JEE Main 2026 — 6 Apr Shift 1 (Previous Year Paper)

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

1. A.2
2. B.5✓
3. C.10
4. D.13

Correct answer: B

Let one root of the quadratic equation in $x$: $(k^2-15k+27)x^2+9(k-1)x+18=0$ be twice the other. Then the length of the latus rectum of the parabola $y^2=6kx$ is equal to:

1. A.4
2. B.6
3. C.8
4. D.12✓

Correct answer: D

Let $e_1$ and $e_2$ be two distinct roots of the equation $x^2-ax+2=0$. Let the sets $\{a\in\mathbb{R} : e_1 \text{ and } e_2 \text{ are the eccentricities of hyperbolas}\}=(\alpha,\beta)$, and $\{a\in\mathbb{R} : e_1 \text{ and } e_2 \text{ are the eccentricities of an ellipse and a hyperbola, respectively}\}=(\gamma,\infty)$. Then $\alpha^2+\beta^2+\gamma^2$ is equal to:

1. A.18
2. B.22
3. C.26✓
4. D.34

Correct answer: C

Let the set of all values of $k\in\mathbb{R}$ such that the equation $z(\bar z+2+i)+k(2+3i)=0$, $z\in\mathbb{C}$, has at least one solution, be the interval $[\alpha,\beta]$. Then $9(\alpha+\beta)$ is equal to:

1. A.$-10$✓
2. B.$-8$
3. C.$10\sqrt{13}$
4. D.$8\sqrt{13}$

Correct answer: A

The value of $1^3-2^3+3^3-\dots+15^3$ is:

1. A.1706
2. B.1856✓
3. C.1982
4. D.2403

Correct answer: B

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

1. A.$\frac{34}{9}$✓
2. B.$\frac{34}{13}$
3. C.$\frac{32}{9}$
4. D.$\frac{32}{13}$

Correct answer: A

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

1. A.2670
2. B.2840
3. C.2920
4. D.3600✓

Correct answer: D

If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}$, $\alpha\ne0$, are equal, then the value of $\alpha$ is:

1. A.1
2. B.$\frac{14}{13}$
3. C.$\frac{27}{7}$
4. D.$\frac{7}{27}$✓

Correct answer: D

A data consists of 20 observations $x_1,x_2,\dots,x_{20}$. If $\sum_{i=1}^{20}(x_i+5)^2=2500$ and $\sum_{i=1}^{20}(x_i-5)^2=100$, then the ratio of mean to standard deviation of this data is:

1. A.2:1
2. B.3:1✓
3. C.3:2
4. D.4:1

Correct answer: B

A bag contains $(N+1)$ coins $-$ N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$, then N is equal to:

1. A.5
2. B.7✓
3. C.8
4. D.9

Correct answer: B

If the eccentricity $e$ of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, passing through $(6,4\sqrt3)$, satisfies $15(e^2+1)=34e$, then the length of the latus rectum of the hyperbola $\frac{x^2}{b^2}-\frac{y^2}{2(a^2+1)}=1$ is:

1. A.10✓
2. B.20
3. C.25
4. D.30

Correct answer: A

Let chord PQ of length $3\sqrt{13}$ of the parabola $y^2=12x$ be such that the ordinates of points P and Q are in the ratio 1:2. If the chord PQ subtends an angle $\alpha$ at the focus of the parabola, then $\sin\alpha$ is equal to:

1. A.$\frac35$✓
2. B.$\frac45$
3. C.$\frac{5}{13}$
4. D.$\frac{12}{13}$

Correct answer: A

Let $0<\alpha<1$, $\beta=\frac{1}{3\alpha}$ and $\tan^{-1}(1-\alpha)+\tan^{-1}(1-\beta)=\frac{\pi}{4}$. Then $6(\alpha+\beta)$ is equal to:

1. A.6
2. B.7✓
3. C.8
4. D.9

Correct answer: B

Let $S=\{\theta\in(-2\pi,2\pi) : \cos\theta+1=\sqrt3\sin\theta\}$. Then $\sum_{\theta\in S}\theta$ is equal to:

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

Correct answer: B

Let the image of the point $P(1,6,a)$ in the line $L : \frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}$, $b>0$, be $\left(\frac{a}{3},0,a+c\right)$. If $S(\alpha,\beta,\gamma)$, $\alpha>0$, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is $2\sqrt{14}$, then $\alpha+\beta+\gamma$ is equal to:

