JEE Main 2026 — 4 Apr Shift 1 (Previous Year Paper)

Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\cos^{-1}\left(\frac{4x+2[x]}{3}\right)$ is $[\alpha,\beta]$, then $12(\alpha+\beta)$ is equal to:

1. A.6✓
2. B.8
3. C.9
4. D.4

Correct answer: A

If the set of all solutions of $|x^2+x-9|=|x|+|x^2-9|$ is $[\alpha,\beta]\cup[\gamma,\infty)$, then $(\alpha^2+\beta^2+\gamma^2)$ is equal to:

1. A.9
2. B.18✓
3. C.36
4. D.72

Correct answer: B

Let z be a complex number such that $|z+2|=|z-2|$ and $\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}$. Then $|z|^2$ is equal to:

1. A.9✓
2. B.4
3. C.5
4. D.1

Correct answer: A

The number of functions $f:\{1,2,3,4\}\to\{a,b,c\}$, which are not onto, is:

1. A.48
2. B.45✓
3. C.51
4. D.35

Correct answer: B

Let $S=\left\{A=\begin{bmatrix}a&b\\c&d\end{bmatrix} : a,b,c,d\in\{0,1,2,3,4\} \text{ and } A^2-4A+3I=0\right\}$ be a set of $2\times2$ matrices. Then the number of matrices in S, for which the sum of the diagonal elements is equal to 4, is:

1. A.20
2. B.17
3. C.21
4. D.19✓

Correct answer: D

Let $A=\begin{bmatrix}1&1&2\\-2&0&1\\1&3&5\end{bmatrix}$. Then the sum of all elements of the matrix $\operatorname{adj}\left(\operatorname{adj}\left(2(\operatorname{adj}A)^{-1}\right)\right)$ is equal to:

1. A.3
2. B.4
3. C.$-4$
4. D.$-3$✓

Correct answer: D

The first term of an A.P. of 30 non-negative terms is $\frac{10}{3}$. If the sum of this A.P. is the cube of its last term, then its common difference is:

1. A.$\frac{5}{87}$✓
2. B.$\frac{25}{83}$
3. C.$\frac{15}{29}$
4. D.$\frac{5}{29}$

Correct answer: A

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

1. A.5040
2. B.3050
3. C.3410
4. D.4320✓

Correct answer: D

Let the smallest value of $k\in\mathbb{N}$, for which the coefficient of $x^3$ in $(1+x)^3+(1+x)^4+(1+x)^5+\dots+(1+x)^{99}+(1+kx)^{100}$, $x\ne0$, is $\left(43n+\frac{101}{4}\right)\left({}^{100}C_3\right)$ for some $n\in\mathbb{N}$, be $p$. Then the value of $p+n$ is:

1. A.10
2. B.11✓
3. C.12
4. D.13

Correct answer: B

Suppose that the mean and median of the non-negative numbers 21, 8, 17, $a$, 51, 103, $b$, 13, 67, $(a>b)$, are 40 and 21, respectively. If the mean deviation about the median is 26, then $2a$ is equal to:

1. A.109
2. B.117
3. C.161
4. D.131✓

Correct answer: D

Let the line $L_1 : x+3=0$ intersect the lines $L_2 : x-y=0$ and $L_3 : 3x+y=0$ at the points A and B, respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point C. Then $BC^2 : AC^2$ is equal to:

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

Correct answer: A

Let the vertex A of a triangle ABC be $(1,2)$, and the mid-point of the side AB be $(5,-1)$. If the centroid of this triangle is $(3,4)$ and its circumcenter is $(\alpha,\beta)$, then $21(\alpha+\beta)$ is equal to:

1. A.309
2. B.403
3. C.497✓
4. D.524

Correct answer: C

Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3y=0$ are bisected by the $y$-axis. If the other ends of these chords are R and S, and the mid point of the line segment RS is $(\alpha,\beta)$, then $6(\alpha+\beta)$ is equal to:

1. A.1
2. B.3✓
3. C.4
4. D.6

Correct answer: B

A line with direction ratios $1,-1,2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and $\frac{x+1}{-1}=\frac{y-2}{1}=\frac{z}{4}$ at the points P and Q, respectively. If the length of the line segment PQ is $\alpha$, then $225\alpha^2$ is equal to:

1. A.1024
2. B.1014✓
3. C.1104
4. D.1204

Correct answer: B

The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line $\frac{x+5}{1}=\frac{y+5}{-1}=\frac{z}{2}$ is equal to:

1. A.3
2. B.6✓
3. C.8
4. D.12

Correct answer: B

If $y=\tan^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2\tan^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right)$, then $\frac{dy}{dx}$ at $x=\frac{\sqrt3}{2}$ is equal to:

1. A.3
2. B.$-1$
3. C.1✓
4. D.2

Correct answer: C

Let $f$ be a real polynomial of degree n such that $f(x)=f'(x)f''(x)$, for all $x\in\mathbb{R}$. If $f(0)=0$, then $36\left(f'(2)+f''(2)+\int_0^2f(x)dx\right)$ is equal to:

1. A.42
2. B.46
3. C.56✓
4. D.66

Correct answer: C

The area of the region $\{(x,y) : y\le\pi-|x|, y\le|x\sin x|, y\ge0\}$ is:

1. A.$1+\frac{\pi^2}{8}$
2. B.$2+\frac{\pi^2}{4}$✓
3. C.$\frac{\pi^2}{8}-1$
4. D.$4+\frac{\pi^2}{2}$

Correct answer: B

Let $\int_{-2}^{2}\left(|\sin x|+[x\sin x]\right)dx=2(3-\cos2)+\beta$, where $[\cdot]$ is the greatest integer function. Then $\beta\sin\left(\frac{\beta}{2}\right)$ equals:

1. A.1
2. B.2✓
3. C.4
4. D.8

Correct answer: B

Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\left(1+x+x^2\right)\left(1-y+y^2\right)$, $y(0)=\frac12$. Then $(2y(1)-1)$ is equal to

1. A.$\sqrt3\tan\left(\frac{11\sqrt3}{6}\right)$
2. B.$\frac{\sqrt3}{2}\tan\left(\frac{11\sqrt3}{12}\right)$
3. C.$\sqrt3\tan\left(\frac{11\sqrt3}{12}\right)$✓
4. D.$\frac{\sqrt3}{2}\tan\left(\frac{11\sqrt3}{6}\right)$

Correct answer: C

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is $p$, then $96p$ is equal to ______.

Correct answer: 9

Consider the parabola $P : y^2=4kx$ and the ellipse $E : \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Let the line segment joining the points of intersection of P and E, be their latus rectums. If the eccentricity of E is $e$, then $e^2+2\sqrt2$ is equal to ______.

Correct answer: 3

If $A=\frac{\sin3^\circ}{\cos9^\circ}+\frac{\sin9^\circ}{\cos27^\circ}+\frac{\sin27^\circ}{\cos81^\circ}$ and $B=\tan81^\circ-\tan3^\circ$, then $\frac{B}{A}$ is equal to ______.

Correct answer: 2

Let $\vec a_k=(\tan\theta_k)\hat i+\hat j$ and $\vec b_k=\hat i-(\cot\theta_k)\hat j$, where $\theta_k=\frac{2^{k-1}\pi}{2^n+1}$, for some $n\in\mathbb{N}$, $n>5$. Then the value of $\frac{\sum_{k=1}^{n}|\vec a_k|^2}{\sum_{k=1}^{n}|\vec b_k|^2}$ is ______.

Correct answer: 3

The number of points, at which the function $f(x)=\max\{6x, 2+3x^2\}+|x-1|\cos\left|x^2-\frac14\right|$, $x\in(-\pi,\pi)$, is not differentiable, is ______.

Correct answer: 3

In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least count of screw gauge is ______ mm.

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

Correct answer: D

The increase in the pressure required to decrease the volume ($\Delta V$) of water is $6.3\times10^7\ \mathrm{N/m^2}$. The percentage decrease in the volume is ______. (Bulk modulus of water = $2.1\times10^9\ \mathrm{N/m^2}$.)

1. A.2 %
2. B.3 %✓
3. C.6 %
4. D.4 %

Correct answer: B

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is 50 % more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at 45° with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ______.

