JEE Main 2025 — 24 Jan Shift 2 (Previous Year Paper)

If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^2}(5+2\alpha)+\frac{1}{7^3}(5+3\alpha)+\ldots\infty$, then the value of $\alpha$ is :

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

Correct answer: B

The number of real solution(s) of the equation $x^2+3x+2=\min\{|x-3|, |x+2|\}$ is :

1. A.0
2. B.3
3. C.2✓
4. D.1

Correct answer: C

Let (2, 3) be the largest open interval in which the function $f(x)=2\log_e(x-2)-x^2+ax+1$ is strictly increasing and (b, c) be the largest open interval, in which the function $g(x)=(x-1)^3(x+2-a)^2$ is strictly decreasing. Then $100(a+b-c)$ is equal to :

1. A.280
2. B.360✓
3. C.420
4. D.160

Correct answer: B

Let $\vec{a}=3\hat{i}-\hat{j}+2\hat{k}$, $\vec{b}=\vec{a}\times(\hat{i}-2\hat{k})$ and $\vec{c}=\vec{b}\times\hat{k}$. Then the projection of $\vec{c}-2\hat{j}$ on $\vec{a}$ is :

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

Correct answer: D

Let the position vectors of three vertices of a triangle be $4\vec{p}+\vec{q}-3\vec{r}$, $-5\vec{p}+\vec{q}+2\vec{r}$ and $2\vec{p}-\vec{q}+2\vec{r}$. If the position vectors of the orthocenter and the circumcenter of the triangle are $\frac{\vec{p}+\vec{q}+\vec{r}}{4}$ and $\alpha\vec{p}+\beta\vec{q}+\gamma\vec{r}$ respectively, then $\alpha+2\beta+5\gamma$ is equal to :

1. A.6
2. B.3✓
3. C.4
4. D.1

Correct answer: B

Suppose A and B are the coefficients of $30^{th}$ and $12^{th}$ terms respectively in the binomial expansion of $(1+x)^{2n-1}$. If 2A = 5B, then n is equal to :

1. A.20
2. B.19
3. C.22
4. D.21✓

Correct answer: D

If the equation of the parabola with vertex $V\left(\frac{3}{2}, 3\right)$ and the directrix $x+2y=0$ is $\alpha x^2+\beta y^2-\gamma xy-30x-60y+225=0$, then $\alpha+\beta+\gamma$ is equal to :

1. A.7
2. B.8
3. C.9✓
4. D.6

Correct answer: C

If the system of equations $x+2y-3z=2$, $2x+\lambda y+5z=5$, $14x+3y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to :

1. A.13
2. B.10
3. C.12✓
4. D.11

Correct answer: C

The function $f:(-\infty, \infty)\to(-\infty, 1)$, defined by $f(x)=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is :

1. A.Both one-one and onto
2. B.Neither one-one nor onto
3. C.One-one but not onto✓
4. D.Onto but not one-one

Correct answer: C

The equation of the chord, of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid-point is (3, 1) is :

1. A.$25x+101y=176$
2. B.$5x+16y=31$
3. C.$48x+25y=169$✓
4. D.$4x+122y=134$

Correct answer: C

Let $f:(0, \infty)\to\mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^2f'(x)=2xf(x)+3$, with $f(1)=4$. Then 2f(2) is equal to :

1. A.29
2. B.19
3. C.39✓
4. D.23

Correct answer: C

Let $A=[a_{ij}]$ be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix. Then the probability P(E) is :

1. A.$\frac{5}{8}$
2. B.$\frac{3}{8}$✓
3. C.$\frac{3}{16}$
4. D.$\frac{1}{8}$

Correct answer: B

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to :

1. A.9100
2. B.8575
3. C.8750
4. D.8925✓

Correct answer: D

Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11$, $x+2y=16$ and $2x+3y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

1. A.33✓
2. B.55
3. C.22
4. D.44

Correct answer: A

In an arithmetic progression, if $S_{40}=1030$ and $S_{12}=57$, then $S_{30}-S_{10}$ is equal to :

1. A.505
2. B.525
3. C.510
4. D.515✓

Correct answer: D

The area of the region enclosed by the curves $y=e^x$, $y=|e^x-1|$ and y-axis is :