1. A.19
2. B.20
3. C.21✓
4. D.22

Correct answer: C

Let a line L be perpendicular to both the lines $L_1 : \frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $L_2 : \frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$. If $\theta$ is the acute angle between the lines L and $L_3 : \frac{x-\frac87}{2}=\frac{y-\frac47}{1}=\frac{z}{2}$, then $\tan\theta$ is equal to:

1. A.$\frac32\sqrt2$
2. B.$\frac52\sqrt2$✓
3. C.$\frac53\sqrt2$
4. D.$\frac43\sqrt2$

Correct answer: B

The value of $\lim_{x\to0}\left(\frac{x^2\sin^2x}{x^2-\sin^2x}\right)$ is:

1. A.2
2. B.3✓
3. C.4
4. D.6

Correct answer: B

The value of the integral $\int_{-\pi/4}^{\pi/4}\left(\frac{32\cos^4x}{1+e^{\sin x}}\right)dx$ is:

1. A.$4\pi+2$
2. B.$3\pi+8$✓
3. C.$3\pi+4$
4. D.$4\pi+3$

Correct answer: B

The area of the region $\{(x,y) : 0\le y\le6-x, y^2\ge4x-3, x\ge0\}$ is:

1. A.8
2. B.9✓
3. C.12
4. D.15

Correct answer: B

Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\}\to\{1,e,e^2,e^3\}$ and $g:\{1,e,e^2,e^3\}\to\left\{1,\frac12,\frac13,\frac14\right\}$ be two bijective functions such that $f$ is strictly decreasing and $g$ is strictly increasing. If $\phi(x)=\left[f^{-1}\left\{g^{-1}\left(\frac12\right)\right\}\right]^x$, then the area of the region $R=\{(x,y) : x^2\le y\le\phi(x), 0\le x\le1\}$ is:

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

Correct answer: A

Let $A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix}$ satisfy $A^2+\alpha\left(\operatorname{adj}(\operatorname{adj}(A))\right)+\beta\left(\operatorname{adj}(A)\left(\operatorname{adj}(\operatorname{adj}(A))\right)\right)=\begin{bmatrix}2&-2&2\\-2&0&-1\\0&0&-1\end{bmatrix}$ for some $\alpha,\beta\in\mathbb{R}$. Then $(\alpha-\beta)^2$ is equal to ______

Correct answer: 4

Let the centre of the circle $x^2+y^2+2gx+2fy+25=0$ be in the first quadrant and lie on the line $2x-y=4$. Let the area of an equilateral triangle inscribed in the circle be $27\sqrt3$. Then the square of the length of the chord of the circle on the line $x=1$ is ______.

Correct answer: 80

If $\vec a=\hat i+\hat j+\hat k$, $\vec b=\hat j-\hat k$ and $\vec c$ be three vectors such that $\vec a\times\vec c=\vec b$ and $\vec a\cdot\vec c=3$, then $\vec c\cdot\left(\vec a-2\vec b\right)$ is equal to ______.

Correct answer: 3

For the functions $f(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta$, and $g(\theta)=\alpha\sin^2\theta+\beta\cos^2\theta$, $\alpha>\beta>0$, let $\min_{0<\theta<\frac{\pi}{2}}f(\theta)=\max_{0<\theta<\pi}g(\theta)$. If the first term of a G.P. is $\left(\frac{\alpha}{2\beta}\right)$, its common ratio is $\left(\frac{2\beta}{\alpha}\right)$ and the sum of its first 10 terms is $\frac{m}{n}$, $\gcd(m,n)=1$, then $m+n$ is equal to ______.

Correct answer: 1279

Let $y=y(x)$ be the solution of the differential equation $\left(x^2-x\sqrt{x^2-1}\right)dy+\left(y\left(x-\sqrt{x^2-1}\right)-x\right)dx=0$, $x\ge1$. If $y(1)=1$, then the greatest integer less than $y(\sqrt5)$ is ______.

Correct answer: 3

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m$, $l$ and $d$ are $97.42\pm0.02$ g, $8.35\pm0.05$ mm and $20.20\pm0.02$ mm, respectively. Calculated percentage fractional error in $\rho$ is ______.

