JEE Main 2026 — 23 Jan Shift 2 (3:00 PM - 6:00 PM) (Previous Year

Let $A=\{0, 1, 2, \ldots, 9\}$. Let R be a relation on A defined by $(x, y)\in R$ if and only if $|x-y|$ is a multiple of 3. Given below are two statements: Statement I: $n(R)=36$. Statement II: R is an equivalence relation. 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 correct
2. B.Both Statement I and Statement II are incorrect
3. C.Statement I is incorrect but Statement II is correct✓
4. D.Statement I is correct but Statement II is incorrect

Correct answer: C

Consider two sets $A=\{x\in\mathbb{Z}: |(|x-3|-3)|\le1\}$ and $B=\left\{x\in\mathbb{R}-\{1, 2\}: \frac{(x-2)(x-4)}{x-1}\log_e(|x-2|)=0\right\}$. Then the number of onto functions $f: A\to B$ is equal to

1. A.32
2. B.62✓
3. C.81
4. D.79

Correct answer: B

The sum of all the real solutions of the equation $\log_{(x+3)}(6x^2+28x+30)=5-2\log_{(6x+10)}(x^2+6x+9)$ is equal to

1. A.1
2. B.0✓
3. C.2
4. D.4

Correct answer: B

If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}$, $i=\sqrt{-1}$, then $(z^{201}-i)^8$ is equal to

1. A.0
2. B.256✓
3. C.-1
4. D.1

Correct answer: B

The system of linear equations $x+y+z=6$, $2x+5y+az=36$, $x+2y+3z=b$ has

1. A.infinitely many solutions for $a=8$ and $b=14$✓
2. B.infinitely many solutions for $a=8$ and $b=16$
3. C.unique solution for $a=8$ and $b=16$
4. D.unique solution for $a=8$ and $b=14$

Correct answer: A

Let $\sum_{k=1}^{n}a_k=\alpha n^2+\beta n$. If $a_{10}=59$ and $a_6=7a_1$, then $\alpha+\beta$ is equal to

1. A.3
2. B.5✓
3. C.7
4. D.12

Correct answer: B

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

1. A.403
2. B.384
3. C.429
4. D.455✓

Correct answer: D

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is $\frac{p}{q}$, $\gcd(p, q)=1$, then $p+q$ is equal to

1. A.23✓
2. B.22
3. C.21
4. D.24

Correct answer: A

If the mean and the variance of the data: Class 4$-$8, 8$-$12, 12$-$16, 16$-$20 with Frequency 3, $\lambda$, 4, 7 are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is

1. A.21
2. B.18
3. C.19✓
4. D.20

Correct answer: C

If the points of intersection of the ellipses $x^2+2y^2-6x-12y+23=0$ and $4x^2+2y^2-20x-12y+35=0$ lie on a circle of radius r and centre $(a, b)$, then the value of $ab+18r^2$ is

1. A.53
2. B.51
3. C.55✓
4. D.52

Correct answer: C

An equilateral triangle OAB is inscribed in the parabola $y^2=4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

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

Correct answer: B

Let PQ be a chord of the hyperbola $\frac{x^2}{4}-\frac{y^2}{b^2}=1$, perpendicular to the x-axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the eccentricity of the hyperbola is $\sqrt{3}$, then the area of the triangle OPQ is

1. A.$\frac{11}{5}$
2. B.$\frac{9}{5}$
3. C.$\frac{8\sqrt{3}}{5}$✓
4. D.$2\sqrt{3}$

Correct answer: C

Let A(1, 2) and C($-$3, $-$6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7x-y=14$. If B$(\alpha, \beta)$ and D$(\gamma, \delta)$ are the other two vertices, then $|\alpha+\beta+\gamma+\delta|$ is equal to

1. A.6✓
2. B.1
3. C.9
4. D.3

Correct answer: A

Let $\frac{\pi}{2}<\theta<\pi$ and $\cot\theta=-\frac{1}{2\sqrt{2}}$. Then the value of $\sin\left(\frac{15\theta}{2}\right)(\cos8\theta+\sin8\theta)+\cos\left(\frac{15\theta}{2}\right)(\cos8\theta-\sin8\theta)$ is equal to

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

Correct answer: C

Let $\vec{a}=\hat{i}-2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}+\hat{j}-\hat{k}$, $\vec{c}=\lambda\hat{i}+\hat{j}+\hat{k}$ and $\vec{v}=\vec{a}\times\vec{b}$. If $\vec{v}\cdot\vec{c}=11$ and the length of the projection of $\vec{b}$ on $\vec{c}$ is p, then $9p^2$ is equal to

