JEE Main 2026 — 22 Jan Shift 2 (3:00 PM - 6:00 PM) (Previous Year

The number of elements in the relation $R=\{(x, y): 4x^2+y^2<52, x, y\in\mathbb{Z}\}$ is

1. A.67
2. B.89
3. C.86
4. D.77✓

Correct answer: D

Let $f$ and $g$ be functions satisfying $f(x+y)=f(x)f(y)$, $f(1)=7$ and $g(x+y)=g(xy)$, $g(1)=1$, for all $x, y\in\mathbb{N}$. If $\sum_{x=1}^{n}\left(\frac{f(x)}{g(x)}\right)=19607$, then n is equal to :

1. A.5✓
2. B.4
3. C.6
4. D.7

Correct answer: A

Let $\alpha, \beta$ be the roots of the quadratic equation $12x^2-20x+3\lambda=0$, $\lambda\in\mathbb{Z}$. If $\frac{1}{2}\le|\beta-\alpha|\le\frac{3}{2}$, then the sum of all possible values of $\lambda$ is :

1. A.1
2. B.6
3. C.4
4. D.3✓

Correct answer: D

Let the domain of the function $f(x)=\log_3\log_5(7-\log_2(x^2-10x+85))+\sin^{-1}\left(\left|\frac{3x-7}{17-x}\right|\right)$ be $(\alpha, \beta]$. Then $\alpha+\beta$ is equal to :

1. A.9✓
2. B.12
3. C.8
4. D.10

Correct answer: A

Let $S=\{z\in\mathbb{C}: 4z^2+\bar{z}=0\}$. Then $\sum_{z\in S}|z|^2$ is equal to :

1. A.$\frac{1}{16}$
2. B.$\frac{3}{16}$✓
3. C.$\frac{5}{64}$
4. D.$\frac{7}{64}$

Correct answer: B

If $X=\begin{bmatrix}x\\ y\\ z\end{bmatrix}$ is a solution of the system of equations $AX=B$, where $\operatorname{adj}A=\begin{bmatrix}4 & 2 & 2\\ -5 & 0 & 5\\ 1 & -2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}4\\ 0\\ 2\end{bmatrix}$, then $|x+y+z|$ is equal to :

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

Correct answer: D

Let n be the number obtained on rolling a fair die. If the probability that the system $x-ny+z=6$, $x+(n-2)y+(n+1)z=8$, $(n-1)y+z=1$ has a unique solution is $\frac{k}{6}$, then the sum of k and all possible values of n is :

1. A.21
2. B.24
3. C.20
4. D.22✓

Correct answer: D

If the mean deviation about the median of the numbers $k, 2k, 3k, \ldots, 1000k$ is 500, then $k^2$ is equal to :

1. A.4✓
2. B.16
3. C.1
4. D.9

Correct answer: A

Let $C_r$ denote the coefficient of $x^r$ in the binomial expansion of $(1+x)^n$, $n\in\mathbb{N}$, $0\le r\le n$. If $P_n=C_0-C_1+\frac{2^2}{3}C_2-\frac{2^3}{4}C_3+\ldots+\frac{(-2)^n}{n+1}C_n$, then the value of $\sum_{n=1}^{25}\frac{1}{P_{2n}}$ equals.

1. A.650
2. B.525
3. C.675✓
4. D.580

Correct answer: C

Let S and S' be the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $P(\alpha, \beta)$ be a point on the ellipse in the first quadrant. If $(SP)^2+(S'P)^2-SP\cdot S'P=37$, then $\alpha^2+\beta^2$ is equal to :

1. A.17
2. B.13✓
3. C.15
4. D.11

Correct answer: B

Let $P(10, 2\sqrt{15})$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, whose foci are S and S'. If the length of its latus rectum is 8, then the square of the area of $\Delta PSS'$ is equal to :

1. A.4200
2. B.900
3. C.1462
4. D.2700✓

Correct answer: D

Let the locus of the mid-point of the chord through the origin O of the parabola $y^2=4x$ be the curve S. Let P be any point on S. Then the locus of the point, which internally divides OP in the ratio 3:1, is :