1. A.$\log_e2$
2. B.$1+\log_e2$
3. C.$2\log_e2-1$
4. D.$1-\log_e2$✓

Correct answer: D

Let $A=\left\{x\in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log_{(2/\pi)}|\sin x|+\log_{(2/\pi)}|\cos x|=2\right\}$ and $B=\{x\ge0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $n(A\cup B)$ is equal to :

1. A.4
2. B.8✓
3. C.2
4. D.6

Correct answer: B

Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f(x)=[x]+|x-2|$, $-2<x<3$, is not continuous and not differentiable. Then m + n is equal to :

1. A.8✓
2. B.9
3. C.6
4. D.7

Correct answer: A

For some a, b, let $f(x)=\begin{vmatrix}a+\frac{\sin x}{x} & 1 & b\\ a & 1+\frac{\sin x}{x} & b\\ a & 1 & b+\frac{\sin x}{x}\end{vmatrix}$, $x\neq0$, $\lim_{x\to0}f(x)=\lambda+\mu a+\nu b$. Then $(\lambda+\mu+\nu)^2$ is equal to :

1. A.25
2. B.36
3. C.9
4. D.16✓

Correct answer: D

If $\alpha>\beta>\gamma>0$, then the expression $\cot^{-1}\left\{\beta+\frac{(1+\beta^2)}{(\alpha-\beta)}\right\}+\cot^{-1}\left\{\gamma+\frac{(1+\gamma^2)}{(\beta-\gamma)}\right\}+\cot^{-1}\left\{\alpha+\frac{(1+\alpha^2)}{(\gamma-\alpha)}\right\}$ is equal to :

1. A.0
2. B.$\frac{\pi}{2}-(\alpha+\beta+\gamma)$
3. C.$3\pi$
4. D.$\pi$✓

Correct answer: D

Let $y=y(x)$ be the solution of the differential equation $2\cos x\frac{dy}{dx}=\sin2x-4y\sin x$, $x\in\left(0, \frac{\pi}{2}\right)$. If $y\left(\frac{\pi}{3}\right)=0$, then $y'\left(\frac{\pi}{4}\right)+y\left(\frac{\pi}{4}\right)$ is equal to ______.

Correct answer: 1

If $\int\frac{2x^2+5x+9}{\sqrt{x^2+x+1}}dx=x\sqrt{x^2+x+1}+\alpha\sqrt{x^2+x+1}+\beta\log_e\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|+C$, where C is the constant of integration, then $\alpha+2\beta$ is equal to ______.

Correct answer: 16

Number of functions $f:\{1, 2, \ldots, 100\}\to\{0, 1\}$, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to ______.

Correct answer: 392

Let $H_1: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $H_2: -\frac{x^2}{A^2}+\frac{y^2}{B^2}=1$ be two hyperbolas having length of latus rectums $15\sqrt{2}$ and $12\sqrt{5}$ respectively. Let their ecentricities be $e_1=\sqrt{\frac{5}{2}}$ and $e_2$ respectively. If the product of the lengths of their transverse axes is $100\sqrt{10}$, then $25e_2^2$ is equal to ______.

Correct answer: 55

Let P be the image of the point Q(7, −2, 5) in the line L: $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$ and R(5, p, q) be a point on L. Then the square of the area of $\triangle PQR$ is ______.

Correct answer: 957

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
2. B.(A) is true but (R) is false
3. C.Both (A) and (R) are true and (R) is the correct explanation of (A)✓
4. D.(A) is false but (R) is true

Correct answer: C

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

1. A.zero
2. B.$40\pi$
3. C.$5\pi$✓
4. D.$10\pi$

Correct answer: C

The output of the circuit is low (zero) for : [X and Y feed an OR gate whose output feeds both inputs of a NAND gate] (A) X=0, Y=0 (B) X=0, Y=1 (C) X=1, Y=0 (D) X=1, Y=1. Choose the correct answer from the options given below :

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

Correct answer: B

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4\times10^{-8}$C charge and then removed to a distance such that the force of repulsion between them is $9\times10^{-3}$ N. The distance between them is (Take $\frac{1}{4\pi\epsilon_0}$ as $9\times10^9$ in SI units)