1. A.0.63%
2. B.0.82%✓
3. C.0.72%
4. D.0.25%

Correct answer: B

The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A\sqrt x}{x+B}$, where A and B are constant with appropriate dimensions. The dimensions of AB are ______.

1. A.$[M^1L^{5/2}T^{-2}]$
2. B.$[M^{3/2}L^{5/2}T^{-2}]$
3. C.$[M^1L^2T^{-2}]$
4. D.$[M^1L^{7/2}T^{-2}]$✓

Correct answer: D

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is ______ J. (take $g=10\ \mathrm{m/s^2}$)

1. A.$-8.75$
2. B.$-8.35$
3. C.$-9.55$
4. D.$-9.98$✓

Correct answer: D

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient friction $\mu$. The cube (S) moves towards the right with acceleration of $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block P and Q remain stationary. The value of $\mu$ is ______. (take $g=10\ \mathrm{m/s^2}$)

1. A.0.33
2. B.0.67✓
3. C.1
4. D.0.5

Correct answer: B

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4\times10^8\ \mathrm{N/m^2}$ and its radius is 4 mm, then maximum acceleration the lift can take is ______ $\mathrm{m/s^2}$. (take $g=10\ \mathrm{m/s^2}$ and $\pi=3.14$)

1. A.2.56✓
2. B.3.89
3. C.4.32
4. D.5.16

Correct answer: A

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ______ respectively.

1. A.$0.128\pi$ Nm, 100
2. B.$0.0128\pi$ Nm, 50
3. C.$0.128\pi$ Nm, 50
4. D.$0.0128\pi$ Nm, 100✓

Correct answer: D

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h=\alpha R$. The value of $\alpha$ is ______.

1. A.2
2. B.4✓
3. C.3
4. D.6

Correct answer: B

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point (p) of normal bisector, as shown in the figure is ______.

1. A.$\left(\frac{\sqrt3}{4},1.25\right)$✓
2. B.$\left(\frac{\sqrt3}{4},1.0\right)$
3. C.(0,0)
4. D.(1.25,0)

Correct answer: A

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is ______ m.

1. A.1.1
2. B.2.22
3. C.1.21✓
4. D.4.44

Correct answer: C

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ______ kPa.

1. A.100✓
2. B.120
3. C.90
4. D.105

Correct answer: A

In interference experiment the path difference between two interfering waves at a point A on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point B the path difference is $\lambda/6$. The ratio of intensities at points A and B is ______.

1. A.3
2. B.4
3. C.1/3✓
4. D.1/4

Correct answer: C

A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from $x=A$ to $x=\frac{A}{\sqrt2}$ is ______ sec.

1. A.1/4
2. B.5/4
3. C.5/8✓
4. D.3/8

Correct answer: C

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is ______ nC. ($\epsilon_0=8.85\times10^{-12}\ \mathrm{C^2/Nm^2}$ and $\pi=3.14$)

1. A.2.14✓
2. B.2.44
3. C.3.25
4. D.0.7

Correct answer: A

The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage of 5 V as shown in the figure below. The current through resistance $R_S$ is 0.5 mA. The minimum value of the resistance of $R_S$, to ensure that the LED is not damaged is ______ k$\Omega$.

1. A.6
2. B.2✓
3. C.4
4. D.5

Correct answer: B

A point light source emits E.M. waves in free space. A detector, placed at a distance of L m, measures the intensity as $I_0$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as 45°. The measured intensity at new location will be ______.

1. A.$\frac{I_0}{4}$
2. B.$I_0$✓
3. C.$\frac{I_0}{\sqrt2}$
4. D.$\frac{I_0}{2}$

Correct answer: B

A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4R in front of spherical interface. The magnitude of the magnification of point source image is ______.

1. A.1.66✓
2. B.2.33
3. C.2.66
4. D.1.33

Correct answer: A

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha\times10^{-14}$ J. The value of $\alpha$ is ______. ($\mu_0=4\pi\times10^{-7}$ Tm/A, $\pi=3.14$)

1. A.6.28✓
2. B.$6.28\times10^{-6}$
3. C.628
4. D.$6.28\times10^{-4}$

Correct answer: A

An inductor of inductance 10 mH having resistance of 100 $\Omega$ is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is ______.