1. A.12✓
2. B.4
3. C.9
4. D.6

Correct answer: A

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $\vec{a}\times\vec{b}=2(\vec{a}\times\vec{c})$. If $|\vec{a}|=1$, $|\vec{b}|=4$, $|\vec{c}|=2$, and the angle between $\vec{b}$ and $\vec{c}$ is $60^\circ$, then $|\vec{a}\cdot\vec{c}|$ is equal to

1. A.4
2. B.2
3. C.0
4. D.1✓

Correct answer: D

If $f(x)=\begin{cases}\frac{a|x|+x^2-2(\sin|x|)(\cos|x|)}{x}, & x\ne0\\ b, & x=0\end{cases}$ is continuous at $x=0$, then $a+b$ is equal to

1. A.0
2. B.1
3. C.4
4. D.2✓

Correct answer: D

The least value of $(\cos^2\theta-6\sin\theta\cos\theta+3\sin^2\theta+2)$ is

1. A.-1
2. B.$4+\sqrt{10}$
3. C.$4-\sqrt{10}$✓
4. D.1

Correct answer: C

Let $I(x)=\int\frac{3dx}{(4x+6)\left(\sqrt{4x^2+8x+3}\right)}$ and $I(0)=\frac{\sqrt{3}}{4}+20$. If $I\left(\frac{1}{2}\right)=\frac{a\sqrt{2}}{b}+c$, where $a, b, c\in\mathbb{N}$, $\gcd(a, b)=1$, then $a+b+c$ is equal to

1. A.29
2. B.28
3. C.30
4. D.31✓

Correct answer: D

The area of the region enclosed between the circles $x^2+y^2=4$ and $x^2+(y-2)^2=4$ is:

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

Correct answer: B

Let $A=\begin{bmatrix}0 & 2 & -3\\ -2 & 0 & 1\\ 3 & -1 & 0\end{bmatrix}$ and B be a matrix such that $B(I-A)=I+A$. Then the sum of the diagonal elements of $B^TB$ is equal to ______

Correct answer: 3

Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers having product of its digits equal to 20. Then $n(S)+n(P)$ is equal to ______

Correct answer: 260

If the image of the point P$(a, 2, a)$ in the line $\frac{x}{2}=\frac{y+a}{1}=\frac{z}{1}$ is Q and the image of Q in the line $\frac{x-2b}{2}=\frac{y-a}{1}=\frac{z+2b}{-5}$ is P, then $a+b$ is equal to ______.

Correct answer: 3

The number of elements in the set $S=\left\{x: x\in[0, 100]\text{ and }\int_0^x t^2\sin(x-t)dt=x^2\right\}$ is ______

Correct answer: 16

If the solution curve $y=f(x)$ of the differential equation $(x^2-4)y'-2xy+2x(4-x^2)^2=0$, $x>2$, passes through the point $(3, 15)$, then the local maximum value of $f$ is ______

Correct answer: 16

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 m/s$^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is ______ m. ($g=10$ m/s$^2$)

1. A.82.5
2. B.92.5✓
3. C.62.5
4. D.20

Correct answer: B

A bead P sliding on a frictionless semi-circular string (ACB) and it is at point S at $t=0$ and at this instant the horizontal component of its velocity is $v$. Another bead Q of the same mass as P is ejected from point A at $t=0$ along the horizontal string AB, with the speed $v$, friction between the beads and the respective strings may be neglected in both cases. Let $t_P$ and $t_Q$ be the respective times taken by beads P and Q to reach the point B, then the relation between $t_P$ and $t_Q$ is

1. A.$t_P>t_Q$
2. B.$t_P>1.25t_Q$
3. C.$t_P=t_Q$
4. D.$t_P<t_Q$✓

Correct answer: D

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is ______ m/s.