1. A.$3y^2=2x$
2. B.$3x^2=2y$
3. C.$2y^2=3x$✓
4. D.$2x^2=3y$

Correct answer: C

Among the statements (S1) : If A(5, $-$1) and B($-$2, 3) are two vertices of a triangle, whose orthocentre is (0, 0), then its third vertex is ($-$4, $-$7) and (S2) : If positive numbers 2a, b, c are three consecutive terms of an A.P., then the lines $ax+by+c=0$ are concurrent at (2, $-$2),

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

Correct answer: A

Let $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda\hat{j}+2\hat{k}$, $\lambda\in\mathbb{Z}$ be two vectors. Let $\vec{c}=\vec{a}\times\vec{b}$ and $\vec{d}$ be a vector of magnitude 2 in $yz$-plane. If $|\vec{c}|=\sqrt{53}$, then the maximum possible value of $(\vec{c}\cdot\vec{d})^2$ is equal to :

1. A.26
2. B.208✓
3. C.104
4. D.52

Correct answer: B

Let L be the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}$ and let S be the set of all points (a, b, c) on L, whose distance from the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z-9}{0}$ along the line L is 7. Then $\sum_{(a, b, c)\in S}(a+b+c)$ is equal to :

1. A.34✓
2. B.40
3. C.6
4. D.28

Correct answer: A

Let $[\cdot]$ denote the greatest integer function, and let $f(x)=\min\{\sqrt{2}x, x^2\}$. Let $S=\{x\in(-2, 2):$ the function $g(x)=|x|[x^2]$ is discontinuous at $x\}$. Then $\sum_{x\in S}f(x)$ equals

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

Correct answer: B

If $\lim_{x\to0}\frac{e^{(a-1)x}+2\cos bx+(c-2)e^{-x}}{x\cos x-\log_e(1+x)}=2$, then $a^2+b^2+c^2$ is equal to :

1. A.3
2. B.7✓
3. C.5
4. D.9

Correct answer: B

Let $f(x)=[x]^2-[x+3]-3$, $x\in\mathbb{R}$, where $[\cdot]$ is the greatest integer funtion. Then

1. A.$f(x)>0$ only for $x\in[4, \infty)$
2. B.$f(x)<0$ only for $x\in[-1, 3)$✓
3. C.$\int_0^2 f(x)dx=-6$
4. D.$f(x)=0$ for finitely many values of $x$

Correct answer: B

The area of the region $A=\{(x, y): 4x^2+y^2\le8$ and $y^2\le4x\}$ is :

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

Correct answer: C

Suppose a, b, c are in A.P. and $a^2, 2b^2, c^2$ are in G.P. If $a<b<c$ and $a+b+c=1$, then $9(a^2+b^2+c^2)$ is equal to ______.

Correct answer: 9

Let S be the set of the first 11 natural numbers. Then the number of elements in $A=\{B\subseteq S: n(B)\ge2$ and the product of all elements of B is even$\}$ is ______.

Correct answer: 1979

Let $\cos(\alpha+\beta)=-\frac{1}{10}$ and $\sin(\alpha-\beta)=\frac{3}{8}$, where $0<\alpha<\frac{\pi}{3}$ and $0<\beta<\frac{\pi}{4}$. If $\tan2\alpha=\frac{3(1-r\sqrt{5})}{\sqrt{11}(s+\sqrt{5})}$, $r, s\in\mathbb{N}$, then $r+s$ is equal to ______.

Correct answer: 20

Let a vector $\vec{a}=\sqrt{2}\hat{i}-\hat{j}+\lambda\hat{k}$, $\lambda>0$, make an obtuse angle with the vector $\vec{b}=-\lambda^2\hat{i}+4\sqrt{2}\hat{j}+4\sqrt{2}\hat{k}$ and an angle $\theta$, $\frac{\pi}{6}<\theta<\frac{\pi}{2}$, with the positive $z$-axis. If the set of all possible values of $\lambda$ is $(\alpha, \beta)-\{\gamma\}$, then $\alpha+\beta+\gamma$ is equal to ______.