1. A.4/3✓
2. B.3/4
3. C.5/3
4. D.3/5

Correct answer: A

The ratio of momentum of the photons of the $1^{st}$ and $2^{nd}$ line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

1. A.27 and 20
2. B.3 and 16
3. C.5 and 36
4. D.20 and 27✓

Correct answer: D

A LCR series circuit driven with $E_{rms}=90$ V at frequency $f_d=30$ Hz has resistance $R=80\ \Omega$, an inductance with inductive reactance $X_L=20.0\ \Omega$ and capacitance with capacitive reactance $X_C=80.0\ \Omega$. The power factor of the circuit is ______.

1. A.0.8✓
2. B.0.64
3. C.0.9
4. D.0.5

Correct answer: A

Refer to the circuit diagram given below. The heat generated across the 6 $\Omega$ resistance in 100 second is $\frac{\alpha}{100}$ J. The value of $\alpha$ is ______. (Nearest integer)

Correct answer: 3477

An unpolarized light of intensity $I_0$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is 0° and intensity of light emerged from analyser is $\frac38I_0$, the angle of rotation of the light by the solution with respect to analyser is ______ degrees.

Correct answer: 30

The energy released when $\frac{7}{17.13}$ kg of ${}^7_3Li$ is converted into ${}^4_2He$ by proton bombardment is $\alpha\times10^{32}$ eV. The value of $\alpha$ is ______. (Nearest integer) (Mass of ${}^7_3Li$ = 7.0183 u, mass of ${}^4_2He$ = 4.004 u, mass of proton = 1.008 u and 1 u = 931 MeV/$c^2$ and Avogadro number = $6.0\times10^{23}$)

Correct answer: 6

A three coulomb charge moves from the point $(0,-2,-5)$ to the point $(5,1,2)$ in an electric field expressed as $\vec E=2x\hat i+3y^2\hat j+4\hat k$ N/C. The work done in moving the charge is ______ J.

Correct answer: 186

A certain gas is isothermally compressed to $\left(\frac13\right)^{rd}$ of its initial volume ($V_0$ = 3 litre) by applying required pressure. If the bulk modulus of the gas is $3\times10^5\ \mathrm{N/m^2}$, the magnitude of work done on the gas is ______ J.

Correct answer: 600

An oxide of iron contains 69.9% iron, its empirical formula, is: (Given : Molar mass of Fe and O are 56 and 16 g $\mathrm{mol^{-1}}$ respectively.)

1. A.FeO
2. B.$\mathrm{Fe_2O_3}$✓
3. C.$\mathrm{Fe_3O_4}$
4. D.$\mathrm{FeO_3}$

Correct answer: B

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $\mathrm{He^+}$ is:

1. A.$\frac{9x}{5}$✓
2. B.$\frac{36x}{5}$
3. C.$\frac{x}{4}$
4. D.$\frac{5x}{9}$

Correct answer: A

Match the LIST-I with LIST-II. LIST-I (Orbital) : A. 2s B. 3s C. 3p D. 4d. LIST-II (Radial nodes and nodal plane) : I. 1 Radial node + two nodal planes II. 1 Radial node + one nodal plane III. 2 Radial nodes + No nodal plane IV. 1 Radial node + No nodal plane. Choose the correct answer from the options given below:

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

Correct answer: D

The pairs among $A=[\mathrm{SO_3^{2-}, CO_3^{2-}}]$, $B=[\mathrm{O_2^{2-}, F_2}]$, $C=[\mathrm{CN^-, CO}]$, $D=[\mathrm{NH_3, H_3O^+}]$ and $E=[\mathrm{MnO_4^{2-}, CrO_4^{2-}}]$ that do not have similar Lewis dot structure are

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

Correct answer: B

Arrange the following isothermal processes in order of the magnitude of the work (p $-$ V) involved between states 1 and 2. A. Expansion in single stage $w_A$ B. Expansion in multi stages $w_B$ C. Compression in single stage $w_C$ D. Compression in multi stages $w_D$. Choose the correct option.

1. A.$|w_B|>|w_A|>|w_C|>|w_D|$
2. B.$|w_C|>|w_D|>|w_A|>|w_B|$
3. C.$|w_C|>|w_D|>|w_B|>|w_A|$✓
4. D.$|w_B|>|w_A|>|w_D|>|w_C|$

Correct answer: C

When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was $x$ % of vapor pressure of pure solvent. What is $x$ %?