1. A.$12\sqrt{2}$✓
2. B.12
3. C.$10\sqrt{2}$
4. D.$24\sqrt{2}$

Correct answer: A

A small metallic sphere of diameter 2 mm and density 10.5 g/cm$^3$ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm$^3$ respectively. The terminal velocity attained by the sphere is ______ cm/s. ($\pi=\frac{22}{7}$ and $g=10$ m/s$^2$)

1. A.1.5
2. B.2.0✓
3. C.3.0
4. D.1.0

Correct answer: B

An air bubble of volume 2.9 cm$^3$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^\circ$C. The volume of the bubble when it reaches the surface, where the water temperature is $27^\circ$C, is ______ cm$^3$. ($g=10$ m/s$^2$, density of water $=10^3$ kg/m$^3$, and 1 atm pressure is $10^5$ Pa)

1. A.2.0
2. B.3.0
3. C.4.5✓
4. D.4.2

Correct answer: C

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature $27^\circ$C and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^\circ$C doing the same amount of work W, then its final temperature will be (close to) ______ $^\circ$C. ($\log_e2=0.693$)

1. A.-56✓
2. B.-30
3. C.-189
4. D.-117

Correct answer: A

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 cm$^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^\circ$C, then the piston will move ______ cm. (atmospheric pressure $=10^5$ Pa)

1. A.15.5✓
2. B.1.55
3. C.1.45
4. D.14.5

Correct answer: A

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is ______.

1. A.2.0✓
2. B.1.0
3. C.1.5
4. D.2.5

Correct answer: A

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I=10\sin(\omega t)$ A, where $\omega=1000$ rad/s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed $v=1$ cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\alpha/\sqrt{2}$ $\mu$A. The value of $\alpha$ is ______. [Resistance of the loop = 10 $\Omega$]

1. A.197✓
2. B.100
3. C.80
4. D.280

Correct answer: A

The current passing through a conducting loop in the form of equilateral triangle of side $4\sqrt{3}$ cm is 2 A. The magnetic field at its centroid is $\alpha\times10^{-5}$ T. The value of $\alpha$ is ______. (Given : $\mu_0=4\pi\times10^{-7}$ SI units)

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

Correct answer: A

Two shorts dipoles (A, B), A having charges $\pm2$ $\mu$C and length 1 cm and B having charges $\pm4$ $\mu$C and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is ______ N/C.

1. A.$4.5\sqrt{2}\times10^4$
2. B.$9\sqrt{2}\times10^4$
3. C.$\frac{9}{16}\sqrt{2}\times10^5$
4. D.$\frac{9}{16}\sqrt{2}\times10^4$✓

Correct answer: D

Two charges 7 $\mu$C and $-2$ $\mu$C are placed at $(-9, 0, 0)$ cm and $(9, 0, 0)$ cm respectively in an external field $E=\frac{A}{r^2}\hat{r}$, where $A=9\times10^5$ N/C.m$^2$. Considering the potential at infinity is 0, the electrostatic energy of the configuration is ______ J.

1. A.24.3
2. B.49.3✓
3. C.-90.7
4. D.1.4

Correct answer: B

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ______ mV.

1. A.13.2
2. B.8.25
3. C.6.6
4. D.1.32✓

Correct answer: D

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $\mu=2\mu_0$, is ($\mu_0$ = permeability of vacuum)

1. A.$\sqrt{6}:1$✓
2. B.6:1
3. C.36:1
4. D.3:2

Correct answer: A

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is ______. ($\tan^{-1}(1.52)=57.7^\circ$, refractive indices of air and glass are 1.00 and 1.52, respectively.)

1. A.$39.6^\circ$
2. B.$32.3^\circ$✓
3. C.$42.6^\circ$
4. D.$36.3^\circ$

Correct answer: B

Which of the following pair of nuclei are isobars of the element?

1. A.$^{236}_{92}$U and $^{238}_{92}$U
2. B.$^{2}_{1}$H and $^{3}_{1}$H
3. C.$^{3}_{1}$H and $^{3}_{2}$He✓
4. D.$^{198}_{80}$Hg and $^{197}_{79}$Au

Correct answer: C

For the given logic gate circuit, which of the following is the correct truth table ?

1. A.n m z: 0 0 0; 0 1 1; 1 1 0; 1 0 1
2. B.0 0 1; 0 1 1; 1 1 0; 1 0 0✓
3. C.0 0 1; 0 1 0; 1 1 1; 1 0 0
4. D.0 0 1; 0 1 0; 1 1 0; 1 0 0

Correct answer: B

Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by $\frac{x}{256}Mr^2$. The value of $x$ is ______.

Correct answer: 109

A ball of radius r and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time t, given by $t=A\rho^ar^b\eta^c\sigma^d$, where A is a constant and a, b, c and d are integers. The value of $\frac{b+c}{a+d}$ is ______.

Correct answer: 1

The velocity of sound in air is doubled when the temperature is raised from $0^\circ$C to $\alpha^\circ$C. The value of $\alpha$ is ______.

Correct answer: 819

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ______ cm.

