A. Alcohol being less polar solvent as compared to water, alcoholic KOH favours elimination reaction with R$-$X. B. Order of reactivity towards $S_N1$ mechanism is $\mathrm{C_6H_5-CH_2-Cl>C_6H_5-CHCl-C_6H_5}$. C. Non substituted aryl halides exhibit properties similar to alkyl halides. D. Vinyl chloride is an example of haloalkene and allyl chloride is an example of haloalkyne. E. R$-$Cl can be prepared by reacting R$-$OH with $\mathrm{SOCl_2}$ but Ar$-$Cl cannot be prepared by reacting Ar$-$OH with $\mathrm{SOCl_2}$. Choose the correct answer from the options given below :

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

Correct answer: C

An organic compound "$x$" where molar ratio of C, O and H are equal, on treatment with 50% KOH under reflux followed by acidification produced "$y$". The most likely structure of "$y$" is : [Molar mass of $x$ is 58 g $\mathrm{mol^{-1}}$]

1. A.$\mathrm{CH_2=CH-COOH}$
2. B.$\mathrm{CH_3-CH=CH-CH=O}$
3. C.$\mathrm{HOCH_2-COOH}$ (drawn as O=C(OH)-CH$_2$-OH)✓
4. D.$\mathrm{CH_3-COOH}$

Correct answer: C

A molecule (X) with following structure under mild acidic condition is hydrolysed to produce (Y) and (Z). Identify the correct statements about (Y) and (Z). [X : $\mathrm{CH_3-CH=CH-O-C(CH_3)=CH_2}$] A. Both (Y) and (Z) have same molar mass. B. (Y) and (Z) can be distinguished from each other by $\mathrm{NaHCO_3}$. C. (Y) and (Z) react with HCN with same rates. D. (Y) and (Z) undergo addition reaction with 2,4-DNP. Choose the correct answer from the options given below :

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

Correct answer: D

Identify compounds A and E in the following reaction sequence. 1-Ethyl-4-nitrobenzene $\xrightarrow{\mathrm{Br_2/AlBr_3}}$ A $\xrightarrow{\mathrm{Sn/HCl}}$ B $\xrightarrow{\mathrm{NaNO_2/HCl,\ 273\text{-}278\ K}}$ C $\xrightarrow{\mathrm{C_2H_5OH}}$ D $\xrightarrow{\mathrm{(i)\ KMnO_4/KOH;\ (ii)\ H_3O^+}}$ E

1. A.A = 2-bromo-4-ethyl-1-nitrobenzene (Br ortho to NO2); E = 3-bromobenzoic acid
2. B.A = 2-bromo-1-ethyl-4-nitrobenzene (Br ortho to C2H5); E = 2-bromobenzoic acid✓
3. C.A = 1-(2-bromoethyl)-4-nitrobenzene; E = benzoic acid
4. D.A = 2-bromo-1-ethyl-4-nitrobenzene (Br ortho to C2H5); E = 2-bromo-4-hydroxybenzoic acid

Correct answer: B

Identify the correct pair having amino acid (A) and the hormone (B) that is iodinated derivative of the amino acid (A). (T and Y represent one letter code for amino acids)

1. A.(A) T, (B) Insulin
2. B.(A) T, (B) Thyroxine
3. C.(A) Y, (B) Thyroxine✓
4. D.(A) Y, (B) Insulin

Correct answer: C

Among $\mathrm{Fe^{2+}, Fe^{3+}, Cr^{2+}}$ and $\mathrm{Zn^{2+}}$, the ion that shows positive borax bead test and with highest ionisation enthalpy is :

1. A.$\mathrm{Fe^{2+}}$
2. B.$\mathrm{Zn^{2+}}$
3. C.$\mathrm{Cr^{2+}}$
4. D.$\mathrm{Fe^{3+}}$✓

Correct answer: D

The surface of sodium metal is irradiated with radiation of wavelength $x$ nm. The kinetic energy of ejected electrons is $2.8\times10^{-20}$ J. The work function of sodium is 2.3 eV. The value of $x$ is ______ $\times10^2$ nm. (Nearest integer) (Given : $h=6.6\times10^{-34}$ J s ; 1 eV = $1.6\times10^{-19}$ J; $c=3.0\times10^8\ \mathrm{m\,s^{-1}}$)

Correct answer: 5

Consider the following gas phase reaction being carried out in a closed vessel at 25°C. $\mathrm{2A(g)\rightarrow4B(g)+C(g)}$. Total pressure of the system (mm Hg): at time 30 min = 300; at time $\infty$ = 600. The pressure of C(g) at 30 minutes time interval would be ______ mm Hg. (nearest integer)

Correct answer: 20

Consider the following two half-cell reactions along with the standard reduction potential given : $\mathrm{CO_2+6H^++6e^-\rightarrow CH_3OH+H_2O}$, $E^o_{red}=0.02$ V; $\mathrm{\frac12O_2+2H^++2e^-\rightarrow H_2O}$, $E^o_{red}=1.23$ V. A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\mathrm{CH_3OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, $\Delta V$ = ______ $\mathrm{m^3}$. (nearest integer) Given : F = 96500 C $\mathrm{mol^{-1}}$

Correct answer: 560

Number of paramagnetic ions among the following d- and f-block metal ions is ______. $\mathrm{Mn^{2+}, Cu^{2+}, Zn^{2+}, Yb^{2+}, Sc^{3+}, La^{3+}, Gd^{3+}, Lu^{3+}, Ti^{4+}, Ce^{4+}}$ (Atomic number of Mn = 25, Cu = 29, Zn = 30, Yb = 70, Sc = 21, La = 57, Gd = 64, Lu = 71, Ti = 22, Ce = 58)

Correct answer: 3

Consider the following reactions sequence : 4-nitrotoluene (p-$\mathrm{CH_3C_6H_4NO_2}$) $\xrightarrow{\mathrm{(i)\ Sn/HCl;\ OH^-\ (ii)\ (CH_3CO)_2O\ (iii)\ Br_2/AlBr_3\ (iv)\ H_3O^+}}$ Major Product (P). When the product (P) is subjected to Carius analysis using $\mathrm{AgNO_3}$, 1.0 g of the product (P) will produce ______ g of the precipitate of AgBr. (Nearest Integer) (Given : molar mass in g $\mathrm{mol^{-1}}$ C : 12, H : 1, O : 16, N : 14, Br : 80, Ag : 108)

Correct answer: 1