1. A.3/4
2. B.2/3
3. C.5/9✓
4. D.4/9

Correct answer: C

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, $\Delta Mc^2$ = ______ MeV.

1. A.6.9
2. B.7.9
3. C.2.2✓
4. D.4.3

Correct answer: C

A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The smaller part having mass $M/8$ is converted into a sphere of radius $r$ and the larger part is converted into a circular disc of thickness $t$ and radius $2R$. If $I_1$ is moment of inertia of a sphere having radius $r$ about an axis through its centre and $I_2$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $I_2/I_1$ = ______.

1. A.35
2. B.70✓
3. C.140
4. D.210

Correct answer: B

The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is $1:x$. The value of $x$ is

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

Correct answer: B

The graph shows variation of stopping potential $V_0$ with the frequency $\nu$ of the incident radiation for three photosensitive metals $X_1$, $X_2$ and $X_3$. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

1. A.$X_1$✓
2. B.$X_2$
3. C.$X_3$
4. D.All the metals will give out photo electrons with same kinetic energies.

Correct answer: A

A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{st}$ and $3^{rd}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is ______.

1. A.$\frac{D\lambda}{a}$
2. B.$1.5\frac{D\lambda}{a}$
3. C.$2\frac{D\lambda}{a}$✓
4. D.$3\frac{D\lambda}{a}$

Correct answer: C

A string A of length 0.314 m and Young's modulus $2\times10^{10}\ \mathrm{N/m^2}$ is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is ______ mm. (radius of both the strings is 0.2 mm and acceleration due to gravity = 10 $\mathrm{m/s^2}$) (Mass of both strings is to be neglected as compared to the mass of load)

1. A.3
2. B.2✓
3. C.1.9
4. D.1

Correct answer: B

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is ______.

1. A.$(T_1+T_2)/2$
2. B.$T_1T_2PV/(T_2P_1V_1+T_1P_2V_2)$✓
3. C.$(T_2P_1V_1+T_1P_2V_2)/(T_1T_2PV)$
4. D.$|T_1-T_2|/2$

Correct answer: B

A voltmeter with internal resistance of $x\ \Omega$ can be used to measure upto 20 V. In order to increase its measuring range to 30 V, the required modification is to ______.

1. A.connect resistor of $\frac{x}{2}\ \Omega$, in series with voltmeter.✓
2. B.connect resistor of $\frac{x}{2}\ \Omega$, in parallel to voltmeter.
3. C.connect a resistor of $x\ \Omega$ in series with voltmeter.
4. D.connect resistor of $2x\ \Omega$ in parallel to voltmeter.

Correct answer: A

Two 4 bits binary numbers, $A=1101$ and $B=1010$ are given in the inputs of a logic circuit shown in figure below. The output ($Y$) will be :

1. A.Y = 1101✓
2. B.Y = 0010
3. C.Y = 0111
4. D.Y = 1000

Correct answer: A

A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.

1. A.2.5
2. B.5✓
3. C.7.5
4. D.7

Correct answer: B

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is ______.

1. A.$-2$✓
2. B.1
3. C.$-1$
4. D.2

Correct answer: A

An insulated wire is wound so that it forms a flat coil with $N=200$ turns. The radius of the innermost turn is $r_1=3$ cm, and of the outermost turn $r_2=6$ cm. If 20 mA current flows in it then the magnetic moment will be $\alpha\times10^{-2}\ \mathrm{A\,m^2}$. The value of $\alpha$ is ______.

1. A.4.4
2. B.2.64✓
3. C.3.25
4. D.1.2

Correct answer: B

Consider a circuit consisting of a capacitor (20 $\mu$F), resistor (100 $\Omega$) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 $\Omega$. The time constant of the circuit is $\alpha\times10^{-3}$ s. The value of $\alpha$ is ______.

1. A.2.2✓
2. B.2.0
3. C.2.1
4. D.2.4

Correct answer: A

The voltage and the current between A and B points shown in the circuit are ______.

1. A.24 V, 12 A
2. B.24 V, 4 A✓
3. C.18 V, 12 A
4. D.27 V, 4 A

Correct answer: B

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5\times10^{-7}$ radian. The value of $R$ is ______ cm.