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

Correct answer: B

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $P_1$ and $P_2$ are orthogonal to each other. The polarizer $P_3$ covers both the slits with its transmission axis at 45° to those of $P_1$ and $P_2$. An unpolarized light of wavelength $\lambda$ and intensity $I_0$ is incident on $P_1$ and $P_2$. The intensity at a point after $P_3$ where the path difference between the light waves from $s_1$ and $s_2$ is $\frac{\lambda}{3}$, is

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

Correct answer: B

The temperature of a body in air falls from 40°C to 24°C in 4 minutes. The temperature of the air is 16°C. The temperature of the body in the next 4 minutes will be :

1. A.$\frac{56}{3}$ °C✓
2. B.$\frac{42}{3}$ °C
3. C.$\frac{28}{3}$ °C
4. D.$\frac{14}{3}$ °C

Correct answer: A

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures ?

1. A.Straight line with positive slope, C-intercept negative (crosses the F-axis at a positive F)✓
2. B.Straight line with negative slope through the origin
3. C.Straight line with negative slope, positive C-intercept
4. D.Straight line with positive slope through the origin

Correct answer: A

In the first configuration (1) as shown in the figure, four identical charges ($q_0$) are kept at the corners A, B, C and D of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points G, E, H and F, of the square. If $K=\frac{1}{4\pi\epsilon_0}$, the difference between the potential energies of configuration (2) and (1) is given by :

1. A.$\frac{Kq_0^2}{a}(3-\sqrt{2})$
2. B.$\frac{Kq_0^2}{a}(3\sqrt{2}-2)$✓
3. C.$\frac{Kq_0^2}{a}(4-2\sqrt{2})$
4. D.$\frac{Kq_0^2}{a}(4\sqrt{2}-2)$

Correct answer: B

Arrange the following in the ascending order of wavelength ($\lambda$) : (A) Microwaves ($\lambda_1$) (B) Ultraviolet rays ($\lambda_2$) (C) Infrared rays ($\lambda_3$) (D) X-rays ($\lambda_4$). Choose the most appropriate answer from the options given below :

1. A.$\lambda_4<\lambda_2<\lambda_3<\lambda_1$✓
2. B.$\lambda_4<\lambda_3<\lambda_1<\lambda_2$
3. C.$\lambda_3<\lambda_4<\lambda_2<\lambda_1$
4. D.$\lambda_4<\lambda_3<\lambda_2<\lambda_1$

Correct answer: A

A long straight wire of a circular cross-section with radius 'a' carries a steady current I. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by

1. A.B decreases exponentially from $B_0$ at r = 0 (to $B_0/e$ at r = a)
2. B.B = 0 inside, jumps at r = a and then decreases as 1/r
3. C.B increases linearly from 0 to r = a and then decreases as 1/r✓
4. D.B constant inside and then decreases as 1/r

Correct answer: C

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. A.$E^2=pc^2+m^2c^2$
2. B.$E^2=p^2c^2+m^2c^2$
3. C.$E^2=p^2c^2+m^2c^4$✓
4. D.$E^2=pc^2+m^2c^4$

Correct answer: C

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

1. A.$t_1=2t_2$
2. B.$t_1<t_2$✓
3. C.$t_1>t_2$
4. D.$t_1=t_2$

Correct answer: B

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :

1. A.(A) is false but (R) is true✓
2. B.Both (A) and (R) are true and (R) is the correct explanation of (A)
3. C.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
4. D.(A) is true but (R) is false

Correct answer: A

In photoelectric effect, the stopping potential ($V_0$) v/s frequency ($\nu$) curve is plotted. (h is the Planck's constant and $\phi_0$ is work function of metal) (A) $V_0$ v/s $\nu$ is linear. (B) The slope of $V_0$ v/s $\nu$ curve $=\frac{\phi_0}{h}$ (C) h constant is related to the slope of $V_0$ v/s $\nu$ line. (D) The value of electric charge of electron is not required to determine h using the $V_0$ v/s $\nu$ curve. (E) The work function can be estimated without knowing the value of h. Choose the correct answer from the options given below :

