JEE Main 2026 — 28 Jan Shift 1 (9:00 AM - 12:00 PM) (Previous Year

Let $S=\{x^3+ax^2+bx+c: a, b, c\in\mathbb{N}\text{ and }a, b, c\le20\}$ be a set of polynomials. Then the number of polynomials in S, which are divisible by $x^2+2$, is

1. A.120
2. B.10✓
3. C.20
4. D.6

Correct answer: B

If $g(x)=3x^2+2x-3$, $f(0)=-3$ and $4g(f(x))=3x^2-32x+72$, then $f(g(2))$ is equal to:

1. A.$-\frac{25}{6}$
2. B.$-\frac{7}{2}$
3. C.$\frac{25}{6}$
4. D.$\frac{7}{2}$✓

Correct answer: D

If $\alpha, \beta$, where $\alpha<\beta$, are the roots of the equation $\lambda x^2-(\lambda+3)x+3=0$ such that $\frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}$, then the sum of all possible values of $\lambda$ is

1. A.8
2. B.6✓
3. C.4
4. D.2

Correct answer: B

Let z be a complex number such that $|z-6|=5$ and $|z+2-6i|=5$. Then the value of $z^3+3z^2-15z+141$ is equal to

1. A.37
2. B.42
3. C.50✓
4. D.61

Correct answer: C

Let A, B and C be three $2\times2$ matrices with real entries such that $B=(I+A)^{-1}$ and $A+C=I$. If $BC=\begin{bmatrix}1 & -5\\ -1 & 2\end{bmatrix}$ and $CB\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}12\\ -6\end{bmatrix}$, then $x_1+x_2$ is

1. A.4
2. B.0✓
3. C.-2
4. D.2

Correct answer: B

The common difference of the A.P.: $a_1, a_2, \ldots, a_m$ is 13 more than the common difference of the A.P.: $b_1, b_2, \ldots, b_n$. If $b_{31}=-277$, $b_{43}=-385$ and $a_{78}=327$, then $a_1$ is equal to

1. A.16
2. B.19✓
3. C.24
4. D.21

Correct answer: B

A bag contains 10 balls out of which k are red and $(10-k)$ are black, where $0\le k\le10$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:

1. A.$\frac{7}{11}$
2. B.$\frac{7}{55}$
3. C.$\frac{14}{55}$✓
4. D.$\frac{7}{110}$

Correct answer: C

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is

1. A.4
2. B.6
3. C.5✓
4. D.7

Correct answer: C

Let $S=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

1. A.$21x=4y$✓
2. B.$45x=7y$
3. C.$56x=9y$
4. D.$29x=5y$

Correct answer: A

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $x+2\sqrt{2}y=4$. If the co-ordinates of the vertex A are $(\alpha, \beta)$, then the greatest integer less than or equal to $|\alpha+\sqrt{2}\beta|$ is

1. A.2
2. B.4✓
3. C.5
4. D.3

Correct answer: B

Let $y=x$ be the equation of a chord of the circle $C_1$ (in the closed half-plane $x\ge0$) of diameter 10 passing through the origin. Let $C_2$ be another circle described on the given chord as its diameter. If the equation of the chord of the circle $C_2$, which passes through the point (2, 3) and is farthest from the center of $C_2$, is $x+ay+b=0$, then $a-b$ is equal to

1. A.-2✓
2. B.10
3. C.-6
4. D.6

Correct answer: A

If $\frac{\tan(A-B)}{\tan A}+\frac{\sin^2C}{\sin^2A}=1$, $A, B, C\in\left(0, \frac{\pi}{2}\right)$, then

1. A.tan A, tan B, tan C are in G.P.
2. B.tan A, tan C, tan B are in G.P.✓
3. C.tan A, tan B, tan C are in A.P.
4. D.tan A, tan C, tan B are in A.P.