1. A.50%
2. B.60%
3. C.70%
4. D.80%✓

Correct answer: D

One mole each of He and A(g) are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium. $\mathrm{A(g)\rightleftharpoons B(g)}$. $K_c$ for this reaction at 400 K is 4.0. The partial pressures (in atm) of He and B(g) are respectively (at equilibrium) (Assume He, A(g) and B(g) behave as ideal gases) (Given : R = 0.082 L atm $\mathrm{K^{-1}mol^{-1}}$)

1. A.3.28, 2.624✓
2. B.2.624, 3.28
3. C.3.28, 0.656
4. D.0.656, 6.56

Correct answer: A

Consider the following data. Electrolyte : $\Lambda^\circ_m$ (S $\mathrm{cm^2\,mol^{-1}}$) — $\mathrm{BaCl_2}$ : $x_1$; $\mathrm{H_2SO_4}$ : $x_2$; HCl : $x_3$. $\mathrm{BaSO_4}$ is sparingly soluble in water. If the conductivity of the saturated $\mathrm{BaSO_4}$ solution is $x$ S $\mathrm{cm^{-1}}$ then the solubility product of $\mathrm{BaSO_4}$ can be given as (Here $\Lambda_m=\Lambda^\circ_m$)

1. A.$\frac{10^6x^2}{\alpha^2(x_1+x_2-2x_3)^2}$✓
2. B.$\frac{x^2}{(x_1+x_2-2x_3)^2}$
3. C.$\frac{\alpha^2(x_1+x_2-2x_3)^2}{10^6x^2}$
4. D.$\frac{x^2}{(x_1+x_2+2x_3)^2}$

Correct answer: A

Given below are two statements: Statement I: Aluminium is more electropositive than thallium as the standard electrode potential value of $E^\circ_{\mathrm{Al^{3+}/Al}}$ is negative and $E^\circ_{\mathrm{Tl^{3+}/Tl}}$ is positive. Statement II: The sum of first three ionization enthalpies of boron is very high when compared to that of aluminium. Due to this reason boron forms covalent compounds only and aluminium forms $\mathrm{Al^{3+}}$ ion. 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. Basic vanadium oxide is used in the manufacture of $\mathrm{H_2SO_4}$. B. The spin-only magnetic moment value of the transition metal halide employed in Ziegler-Natta polymerization is 2.84 BM. C. The p-block metal compound employed in Ziegler-Natta polymerization has the metal in +3 oxidation state. D. The number of electrons present in the outer most 'd' orbital of metal halide employed in Wacker process is 8. Choose the correct answer from the options given below:

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

Correct answer: C

Match the LIST-I with LIST-II. LIST-I (Electronic configuration of tetrahedral metal ion) : A. $d^2$ B. $d^4$ C. $d^6$ D. $d^8$. LIST-II (Crystal Field Stabilization Energy, $\Delta_t$) : I. $-0.6$ II. $-0.8$ III. $-1.2$ IV. $-0.4$. Choose the correct answer from the options given below:

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

Correct answer: C

Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex? A. $d_{xy}=d_{xz}>d_{x^2-y^2}$ B. $d_{xy}=d_{yz}>d_{z^2}$ C. $d_{x^2-y^2}>d_{z^2}>d_{xz}$ D. $d_{x^2-y^2}=d_{z^2}<d_{xz}$. Choose the correct answer from the given below:

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

Correct answer: A

$R_f$ value for 2-methylpropene in a solvent system (Ethyl acetate + ether) is 0.42. 2-methylpropene is treated with dilute $\mathrm{H_2SO_4}$ to give major organic product (X). $R_f$ value for (X) in the same solvent system under identical condition will be:

1. A.0.42
2. B.0.82
3. C.0.62
4. D.0.12✓

Correct answer: D

Given below are two statements: Statement I: 2,6-diethylcyclohexanone and 6-methyl-2-n-propylcyclohexanone are metamers. Statement II: 2,2,6,6-tetramethylcyclohexanone exhibits keto-enol tautomerism. 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: C

Given below are two statements: Statement I: Methane can be prepared by decarboxylation of sodium ethanoate, Kolbe's electrolysis of sodium acetate and reaction of $\mathrm{CH_3MgBr}$ with water. Statement II: Methane cannot be prepared from unsaturated hydrocarbons and by Wurtz reaction. 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