Correct answer: 16

The average energy released per fission for the nucleus of $^{235}_{92}$U is 190 MeV. When all the atoms of 47 g pure $^{235}_{92}$U undergo fission process, the energy released is $\alpha\times10^{23}$ MeV. The value of $\alpha$ is ______. (Avogadro Number $=6\times10^{23}$ per mole)

Correct answer: 228

The work functions of two metals (M$_A$ and M$_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of M$_A$ : M$_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of M$_A$ and M$_B$ are respectively.

1. A.2.3, 4.6✓
2. B.3.1, 6.2
3. C.1.4, 2.8
4. D.1.5, 3.0

Correct answer: A

Identify the INCORRECT statements from the following: A. Notation $^{24}_{12}$Mg represents 24 protons and 12 neutrons. B. Wavelength of a radiation of frequency $4.5\times10^{15}$ s$^{-1}$ is $6.7\times10^{-8}$ m. C. One radiation has wavelength = $\lambda_1$ (900 nm) and energy = E$_1$. Other radiation has wavelength = $\lambda_2$ (300 nm) and energy = E$_2$. E$_1$ : E$_2$ = 3 : 1. D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is $1.006\times10^{16}$. Choose the correct answer from the options given below:

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

Correct answer: B

Which statements are NOT TRUE about XeO$_2$F$_2$? A. It has a see-saw shape. B. Xe has 5 electron pairs in its valence shell in XeO$_2$F$_2$. C. The O$-$Xe$-$O bond angle is close to $180^\circ$. D. The F$-$Xe$-$F bond angle is close to $180^\circ$. E. Xe has 16 valence electrons in XeO$_2$F$_2$. Choose the correct answer from the options given below:

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

Correct answer: B

It is noticed that Pb$^{2+}$ is more stable than Pb$^{4+}$ but Sn$^{2+}$ is less stable than Sn$^{4+}$. Observe the following reactions. PbO$_2$ + Pb $\to$ 2PbO; $\Delta_rG^\circ(1)$. SnO$_2$ + Sn $\to$ 2SnO; $\Delta_rG^\circ(2)$. Identify the correct set from the following

1. A.$\Delta_rG^\circ(1)>0$; $\Delta_rG^\circ(2)<0$
2. B.$\Delta_rG^\circ(1)<0$; $\Delta_rG^\circ(2)>0$✓
3. C.$\Delta_rG^\circ(1)>0$; $\Delta_rG^\circ(2)>0$
4. D.$\Delta_rG^\circ(1)<0$; $\Delta_rG^\circ(2)<0$

Correct answer: B

Consider the electrochemical cell shown: two identical metal electrodes M dip into MX solutions separated by a semi permeable membrane; the left compartment has M$^+$ at concentration $c_2$ and the right compartment M$^+$ at concentration $c_1$. A metal electrode (M) is undergoing redox reaction by forming M$^+$ (M $\to$ M$^+$ + e$^-$). The cation M$^+$ is present in two different concentrations $c_1$ and $c_2$ as shown above. Which of the following statement is correct for generating a positive cell potential?

1. A.If $c_1$ is present at anode, then $c_1>c_2$.
2. B.If $c_1$ is present at cathode, then $c_1>c_2$.✓
3. C.If $c_1$ is present at anode, then $c_1=c_2$.
4. D.If $c_1$ is present at cathode, then $c_1<c_2$.

Correct answer: B

Given above is the concentration vs time plot for a dissociation reaction : A $\to$ nB. Based on the data of the initial phase of the reaction (initial 10 min), the value of n is ______.

1. A.4
2. B.5
3. C.2
4. D.3✓

Correct answer: D

Observe the following reactions at T(K). I. A $\to$ products. II. 5Br$^-$(aq) + BrO$_3^-$(aq) + 6H$^+$(aq) $\to$ 3Br$_2$(aq) + 3H$_2$O($l$). Both the reactions are started at 10.00 am. The rates of these reactions at 10.10 am are same. The value of $-\frac{\Delta[Br^-]}{\Delta t}$ at 10.10 am is $2\times10^{-4}$ mol L$^{-1}$ min$^{-1}$. The concentration of A at 10.10 am is $10^{-2}$ mol L$^{-1}$. What is the first order rate constant (in min$^{-1}$) of reaction I?