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

Correct answer: D

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

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

Correct answer: D

Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm. The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m, will be :

1. A.0.63 mm
2. B.0.33 mm
3. C.0.46 mm
4. D.0.23 mm✓

Correct answer: D

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm × 2 cm and the area of the landscape photographed is 400 $km^2$. The focal length of the lens in the drone camera is :

1. A.2.5 cm
2. B.0.9 cm
3. C.1.8 cm✓
4. D.2.8 cm

Correct answer: C

The position vector of a moving body at any instant of time is given as $\vec{r}=(5t^2\hat{i}-5t\hat{j})$m. The magnitude and direction of velocity at t = 2s is,

1. A.$5\sqrt{15}$ m/s, making an angle of $\tan^{-1}4$ with −ve Y axis
2. B.$5\sqrt{15}$ m/s, making an angle of $\tan^{-1}4$ with +ve X axis
3. C.$5\sqrt{17}$ m/s, making an angle of $\tan^{-1}4$ with +ve X axis
4. D.$5\sqrt{17}$ m/s, making an angle of $\tan^{-1}4$ with −ve Y axis✓

Correct answer: D

A particle oscillates along the x-axis according to the law, $x(t)=x_0\sin^2\left(\frac{t}{2}\right)$ where $x_0$ = 1 m. The kinetic energy (K) of the particle as a function of x is correctly represented by the graph

1. A.K is maximum at x = 0 and x = 1 and zero at x = 1/2 (U-shaped parabola)
2. B.K is zero at x = 0 and x = 1 and maximum at x = 1/2 (inverted parabola)✓
3. C.K flat near x = 0 and 1, dropping to a cusp at zero at x = 1/2
4. D.K zero at x = 0 and 1 with a cusp maximum at x = 1/2

Correct answer: B

N equally spaced charges each of value q, are placed on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A-I_B$, for the given Amperian loops is

1. A.$\frac{N}{2\pi}q\omega$✓
2. B.$\frac{2\pi}{N}q\omega$
3. C.$\frac{N}{\pi}q\omega$
4. D.$\frac{N^2}{2\pi}q\omega$

Correct answer: A

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ______ g.

Correct answer: 9

The increase in pressure required to decrease the volume of a water sample by 0.2% is $P\times10^5\ Nm^{-2}$. Bulk modulus of water is $2.15\times10^9\ Nm^{-2}$. The value of P is ______.

Correct answer: 43

The ratio of the power of a light source $S_1$ to that the light source $S_2$ is 2. $S_1$ is emitting $2\times10^{15}$ photons per second at 600 nm. If the wavelength of the source $S_2$ is 300 nm, then the number of photons per second emitted by $S_2$ is ______ $\times10^{14}$.

Correct answer: 5

A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes $\left(\frac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ______ ML.

Correct answer: 36

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is ______. [Take mass of electron $m_e=9\times10^{-31}$ kg, charge of electron $|q_e|=1.6\times10^{-19}$ C, $\mu_0=4\pi\times10^{-7}\ \frac{N}{A^2}$, 1 ns = $10^{-9}$ s]

Correct answer: 250

When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be :

1. A.Green → Pale Blue → Blue → Violet✓
2. B.Violet → Blue → Pale Blue → Green
3. C.Pale Blue → Blue → Green → Violet
4. D.Pale Blue → Blue → Violet → Green

Correct answer: A

Given below are two statements : Statement (I) : [graph of $t_{1/2}$ vs $[R]_0$ is a horizontal line] is valid for first order reaction. Statement (II) : [graph of $\log\frac{[R]}{[R]_0}$ vs time is a straight line through the origin with positive slope = $\frac{k}{2.303}$] is valid for first order 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 false
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are true
4. D.Statement I is true but Statement II is false✓

Correct answer: D

Match List - I with List - II. List - I: (A) Adenine (B) Cytosine (C) Thymine (D) Uracil. List - II: (I) pyrimidine-2,4-dione (uracil skeleton, no methyl) (II) 5-methylpyrimidine-2,4-dione (III) 6-aminopurine (IV) 4-aminopyrimidin-2-one. 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)-(IV), (B)-(III), (C)-(II), (D)-(I)