1. A.61
2. B.122✓
3. C.244
4. D.305

Correct answer: B

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

1. A.$(E_x\hat i+E_y\hat j)\sin(kx-kz-\omega t)$✓
2. B.$(E_x\hat i+E_z\hat k)\sin(kx+ky-\omega t)$
3. C.$(E_x\hat j+E_y\hat k)\sin(ky+kz-\omega t)$
4. D.$(E_x\hat i+E_y\hat j+E_z\hat k)\sin(kx+ky-kz-\omega t)$

Correct answer: A

A 1 kg block subjected to two simultaneous forces $\left(2\hat i+3\hat j+4\hat k\right)$ N and $\left(3\hat i-\hat j-2\hat k\right)$ N is moved a distance of 25 m along $\left(3\hat i-4\hat j\right)$ direction. The work done in this process is ______ J.

Correct answer: 35

The surface tension of a soap solution is $3.5\times10^{-2}$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha\times10^{-6}$ J. The value of $\alpha$ is ______. ($\pi=22/7$)

Correct answer: 264

The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2=50-x^2$, where $x$ represents displacement. If the time period of motion is $\frac{x}{7}$ s, the value of $x$ is ______.

Correct answer: 44

A body of mass 2 kg begins to move under the influence of time dependent force $\vec F=\left(2t\hat i+6t^2\hat j\right)$ N, where $\hat i$ and $\hat j$ are unit vectors along $x$ and $y$-axis respectively. The power produced by the force at $t=2$ s is ______ W.

Correct answer: 200

An inductor of 10 mH, capacitor of 0.1 $\mu$F and a resistor of 100 $\Omega$ are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is $\sqrt3\,\alpha\ \Omega$. The value of $\alpha$ is ______.

Correct answer: 100

Number of moles and number of molecules in 1.4187 L of $\mathrm{SO_2}$ at STP respectively are

1. A.0.1266; $3.812\times10^{22}$
2. B.0.0633; $3.812\times10^{22}$✓
3. C.0.1266; $7.6238\times10^{22}$
4. D.0.0633; $7.6238\times10^{22}$

Correct answer: B

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

1. A.5:1
2. B.5:0.81✓
3. C.5:1.75
4. D.5:27

Correct answer: B

Which of the following is correct set of 4 quantum numbers of $19^{th}$ electron in Chromium (Atomic number = 24) in accordance with Aufbau principle?

1. A.$n=3, l=2, m=+2, s=+\frac12$
2. B.$n=3, l=2, m=-2, s=+\frac12$
3. C.$n=4, l=1, m=0, s=+\frac12$
4. D.$n=4, l=0, m=0, s=+\frac12$✓

Correct answer: D

Given below are two statements: Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure. Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: D

At T(K), the equilibrium constant of $\mathrm{A_2(g)+B_2(g)\rightleftharpoons C(g)}$ is $2.7\times10^{-5}$. What is the equilibrium constant for $\mathrm{\frac13A_2(g)+\frac13B_2(g)\rightleftharpoons\frac13C(g)}$ at the same temperature?

1. A.$(2.7\times10^{-5})^3$
2. B.$6\times10^{-2}$
3. C.$\sqrt{2.7\times10^{-5}}$
4. D.$3\times10^{-2}$✓

Correct answer: D

In order to oxidise a mixture of 1 mole each of $\mathrm{FeC_2O_4}$, $\mathrm{Fe_2(C_2O_4)_3}$, $\mathrm{FeSO_4}$ and $\mathrm{Fe_2(SO_4)_3}$ in acidic medium, the number of moles of $\mathrm{KMnO_4}$ required is

1. A.3
2. B.2✓
3. C.5
4. D.7

Correct answer: B

Consider the first order reaction R $\rightarrow$ P. The fraction of molecules decomposed in the given first order reaction can be expressed as

1. A.$1-e^{k_1t}$
2. B.$1+e^{k_1t}$
3. C.$1+e^{-k_1t}$
4. D.$1-e^{-k_1t}$✓

Correct answer: D

A monoatomic anion ($\mathrm{A^-}$) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element (A) respectively are