Correct answer: B

If the distances of the point $(1, 2, a)$ from the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$ along the lines $L_1: \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$ and $L_2: \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$ are equal, then $a+b+c$ is equal to

1. A.5
2. B.6
3. C.4
4. D.7✓

Correct answer: D

For three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfying $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2=9$ and $|2\vec{a}+k\vec{b}+k\vec{c}|=3$, the positive value of k is

1. A.3
2. B.6
3. C.4
4. D.5✓

Correct answer: D

The value of $\sum_{k=1}^{\infty}(-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)$ is

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

Correct answer: A

Let f be a polynomial function such that $f(x^2+1)=x^4+5x^2+2$, for all $x\in\mathbb{R}$. Then $\int_0^3f(x)dx$ is equal to

1. A.$\frac{5}{3}$
2. B.$\frac{27}{2}$
3. C.$\frac{33}{2}$✓
4. D.$\frac{41}{3}$

Correct answer: C

The area of the region $R=\{(x, y): xy\le8, 1\le y\le x^2, x\ge0\}$ is

1. A.$\frac{2}{3}(20\log_e(2)+9)$
2. B.$\frac{1}{3}(40\log_e(2)+27)$
3. C.$\frac{1}{3}(49\log_e(2)-15)$
4. D.$\frac{2}{3}(24\log_e(2)-7)$✓

Correct answer: D

The value of $\lim_{x\to0}\frac{\log_e(\sec(ex)\cdot\sec(e^2x)\cdots\sec(e^{10}x))}{e^2-e^{2\cos x}}$ is equal to

1. A.$\frac{(e^{10}-1)}{2e^2(e^2-1)}$
2. B.$\frac{(e^{20}-1)}{2e^2(e^2-1)}$
3. C.$\frac{(e^{10}-1)}{2(e^2-1)}$
4. D.$\frac{(e^{20}-1)}{2(e^2-1)}$✓

Correct answer: D

Let $y=y(x)$ be the solution of the differential equation $x\frac{dy}{dx}-\sin2y=x^3(2-x^3)\cos^2y$, $x\ne0$. If $y(2)=0$, then $\tan(y(1))$ is equal to

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

Correct answer: C

If $\int\left(\frac{1-5\cos^2x}{\sin^5x\cos^2x}\right)dx=f(x)+C$, where C is the constant of integration, then $f\left(\frac{\pi}{6}\right)-f\left(\frac{\pi}{4}\right)$ is equal to

1. A.$\frac{1}{\sqrt{3}}(26-\sqrt{3})$
2. B.$\frac{1}{\sqrt{3}}(26+\sqrt{3})$
3. C.$\frac{4}{\sqrt{3}}(8-\sqrt{6})$✓
4. D.$\frac{2}{\sqrt{3}}(4+\sqrt{6})$

Correct answer: C

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is $\mathbb{R}-(a, b)$, then $a^2+b^2$ is equal to ______.

Correct answer: 90

If $k=\tan\left(\frac{\pi}{4}+\frac{1}{2}\cos^{-1}\left(\frac{2}{3}\right)\right)+\tan\left(\frac{1}{2}\sin^{-1}\left(\frac{2}{3}\right)\right)$, then the number of solutions of the equation $\sin^{-1}(kx-1)=\sin^{-1}x-\cos^{-1}x$ is ______

Correct answer: 1

The value of $\sum_{r=1}^{20}\left(\left|\sqrt{\pi\left(\int_0^rx|\sin\pi x|dx\right)}\right|\right)$ is ______

Correct answer: 210

For some $\theta\in\left(0, \frac{\pi}{2}\right)$, let the eccentricity and the length of the latus rectum of the hyperbola $x^2-y^2\sec^2\theta=8$ be $e_1$ and $l_1$, respectively, and let the eccentricity and the length of the latus rectum of the ellipse $x^2\sec^2\theta+y^2=6$ be $e_2$ and $l_2$, respectively. If $e_1^2=e_2^2(\sec^2\theta+1)$, then $\left(\frac{l_1l_2}{e_1e_2}\right)\tan^2\theta$ is equal to ______

Correct answer: 8

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4$^{th}$ mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5$^{th}$ division of vernier scale coincides with a main scale division. Measured length of cylinder is ______ mm. (Least count of Vernier calliper = 0.1 mm)

1. A.15.4
2. B.15.5
3. C.15.9
4. D.15.1✓

Correct answer: D

In the potentiometer, when the cell in the secondary circuit is shunted with 4 $\Omega$ resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with 12 $\Omega$ resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is ______ $\Omega$

1. A.12
2. B.4✓
3. C.6
4. D.3

Correct answer: B

A particle of mass m falls from rest through a resistive medium having resistive force, $F=-kv$, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t)?