Correct answer: 5

Let $[\cdot]$ be the greatest integer function. If $\alpha=\int_0^{64}(x^{1/3}-[x^{1/3}])dx$, then $\frac{1}{\pi}\int_0^{\alpha\pi}\left(\frac{\sin^2\theta}{\sin^6\theta+\cos^6\theta}\right)d\theta$ is equal to ______.

Correct answer: 36

Using a simple pendulum experiment $g$ is determind by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T ?

1. A.Concave-down curve falling with L
2. B.Straight line with negative slope
3. C.Concave-up curve rising with L
4. D.Decreasing hyperbola-like curve ($1/T^2\propto1/L$)✓

Correct answer: D

If $\epsilon$, E and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :

1. A.A/m
2. B.Am$^2$
3. C.A/m$^2$✓
4. D.Am

Correct answer: C

A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2m are moving in opposite directions with same speed of $v$ and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$. The ratio of $v$ and $\omega$ is :

1. A.32
2. B.$2\sqrt{88}$
3. C.66
4. D.33✓

Correct answer: D

Given below are two statements : Statement I : An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-\int_{r_1}^{r_2}\vec{F}\cdot d\vec{r}$. Statement II : Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. 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: D

Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles. Statement II : The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference. 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: A

Given below are two statements : Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. Statement II : The time period of revolution of the satellite is $T=2\pi\sqrt{\frac{R_e}{g}}$ (for satellite very close to the earth surface), where $R_e$ radius of earth and $g$ acceleration due to gravity. 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.Both Statement I and Statement II are true✓
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are false

Correct answer: B

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by ______ %.

1. A.-1
2. B.-3
3. C.+1✓
4. D.+3

Correct answer: C

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

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

Correct answer: C

Figure shows the circuit that contains three resistances (9 $\Omega$ each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is ______ A.

1. A.zero
2. B.2
3. C.3
4. D.1✓

Correct answer: D

In an open organ pipe $\nu_3$ and $\nu_6$ are 3$^{rd}$ and 6$^{th}$ harmonic frequencies, respectively. If $\nu_6-\nu_3=2200$ Hz then length of the pipe is ______ mm. (Take velocity of sound in air is 330 m/s.)

1. A.200
2. B.225✓
3. C.250
4. D.275

Correct answer: B

Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field $(\vec{E})$ at the center O of the pentagon due to these five positive charges are :

1. A.$V=\frac{5q}{4\pi\epsilon_0r}$ and $\vec{E}=\frac{5\sqrt{3}q}{8\pi\epsilon_0r^2}\hat{r}$
2. B.$V=0$ and $\vec{E}=0$
3. C.$V=\frac{5q}{4\pi\epsilon_0r}$ and $\vec{E}=\frac{5q}{4\pi\epsilon_0r^2}\hat{r}$
4. D.$V=\frac{5q}{4\pi\epsilon_0r}$ and $\vec{E}=0$✓

Correct answer: D

An electric power line having total resistance of 2 $\Omega$, delivers 1 kW of power at 250 V. The percentage efficiency of transmission line is ______.

1. A.92.5
2. B.96.9✓
3. C.86.5
4. D.100

Correct answer: B

A laser beam has intensity of $4.0\times10^{14}$ W/m$^2$. The amplitude of magnetic field associated with beam is ______ T. (Take $\epsilon_0=8.85\times10^{-12}$ C$^2$/Nm$^2$ and $c=3\times10^8$ m/s)

1. A.18.3
2. B.1.83✓
3. C.5.5
4. D.2.0

Correct answer: B

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is $4/3$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $3/2$ is ______ nm.

1. A.480✓
2. B.840
3. C.380
4. D.540

Correct answer: A

In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

1. A.at any point beyond the focus(F) of the mirror✓
2. B.between the focus(F) and the centre of curvature(C) of the mirror ONLY
3. C.beyond the centre of the curvature(C) of the mirror ONLY
4. D.between the pole(P) and the focus(F) of the concave mirror ONLY

Correct answer: A

Light is incident on a metallic plate having work function $110\times10^{-20}$ J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ rad/s. ($h=6.63\times10^{-34}$ J.s).