1. A.80, 17, liquid✓
2. B.81, 16, solid
3. C.80, 16, gas
4. D.81, 15, gas

Correct answer: A

Given below are two statements: Statement I: The covalency of oxygen is generally two but it can exceed upto four. The oxidation state of oxygen in $\mathrm{SO_2}$ is $-2$ and in $\mathrm{OF_2}$ it is $+2$. Statement II: The anomalous behaviour of oxygen when compared to the other elements of group 16 is due to its small size and high electronegativity. 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 correct statements among the following are, A. Mo(VI) and W(VI) are less stable than Cr(VI). B. $\mathrm{Ce^{4+}}$ and $\mathrm{Tb^{4+}}$ are oxidant while $\mathrm{Eu^{2+}}$ and $\mathrm{Yb^{2+}}$ are reductant. C. Cm and Am have seven unpaired electrons. D. Actinoid contraction is greater from element to element than lanthanoid contraction. Choose the correct answer from the options given below:

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

Correct answer: C

Correct statements from the following are A. Potassium dichromate is an oxidising agent and it oxidises $\mathrm{FeSO_4}$ to $\mathrm{Fe_2(SO_4)_3}$ in acidic medium. B. Sodium dichromate can be used as primary standard in volumetric estimation. C. $\mathrm{CrO_4^{2-}}$ and $\mathrm{Cr_2O_7^{2-}}$ are interconvertible in aqueous solution by varying the pH of the solution. D. Cr-O-Cr bond angle in $\mathrm{Cr_2O_7^{2-}}$ is 126°. Choose the correct answer from the options given below:

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

Correct answer: B

Match the LIST-I with LIST-II. LIST-I (Complex ion) : A. $\mathrm{[Cr(H_2O)_6]^{2+}}$ B. $\mathrm{[Co(H_2O)_6]^{2+}}$ C. $\mathrm{[Cu(H_2O)_6]^{2+}}$ D. $\mathrm{[Mn(H_2O)_6]^{2+}}$. LIST-II (Calculated spin only magnetic moment, BM) : I. 3.87 II. 5.92 III. 4.90 IV. 1.73. Choose the correct answer from the options given below:

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

Correct answer: D

Increasing order of electron withdrawing power of following functional groups is: a. $-$CN b. $-$COOH c. $-\mathrm{NO_2}$ d. $-$I

1. A.c < b < d < a
2. B.c < a < b < d
3. C.d < b < a < c✓
4. D.a < b < c < d

Correct answer: C

An alkene (X) on ozonolysis followed by reduction gives following products : HCHO (2 moles), $\mathrm{OHC-CO-CHO}$ and $\mathrm{CH_3-CO-CO-CO-CH_3}$. The alkene (X) is:

1. A.Structure (A): one ring C=C, two exocyclic =CH2, two CH3 (see figure description)
2. B.Structure (B): one ring C=C, three exocyclic =CH2, one CH3 (see figure description)
3. C.Structure (C): two ring C=C, two exocyclic =CH2, three CH3 (see figure description)
4. D.Structure (D): ring C=C at C6=C1 and C3=C4, CH3 at C1 and C3, exocyclic =CH2 at C2 and C5 (see figure description)✓

Correct answer: D

Match the LIST-I with LIST-II. LIST-I (Name of reaction) : A. Finkelstein reaction B. Swarts reaction C. Sandmeyer's reaction D. Fittig reaction. LIST-II (Reagent or catalyst used) : I. $\mathrm{SbF_3}$ II. Na, dry ether III. NaI IV. $\mathrm{Cu_2Cl_2}$. Choose the correct answer from the options given below:

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

Correct answer: B

Amongst the following, the total number of compounds soluble in aqueous NaOH at room temperature is: (I) benzaldehyde (II) 1-naphthol (III) 4-(dimethylamino)phenol (IV) 4-methylphenol (V) benzoic acid (VI) N,N-dimethylcyclohexanamine (VII) naphthalene-1-carboxylic acid (VIII) 1,4-di-tert-butylbenzene (IX) (naphthalen-1-yl)methanol