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

Correct answer: B

Given below are two statements: Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg. Statement II: The ionic radius of O$^{2-}$ is larger than that of F$^-$. 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

Elements X and Y belong to Group 15. The difference between the electronegativity values of 'X' and phosphorus is higher than that of the difference between phosphorus and 'Y'. 'X' & 'Y' are respectively

1. A.As & Bi
2. B.Bi & N
3. C.As & Sb
4. D.N & As✓

Correct answer: D

The oxidation state of chromium in the final product formed in the reaction between KI and acidified K$_2$Cr$_2$O$_7$ solution is:

1. A.+3✓
2. B.+6
3. C.+2
4. D.+4

Correct answer: A

Identify the CORRECT set of details from the following: A. [Co(NH$_3$)$_6$]$^{3+}$ : Inner orbital complex; d$^2$sp$^3$ hybridized B. [MnCl$_6$]$^{3-}$ : Outer orbital complex; sp$^3$d$^2$ hybridized C. [CoF$_6$]$^{3-}$ : Outer orbital complex; d$^2$sp$^3$ hybridized D. [FeF$_6$]$^{3-}$ : Outer orbital complex; sp$^3$d$^2$ hybridized E. [Ni(CN)$_4$]$^{2-}$ : Inner orbital complex; sp$^3$ hybridized. Choose the correct answer from the options given below:

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

Correct answer: C

In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is

1. A.37.57%
2. B.34.79%
3. C.53.58%✓
4. D.87.65%

Correct answer: C

Given below are two statements: Statement I: $(CH_3)_3\overset{+}{C}$ is more stable than $\overset{+}{C}H_3$ as nine hyperconjugation interactions are possible in $(CH_3)_3\overset{+}{C}$. Statement II: $\overset{+}{C}H_3$ is less stable than $(CH_3)_3\overset{+}{C}$ as only three hyperconjugation interactions are possible in $\overset{+}{C}H_3$. 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 false but Statement II is true
4. D.Statement I is true but Statement II is false✓

Correct answer: D

A vicinal dibromide on a substituted cyclopentane (shown in figure) is treated with (i) Zn, $\Delta$ (ii) HBr to give the major product (P). Identify (P)

1. A.Tertiary bromide: Br on the substituted ring carbon (see figure)✓
2. B.Br on the side chain carbon next to the ring (see figure)
3. C.Br on a secondary ring carbon (see figure)
4. D.Br on the ring carbon between the two alkyl groups (see figure)

Correct answer: A

Which of the following statements are TRUE about Haloform reaction?: A. Sodium hypochlorite reacts with KI to give KOI. B. KOI is a reducing agent. C. $\alpha,\beta$-unsaturated methylketone (CH$_3-$CH=CH$-$CO$-$CH$_3$) will give iodoform reaction. D. Isopropyl alcohol will not give iodoform test. E. Methanoic acid will give positive iodoform test. Choose the correct answer from the options given below:

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

Correct answer: C

A mixed ether (P), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give compounds (Q) and (R). Both (Q) and (R) give yellow precipitate with NaOI. Identify the mixed ether (P):

1. A.CH$_3$CH$_2-$O$-$C(CH$_3$)$_2$CH$_2$CH$_3$
2. B.CH$_3$CH$_2-$O$-$CH(CH$_3$)CH(CH$_3$)$_2$ (ethyl 3-methylbutan-2-yl ether)✓
3. C.CH$_3$CH$_2-$O$-$CH(Ph)CH(CH$_3$)$_2$
4. D.PhCH$_2-$O$-$CH(CH$_3$)$_2$

Correct answer: B

Given below are two statements: Statement I: benzene-1,2-diamine can be synthesized from 1,2-dipropylbenzene (C$_6$H$_4$(CH$_2$CH$_2$CH$_3$)$_2$, ortho) using simpler reagents in the order i) Acidic KMnO$_4$, ii) Ammonia, iii) Bromine and alkali. Statement II: 4-methylaniline ($p$-toluidine) can be converted into 3,5-dibromotoluene using reagents in the order i) Bromine-H$_2$O ii) NaNO$_2$/HCl (0 - 5 $^\circ$C) (iii) Aq. H$_3$PO$_2$. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: D

A student has been given a compound \"x\" of molecular formula- C$_6$H$_7$N. 'x' is sparingly soluble in water. However, on addition of dilute mineral acid, 'x' becomes soluble in water. 'x' when treated with CHCl$_3$ and KOH(alc), 'y' is produced. 'y' has a specific unpleasant smell. On treatment with benzenesulphonyl chloride, 'x' gives a compound 'z' which is soluble in alkali. The number of different \"H\" atoms present in 'z' is:-