1. A.$1.66\times10^{16}$
2. B.$1.04\times10^{13}$
3. C.$1.66\times10^{15}$
4. D.$1.04\times10^{16}$✓

Correct answer: D

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly ______ nm.

1. A.1784
2. B.1217✓
3. C.1875
4. D.1550

Correct answer: B

The correct truth table for the given input data of the following logic gate is :

1. A.ABCD = 1101: Y=1; 0011: Y=0; 1010: Y=0; 1111: Y=1✓
2. B.1101: Y=1; 0011: Y=0; 1010: Y=1; 1111: Y=0
3. C.1101: Y=0; 0011: Y=0; 1010: Y=1; 1111: Y=1
4. D.1101: Y=0; 0011: Y=1; 1010: Y=1; 1111: Y=1

Correct answer: A

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius $r=0.1$ m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is ______ m/s. (Assume string does not slip and $g=10$ m/s$^2$)

Correct answer: 2

A capacitor P with capacitance $10\times10^{-6}$ F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance $20\times10^{-6}$ F. The charge on capacitor Q when equilibrium is established will be $\alpha\times10^{-5}$ C (assume capacitor Q does not have any charge initially), the value of $\alpha$ is ______.

Correct answer: 4

A cylindrical conductor of length 2 m and area of cross-section 0.2 mm$^2$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha\times10^{-3}$ m$^2$/V.s. The value of $\alpha$ is : (electron concentration $=5\times10^{28}$/m$^3$ and electron charge $=1.6\times10^{-19}$ C)

Correct answer: 1

An insulated cylinder of volume 60 cm$^3$ is filled with a gas at $27^\circ$C and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm$^3$ while allowing the temperature to rise to $77^\circ$C. The final pressure is ______ atmospheric pressure.

Correct answer: 7

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30^\circ$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is ______ mm. (Take $\pi=\frac{22}{7}$)

Correct answer: 14

A + 2B $\to$ AB$_2$. 36.0 g of 'A' (Molar mass : 60 g mol$^{-1}$) and 56.0 g of 'B' (Molar mass : 80 g mol$^{-1}$) are allowed to react. Which of the following statements are **correct** ? A. 'A' is the limiting reagent. B. 77.0 g of AB$_2$ is formed. C. Molar mass of AB$_2$ is 140 g mol$^{-1}$. D. 15.0 g of A is left unreacted after the completion of reaction. Choose the correct answer from the options given below :

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

Correct answer: C

The energy of first (lowest) Balmer line of H atom is $x$ J. The energy (in J) of second Balmer line of H atom is :

1. A.$\frac{x}{1.35}$
2. B.$x^2$
3. C.$1.35x$✓
4. D.$2x$

Correct answer: C

At T(K), 100 g of 98% H$_2$SO$_4$ (w/w) aqueous solution is mixed with 100 g of 49% H$_2$SO$_4$ (w/w) aqueous solution. What is the mole fraction of H$_2$SO$_4$ in the resultant solution ? (Given : Atomic mass H = 1 u; S = 32 u; O = 16 u). (Assume that temperature after mixing remains constant)

1. A.0.337✓
2. B.0.1
3. C.0.9
4. D.0.663

Correct answer: A

Which of the following mixture gives a buffer solution with pH = 9.25 ? Given : p$K_b$ (NH$_4$OH) = 4.75

1. A.0.2 M NH$_4$OH (0.5 L) + 0.1 M HCl (0.5 L)✓
2. B.0.4 M NH$_4$OH (1 L) + 0.1 M HCl (1 L)
3. C.0.2 M NH$_4$OH (0.4 L) + 0.1 M HCl (1 L)
4. D.0.5 M NH$_4$OH (0.2 L) + 0.2 M HCl (0.5 L)