1. A.Rises from zero and saturates at a terminal value✓
2. B.Rises ever more steeply (concave up)
3. C.Straight line through the origin
4. D.Decays from a high value toward zero

Correct answer: A

A block of mass 5 kg is moving on an inclined plane which makes an angle of $30^\circ$ with the horizontal. Friction coefficient between the block and inclined plane surface is $\frac{\sqrt{3}}{2}$. The force to be applied on the block so that the block will move down without acceleration is ______ N. ($g=10$ m/s$^2$).

1. A.7.5
2. B.15
3. C.25
4. D.12.5✓

Correct answer: D

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ______ m. ($g=10$ m/s$^2$)

1. A.4.0
2. B.3.8
3. C.4.2✓
4. D.2.5

Correct answer: C

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is $43\times10^5$ dyne.cm, the angular acceleration of the discs about the given axis AB is ______ rad/s$^2$.

1. A.22
2. B.100
3. C.27
4. D.11✓

Correct answer: D

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections $3.0\times10^{-5}$ m$^2$ and $4.5\times10^{-5}$ m$^2$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x is ______.

1. A.5✓
2. B.4
3. C.2
4. D.1

Correct answer: A

10 kg of ice at $-10^\circ$C is added to 100 kg of water to lower its temperature from $25^\circ$C. Consider no heat exchange to surroundings. The decrement to the temperature of water is ______ $^\circ$C. (specific heat of ice = 2100 J/Kg.$^\circ$C, specific heat of water = 4200 J/Kg.$^\circ$C, latent heat of fusion of ice $=3.36\times10^5$ J/Kg)

1. A.15
2. B.10✓
3. C.11.6
4. D.6.67

Correct answer: B

In the following p-V diagram the equation of state along the curved path is given by $(V-2)^2=4ap$ where a is a constant. The total work done in the closed path is

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

Correct answer: A

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^\circ$C to $120^\circ$C ?

1. A.Plateau only at 100 °C
2. B.No plateaus (straight line)
3. C.Plateau at 0 °C (shorter) and at 100 °C (longer), sloped segments between✓
4. D.Three plateaus including one above 100 °C

Correct answer: C

The magnetic field at the centre of a current carrying circular loop of radius R is 16 $\mu$T. The magnetic field at a distance $x=\sqrt{3}R$ on its axis from the centre is ______ $\mu$T.

1. A.4
2. B.8
3. C.$2\sqrt{2}$
4. D.2✓

Correct answer: D

For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 $\Omega$ is same when both the cells are connected either in parallel or in series. The value of internal resistance r is ______ $\Omega$.

1. A.9
2. B.3
3. C.6✓
4. D.4

Correct answer: C

The electric current in the circuit is given as $i=i_0(t/T)$. The r.m.s current for the period $t=0$ to $t=T$ is ______.

1. A.$i_0$
2. B.$\frac{i_0}{\sqrt{6}}$
3. C.$\frac{i_0}{\sqrt{2}}$
4. D.$\frac{i_0}{\sqrt{3}}$✓

Correct answer: D

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is ______. ($\mu_0=4\pi\times10^{-7}$ T.m/A)

1. A.$6\times10^{-7}$ N towards P
2. B.$6\times10^{-6}$ N towards P
3. C.$6\times10^{-7}$ N towards R
4. D.$6\times10^{-6}$ N towards R✓

Correct answer: D

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ______ $\mu$J. $\frac{1}{4\pi\epsilon_0}=9\times10^9$ N.m$^2$/C$^2$

1. A.5.4
2. B.27
3. C.3.3
4. D.2.7✓

Correct answer: D

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t)=25\sin(2.0\times10^{15}t-10^7x)\hat{n}$ then the refractive index of the medium is ______. (All given measurement are in SI units)

1. A.1.7
2. B.1.5✓
3. C.1.2
4. D.2

Correct answer: B

Given below are two statements: Statement I: A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave. Statement II: The curvature of a spherical wave emerging from a slit will increase for increasing slit width. 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: D

The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index = 1.7) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ______.

1. A.5 : 2✓
2. B.5 : 12
3. C.12 : 5
4. D.2 : 5

Correct answer: A

An atom $^8_3X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by:

1. A.150 %
2. B.250%
3. C.900%
4. D.225%✓

Correct answer: D

Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through diode $D_1$ in the circuit is ______ mA. (Assume all diodes in the given circuit are identical)

1. A.11.7
2. B.17.6
3. C.20.15
4. D.18.8✓

Correct answer: D

A convex lens of refractive index 1.5 and focal length $f=18$ cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $\alpha\times f$. The value of $\alpha$ is ______. (refractive index of water = 4/3)

Correct answer: 3

The equivalent resistance between the points A and B in the following circuit is $\frac{x}{5}$ $\Omega$. The value of x is ______.