1. A.5✓
2. B.4
3. C.6
4. D.3

Correct answer: A

Product C of the following reaction sequence will be : Aniline $\xrightarrow{\mathrm{Br_2/water}}$ A (Major Product) $\xrightarrow{\mathrm{NaNO_2/HCl,\ 273-278\ K}}$ B $\xrightarrow{\mathrm{(i)\ HBF_4;\ (ii)\ NaNO_2,\ Cu,\ \Delta}}$ C

1. A.1-Bromo-4-nitrobenzene
2. B.1, 3, 5-Tribromo-2-nitrobenzene✓
3. C.4-Bromo-1-nitrobenzene
4. D.1, 3, 5-Tribromobenzene

Correct answer: B

Given below are two statements: Statement I: The structure of Maltose is given below (two glucopyranose units joined by an O-glycosidic bridge between C1 of one unit and C4 of the other, the second unit having a free anomeric OH). Maltose is a non-reducing sugar. Statement II: The structure of Lactose is given below (a galactopyranose unit linked through C1 to C4 of a glucopyranose unit that has a free anomeric OH). Lactose is a reducing sugar. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: D

Match the LIST-I with LIST-II. LIST-I (Name of amino acid) : A. Arginine B. Aspartic acid C. Lysine D. Glutamic acid. LIST-II (One letter symbol/type) : I. D/Non-essential II. R/Essential III. E/Non-essential IV. K/Essential. Choose the correct answer from the options given below:

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

Correct answer: A

Identify the colour of compound 'X' in the sequence of the reaction. 2 Phenol + phthalic anhydride $\xrightarrow{\text{conc. }\mathrm{H_2SO_4}}$ phenolphthalein (lactone) $\xrightarrow{\mathrm{NaOH}}$ quinonoid dianion (Pink) $\xrightarrow{\text{Excess NaOH}}$ X, where X is the carbinol trianion $\mathrm{(^-OC_6H_4)_2C(OH)-C_6H_4-COO^-}$.

1. A.Violet
2. B.Green
3. C.Red
4. D.Colourless✓

Correct answer: D

According to Lewis theory, the total number of $\sigma$ bond-pairs and lone pair of electrons around the central atom of $\mathrm{XeO_6^{4-}}$ ion is ______.

Correct answer: 6

Consider the following sequence of reactions to give the major product (X) : Benzene $\xrightarrow{\mathrm{(i)\ CH_3Cl/anhydrous\ AlCl_3;\ (ii)\ Cl_2/FeCl_3;\ (iii)\ K_2Cr_2O_7/H_2SO_4}}$ (X) Major Product. P g of the major product (X) formed is reacted with $\mathrm{NaHCO_3}$ solution to liberate a gas which occupied 11.2 $\mathrm{dm^3}$ at STP. P = ______ g. (Given molar mass in g $\mathrm{mol^{-1}}$ H:1, C:12, O:16, Cl:35.5)

Correct answer: 78

2.0 g of a bromo hydrocarbon (X) was subjected to Carius analysis, gave 3.36 g of AgBr. The percentage of carbon in the compound (X) is 26.7%. Total number of carbon atoms in the empirical formula for compound (X) is ______. (Given molar mass in g $\mathrm{mol^{-1}}$ H:1, C:12, Br : 80, Ag : 108)

Correct answer: 5

The pH of a solution obtained by mixing 5 mL of 0.1 M $\mathrm{NH_4OH}$ solution with 250 mL of 0.1 M $\mathrm{NH_4Cl}$ solution is ______ $\times10^{-2}$. (Nearest integer) Given: $pK_b(\mathrm{NH_4OH})=4.74$, log 2 = 0.30, log 3 = 0.48, log 5 = 0.70

Correct answer: 756

A non-volatile, non-electrolyte solid solute when dissolved in 40 g of a solvent, the vapour pressure of the solvent decreased from 760 mm Hg to 750 mm Hg. If the same solution boils at 320 K, then the number of moles of the solvent present in the solution is ______. (Nearest integer) [Given: boiling point of the pure solvent = 319.5 K, $K_b$ of the solvent = 0.3 K kg $\mathrm{mol^{-1}}$]

Correct answer: 5