Correct answer: A

Consider the following reduction processes : Al$^{3+}$ + 3e$^-$ $\to$ Al(s), $E^\circ=-1.66$ V; Fe$^{3+}$ + e$^-$ $\to$ Fe$^{2+}$, $E^\circ=+0.77$ V; Co$^{3+}$ + e$^-$ $\to$ Co$^{2+}$, $E^\circ=+1.81$ V; Cr$^{3+}$ + 3e$^-$ $\to$ Cr(s), $E^\circ=-0.74$ V. The tendency to act as reducing agent decreases in the order :

1. A.Cr > Fe$^{2+}$ > Al > Co$^{2+}$
2. B.Al > Cr > Co$^{2+}$ > Fe$^{2+}$
3. C.Al > Cr > Fe$^{2+}$ > Co$^{2+}$✓
4. D.Al > Fe$^{2+}$ > Cr > Co$^{2+}$

Correct answer: C

Correct statements regarding Arrhenius equation among the following are : A. Factor $e^{-E_a/RT}$ corresponds to fraction of molecules having kinetic energy less than $E_a$. B. At a given temperature, lower the $E_a$, faster is the reaction. C. Increase in temperature by about $10^\circ$C doubles the rate of reaction. D. Plot of log k vs $\frac{1}{T}$ gives a straight line with slope $=-\frac{E_a}{R}$. Choose the correct answer from the options given below :

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

Correct answer: D

Among H$_2$S, H$_2$O, NF$_3$, NH$_3$ and CHCl$_3$, identify the molecule (X) with lowest dipole moment value. The number of lone pairs of electrons present on the central atom of the molecule (X) is :

1. A.1✓
2. B.0
3. C.3
4. D.2

Correct answer: A

Given below are two statements : Statement I : C < O < N < F is the correct order in terms of first ionization enthalpy values. Statement II : S > Se > Te > Po > O is the correct order in terms of the magnitude of electron gain enthalpy values. 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 true✓
3. C.Both Statement I and Statement II are false
4. D.Statement I is true but Statement II is false

Correct answer: B

Given below are two statements : Statement I : Elements 'X' and 'Y' are the most and least electronegative elements, respectively among N, As, Sb and P. The nature of the oxides X$_2$O$_3$ and Y$_2$O$_3$ is acidic and amphoteric, respectively. Statement II : BCl$_3$ is covalent in nature and gets hydrolysed in water. It produces [B(OH)$_4$]$^-$ and [B(H$_2$O)$_6$]$^{3+}$ in aqueous medium. 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.Both Statement I and Statement II are true
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are false

Correct answer: A

Given below are two statements : Statement I : The first ionization enthalpy of Cr is lower than that of Mn. Statement II : The second and third ionization enthalpies of Cr are higher than those of Mn. 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 true but Statement II is false✓
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are false

Correct answer: B

[Ni(PPh$_3$)$_2$Cl$_2$] is a paramagnetic complex. Identify the **INCORRECT** statements about this complex. A. The complex exhibits geometrical isomerism. B. The complex is white in colour. C. The calculated spin-only magnetic moment of the complex is 2.84 BM. D. The calculated CFSE (Crystal Field Stabilization Energy) of Ni in this complex is $-0.8\Delta_o$. E. The geometrical arrangement of ligands in this complex is similar to that in Ni(CO)$_4$. Choose the correct answer from the options given below :

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

Correct answer: C

Identify the correct statements : A. Hydrated salts can be used as primary standard. B. Primary standard should not undergo any reaction with air. C. Reactions of primary standard with another substance should be instantaneous and stoichiometric. D. Primary standard should not be soluble in water. E. Primary standard should have low relative molar mass. Choose the correct answer from the options given below :

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

Correct answer: A

When 1 g of compound (X) is subjected to Kjeldahl's method for estimation of nitrogen, 15 mL 1 M H$_2$SO$_4$ was neutralized by ammonia evolved. The percentage of nitrogen in compound (X) is :