Correct answer: 21

The ratio of de Broglie wavelength of a deutron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n : 1. The value of n is ______. (Assume mass of proton = mass of neutron) :

Correct answer: 2

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is $\sqrt{n}$ cm. The value of n is

Correct answer: 265

The displacement of a particle, executing simple harmonic motion with time period T, is expressed as $x(t)=A\sin\omega t$, where A is the amplitude. The maximum value of potential energy of this oscillator is found at $t=T/2\beta$. The value of $\beta$ is ______.

Correct answer: 2

Figure 1 shows the electron probability density for the 2s orbital with a spherical nodal surface; Figure 2 shows the wave function $\psi_{2s}(x)$ along +x with marked points A, B, C and D. Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1?

1. A.C
2. B.D
3. C.B✓
4. D.A

Correct answer: C

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. (R = Rydberg constant)

1. A.$\frac{5R}{36}, \frac{8R}{9}, \frac{15R}{16}$
2. B.$\frac{7R}{144}, \frac{3R}{16}, \frac{16R}{255}$
3. C.$\frac{3R}{4}, \frac{3R}{16}, \frac{7R}{144}$
4. D.$\frac{5R}{36}, \frac{3R}{16}, \frac{21R}{100}$✓

Correct answer: D

Given below are two statements: Statement I: The number of species among BF$_4^-$, SiF$_4$, XeF$_4$ and SF$_4$, that have unequal E$-$F bond lengths is two. Here, E is the central atom. Statement II: Among O$_2^-$, O$_2^{2-}$, F$_2$ and O$_2^+$, O$_2^-$ has the highest bond order. 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.Both Statement I and Statement II are false✓
4. D.Statement I is true but Statement II is false

Correct answer: C

20.0 dm$^3$ of an ideal gas 'X' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa. Which of the following option is correct? (Given: log 2 = 0.3010 and log 5 = 0.6989)

1. A.w = $-$3.9 kJ, $\Delta$U = 0, $\Delta$H = 0; q = 3.9 kJ
2. B.w = 9.1 J, $\Delta$U = 9.1 J, $\Delta$H = 0; q = 0
3. C.w = $-$9.1 kJ, $\Delta$U = 0, $\Delta$H = 0, q = 9.1 kJ✓
4. D.w = +4.1 kJ, $\Delta$U = 0 , $\Delta$H = 0; q = $-$4.1 kJ

Correct answer: C

At T(K), 2 moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg. At this stage, one mole of A and one mole of B are added to the solution. The vapour pressure is now measured as 328.6 mm Hg. The vapour pressure (in mm Hg) of A and B are respectively:

1. A.600, 400
2. B.500, 200✓
3. C.400, 300
4. D.300, 200

Correct answer: B

Consider a weak base 'B' of p$K_b$ = 5.699. 'x' mL of 0.02 M HCl and 'y' mL of 0.02 M weak base 'B' are mixed to make 100 mL of a buffer of pH 9 at 25 $^\circ$C. The values of 'x' and 'y' respectively are: [Given: log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.699]

1. A.x = 42.7, y = 57.3
2. B.x = 11.1, y = 88.9
3. C.x = 85.7, y = 14.3
4. D.x = 14.3, y = 85.7✓

Correct answer: D

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{th}$ and $\left(\frac{1}{10}\right)^{th}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}}\times10$ ? (log 2 = 0.3)

1. A.3
2. B.30
3. C.9✓
4. D.0.9

Correct answer: C

In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.