Given below are two statements: Statement I: 3-phenylpropene reacts with HBr and gives secondary alkyl bromide having a chiral carbon atom as the major product. Statement II: Aryl chlorides and aryl cyanides can be prepared by Sandmeyer reaction as well as Gattermann reaction. 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: C

Consider the following sequence of reactions: tert-butyl alcohol $\mathrm{(CH_3)_3C-OH}$ $\xrightarrow{\mathrm{(i)\ Cu/573K;\ (ii)\ H^+,\ PhCOOH}}$ P. The major product P is:

1. A.4-tert-butylbenzoic acid
2. B.3-tert-butylbenzoic acid✓
3. C.tert-butyl benzoate, $\mathrm{C_6H_5COOC(CH_3)_3}$
4. D.2-methylallyl benzoate, $\mathrm{C_6H_5COOCH_2C(CH_3)=CH_2}$

Correct answer: B

Arrange the following compounds according to increasing order of boiling points. n-$\mathrm{C_4H_9OH}$ (A), n-$\mathrm{C_4H_9NH_2}$ (B), n-$\mathrm{C_4H_{10}}$ (C) and $\mathrm{C_2H_5NHC_2H_5}$ (D).

1. A.C < B < A < D
2. B.D < C < B < A
3. C.C < D < B < A✓
4. D.D < B < A < C

Correct answer: C

Match the LIST-I with LIST-II. LIST-I (Deficiency Disease) : A. Scurvy B. Convulsions C. Cheilosis D. Xerophthalmia. LIST-II (Vitamin) : I. Pyridoxine II. Vitamin A III. Ascorbic Acid IV. Riboflavin. Choose the correct answer from the options given below:

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

Correct answer: C

Match the LIST-I with LIST-II. LIST-I (Amino acid) : A. Glutamine B. Lysine C. Tyrosine D. Serine. LIST-II (Positive reaction/Test for functional group present in side chain of amino acid) : I. Hinsberg's test II. Neutral $\mathrm{FeCl_3}$ test III. Ceric ammonium nitrate test IV. Hoffman bromamide degradation. Choose the correct answer from the options given below:

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

Correct answer: B

First and second ionization enthalpies of lithium are 520 kJ $\mathrm{mol^{-1}}$ and 7297 kJ $\mathrm{mol^{-1}}$ respectively. Energy required to convert 3.5 mg lithium (g) into $\mathrm{Li^{2+}(g)}$ [$\mathrm{Li(g)\rightarrow Li^{2+}(g)}$] is ______ kJ $\mathrm{mol^{-1}}$. (nearest integer) [Molar mass of Li = 7 g $\mathrm{mol^{-1}}$]

Correct answer: 4

Consider the following sequence of reactions. Diazoaminobenzene ($\mathrm{C_6H_5-N=N-NH-C_6H_5}$) $\xrightarrow{\mathrm{(i)\ HCl;\ (ii)\ Aniline\ (in\ excess);\ (iii)\ Warm\ 40-45^\circ C;\ (iv)\ Cool,\ acetic\ acid}}$ Yellow Product (X). The percentage of nitrogen in the yellow product (X) formed is ______ %. (Nearest Integer) (Given Molar mass in g $\mathrm{mol^{-1}}$ H:1, C:12, N:14)

Correct answer: 21

4.7 g of phenol is heated with Zn to give product X. If this reaction goes to 60% completion then the number of moles of compound X formed will be ______ $\times10^{-2}$. (Nearest Integer) (Given molar mass in g $\mathrm{mol^{-1}}$ : H:1, C:12, O:16)

Correct answer: 3

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1/2}$ = 3 hour. The percentage of sucrose remaining after 6 hours is ______. (Nearest integer) (Given : log 2 = 0.3010 and log 3 = 0.4771)

Correct answer: 25

Consider the reaction $\mathrm{X\rightleftharpoons Y}$ at 300 K. If $\Delta H^\ominus$ and K are 28.40 kJ $\mathrm{mol^{-1}}$ and $1.8\times10^{-7}$ at the same temperature, then the magnitude of $\Delta S^\ominus$ for the reaction in J $\mathrm{K^{-1}mol^{-1}}$ is ______. (Nearest integer) (Given : R = 8.3 J $\mathrm{K^{-1}mol^{-1}}$, ln 10 = 2.3, log 3 = 0.48, log 2 = 0.30)

Correct answer: 34