1. A.21
2. B.42✓
3. C.0.21
4. D.0.42

Correct answer: B

The IUPAC name of the following compound is : [skeletal structure: CH$_3$CH$_2$CH(CH$_3$)CH$_2$CH$_2$CH(Br)C(=O)O$-$CH$_2$CH$_2$CH$_3$]

1. A.n-propyl-2-bromo-5-methylheptanoate✓
2. B.2-bromo-5-methylhexylpropanoate
3. C.2-bromo-5-methylpropanoate
4. D.n-propyl-1-bromo-4-methylhexanoate

Correct answer: A

Consider the following reaction : 1,2-dibromobutane (CH$_3$CH$_2$CHBrCH$_2$Br) + 2NaNH$_2$ $\to$ X $\xrightarrow{\text{(i) NaNH}_2\text{; (ii) (CH}_3)_2\text{CHBr}}$ Y. The product Y formed is :

1. A.2-methylhex-3-yne✓
2. B.2-methylhex-2-yne
3. C.5-methylhex-2-yne
4. D.Isopropylbut-1-yne

Correct answer: A

The dibromo compound [P] (molecular formula : C$_9$H$_{10}$Br$_2$) when heated with excess sodamide followed by treatment with dilute HCl gives [Q]. On warming [Q] with mercuric sulphate and dilute sulphuric acid yield [R] which gives positive Iodoform test but negative Tollen's test. The compound [P] is :

1. A.4-methyl-1,2-bis(bromomethyl)benzene (two CH$_2$Br groups ortho on a toluene ring)
2. B.1-(1,1-dibromoethyl)-4-methylbenzene ($p$-CH$_3$C$_6$H$_4$CBr$_2$CH$_3$)✓
3. C.1-methyl-4-(1,2-dibromovinyl)cyclohexa-1,4-diene type structure
4. D.(1,2-dibromopropan-2-yl)benzene (C$_6$H$_5$C(Br)(CH$_3$)CH$_2$Br)

Correct answer: B

The compound A, C$_8$H$_8$O$_2$ reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as one of the two products. The compound A is :

1. A.4-methyl benzoic acid
2. B.2-hydroxy acetophenone
3. C.4-hydroxy benzylaldehyde
4. D.4-methoxy benzaldehyde✓

Correct answer: D

3, 3-Dimethyl-2-butanol **cannot** be prepared by : A. (CH$_3$)$_3$C$-$CHO + MeMgBr (dry ether), then H$_3$O$^+$; B. the alkene drawn as CH$_3$CH$_2$C(CH$_3$)$_2$CH=CH$_2$ (skeletal drawing) with H$_2$O/H$^+$; C. (CH$_3$)$_3$C$-$C(CH$_3$)=C(CH$_3$)$-$C(CH$_3$)$_3$-type tetrasubstituted alkene with (i) O$_3$/Zn-H$_2$O (ii) NaBH$_4$/MeOH; D. (CH$_3$)$_3$C$-$CO$-$CH$_3$ with LiAlH$_4$/H$_3$O$^+$; E. (CH$_3$)$_3$C$-$C$\equiv$CH with H$_2$O, Hg$^{2+}$/H$^+$. Choose the correct answer from the options given below :

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

Correct answer: C

Cyclohexylmethanamine (C$_6$H$_{11}$CH$_2$NH$_2$) $\xrightarrow{C_6H_5COCl,\ NaOH}$ [A] $\xrightarrow{LiAlH_4,\ H_2O}$ [B]. The final product [B] is :

1. A.N-benzyl cyclohexanecarboxamide (C$_6$H$_5$CH$_2$NHCO$-$C$_6$H$_{11}$)
2. B.N-(cyclohexylmethyl)benzamide (C$_6$H$_{11}$CH$_2$NHCOC$_6$H$_5$)
3. C.N-benzyl-1-cyclohexylmethanamine (C$_6$H$_{11}$CH$_2$NHCH$_2$C$_6$H$_5$)✓
4. D.C$_6$H$_{11}$CH$_2$NH$-$CH(OH)C$_6$H$_5$