1. A.K & Se
2. B.K & Br✓
3. C.Rb & Br
4. D.Na & Cl

Correct answer: B

Regarding the hydrides of group 15 elements EH$_3$ (E = N, P, As, Sb), select the correct statement from the following: A. The stability of hydrides decreases down the group. B. The basicity of hydrides decreases down the group. C. The reducing character increases down the group. D. The boiling point increases down the group. Choose the correct answer from the options given below:

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

Correct answer: B

The correct statement among the following is:

1. A.Ni(CO)$_4$ is diamagnetic and [NiCl$_4$]$^{2-}$ and [Ni(CN)$_4$]$^{2-}$ are paramagnetic.
2. B.Ni(CO)$_4$ and [NiCl$_4$]$^{2-}$ are diamagnetic and [Ni(CN)$_4$]$^{2-}$ is paramagnetic.
3. C.[Ni(CN)$_4$]$^{2-}$ and [NiCl$_4$]$^{2-}$ are diamagnetic and Ni(CO)$_4$ is paramagnetic.
4. D.Ni(CO)$_4$ and [Ni(CN)$_4$]$^{2-}$ are diamagnetic and [NiCl$_4$]$^{2-}$ is paramagnetic.✓

Correct answer: D

Given below are two statements: Statement I: The number of pairs, from the following, in which both the ions are coloured in aqueous solution is 3. [Sc$^{3+}$, Ti$^{3+}$], [Mn$^{2+}$, Cr$^{2+}$], [Cu$^{2+}$, Zn$^{2+}$] and [Ni$^{2+}$, Ti$^{4+}$]. Statement II: Th$^{4+}$ is the strongest reducing agent among Th$^{4+}$, Ce$^{4+}$, Gd$^{3+}$ and Eu$^{2+}$. 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 false✓
4. D.Both Statement I and Statement II are true

Correct answer: C

Method used for separation of mixture of products (B and C) obtained in the following reaction is: Benzene + Br$_2$ $\xrightarrow{FeBr_3}$ A $\xrightarrow{\text{Conc. HNO}_3\text{, Conc. H}_2\text{SO}_4}$ B + C

1. A.simple distillation
2. B.sublimation
3. C.fractional distillation✓
4. D.steam distillation

Correct answer: C

CORRECT order of stability for the following is CH$_2$=CH$^-$, CH$_3-$CH$_2^-$, CH$\equiv$C$^-$

1. A.CH$\equiv$C$^-$ > CH$_2$=CH$^-$ > CH$_3-$CH$_2^-$✓
2. B.CH$_3-$CH$_2^-$ > CH$_2$=CH$^-$ > CH$\equiv$C$^-$
3. C.CH$_2$=CH$^-$ > CH$\equiv$C$^-$ > CH$_3-$CH$_2^-$
4. D.CH$\equiv$C$^-$ > CH$_3-$CH$_2^-$ > CH$_2$=CH$^-$

Correct answer: A

Ph$-$CH=CH$_2$ $\xrightarrow{(PhCOO)_2,\ HBr}$ Product. Consider the above reaction. A. The reaction proceeds through a more stable radical intermediate. B. The role of peroxide is to generate H$^\bullet$ (Hydrogen radical). C. During this reaction, benzene is formed as a byproduct. D. 1$-$Bromo$-$2$-$phenylethane is formed as the minor product. E. The same reaction in absence of peroxide proceeds via carbocation intermediate. Identify the correct statements. Choose the correct answer from the options given below:

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

Correct answer: C

Given below are two statements for the following reaction sequence. Compound 'X' (molecular formula C$_3$H$_6$Cl$_2$) $\xrightarrow{\text{excess of NaNH}_2}$ Compound 'Y'; Y $\xrightarrow{\text{dil. H}_2\text{SO}_4\text{, Hg}^{2+}}$ Compound 'Z'; Y $\xrightarrow{\text{Red hot iron tube, }\Delta}$ Compound 'Q' (Molecular formula C$_9$H$_{12}$). Statement I: Compound 'Z' will give yellow precipitate with NaOI. Statement II: Compound 'Q' has two different types of 'H' atoms (aromatic : aliphatic) in the ratio 1:3. 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.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: A

Consider the following reaction sequence: Compound (x) [76.6% C, 6.38% H, vapour density 47] $\xrightarrow{\text{(i) CO}_2\text{, NaOH, 120}^\circ\text{C, high pressure; (ii) H}_3\text{O}^+}$ Compound (y) (Major Product). Compound (y) develops characteristic colour with neutral FeCl$_3$ solution. Identify the INCORRECT statement from the following for the above sequence.

1. A.Compound y will dissolve in NaHCO$_3$ and evolve a gas.
2. B.Both compounds x and y will burn with sooty flame.
3. C.Compound x is more acidic than compound y.✓
4. D.Both compounds x and y will dissolve in NaOH.