Correct answer: A

Given below are two statements : Statement (I) : The first ionization energy of Pb is greater than that of Sn. Statement (II) : The first ionization energy of Ge is greater than that of Si. In the light of the above statements, choose the correct answer from the options given below :

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

Correct answer: A

For the reaction, $H_2(g)+I_2(g)\rightleftharpoons2HI(g)$. Attainment of equilibrium is predicted correctly by :

1. A.$H_2$ and $I_2$ curves fall from high values and level off ($H_2$ above $I_2$); HI rises from 0 and levels off below both✓
2. B.All three ($H_2$, $I_2$, HI) rise from 0 and level off
3. C.$H_2$ rises and levels off at top; $I_2$ and HI fall and level off
4. D.$I_2$ rises and levels off at top; $H_2$ falls; HI rises and levels off below

Correct answer: A

In the given structure, number of sp and $sp^2$ hybridized carbon atoms present respectively are : $CH_3-CO-CH=CH-CH_2-C\equiv C-CH=CH-C\equiv N$

1. A.4 and 6
2. B.4 and 5
3. C.3 and 6
4. D.3 and 5✓

Correct answer: D

Given below are two statements : Statement (I) : Experimentally determined oxygen-oxygen bond lengths in the $O_3$ are found to be same and the bond length is greater than that of a O=O (double bond) but less than that of a single (O−O) bond. Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond (O=O) but more than that of a single bond (O−O). 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.Both Statement I and Statement II are false
4. D.Statement I is false but Statement II is true

Correct answer: B

For hydrogen atom, the orbital/s with lowest energy is/are : (A) 4s (B) $3p_x$ (C) $3d_{x^2-y^2}$ (D) $3d_{z^2}$ (E) $4p_z$. Choose the correct answer from the options given below :

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

Correct answer: D

$S(g)+\frac{3}{2}O_2(g)\to SO_3(g)+2x$ kcal; $SO_2(g)+\frac{1}{2}O_2(g)\to SO_3(g)+y$ kcal. The heat of formation of $SO_2(g)$ is given by :

1. A.y − 2x kcal✓
2. B.$\frac{2x}{y}$ kcal
3. C.x + y kcal
4. D.2x + y kcal

Correct answer: A

The conditions and consequence that favours the $t_{2g}^3e_g^1$ configuration in a metal complex are :

1. A.strong field ligand, high spin complex
2. B.strong field ligand, low spin complex
3. C.weak field ligand, low spin complex
4. D.weak field ligand, high spin complex✓

Correct answer: D

Match List - I with List - II. List - I: (A) $RCN\xrightarrow{\text{(i) } SnCl_2, HCl;\ \text{(ii) } H_3O^+}RCHO$ (B) Benzoyl chloride $\xrightarrow{H_2, Pd-BaSO_4}$ benzaldehyde (C) Toluene $\xrightarrow{\text{(i) } CrO_2Cl_2, CS_2;\ \text{(ii) } H_3O^+}$ benzaldehyde (D) Benzene $\xrightarrow{\text{(i) CO, HCl; (ii) anhydrous } AlCl_3/CuCl}$ benzaldehyde. List - II: (I) Etard reaction (II) Gatterman-Koch reaction (III) Rosenmund reduction (IV) Stephen reaction. Choose the correct answer from the options given below :

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

Correct answer: D

The structure of the major product formed in the following reaction is : 3-bromo-5-iodobenzyl chloride $\xrightarrow{AgCN}$ major product

1. A.1-bromo-3-(chloromethyl)-5-cyanobenzene (CN replaces ring I)
2. B.3-bromo-5-iodobenzyl cyanide ($ArCH_2CN$)
3. C.3-bromo-5-iodobenzyl isocyanide ($ArCH_2NC$)✓
4. D.3-iodo-5-cyanobenzyl chloride (CN replaces ring Br)

Correct answer: C

Based on the data given below : $E^\circ_{Cr_2O_7^{2-}/Cr^{3+}}=1.33$ V, $E^\circ_{Cl_2/Cl^-}=1.36$ V, $E^\circ_{MnO_4^-/Mn^{2+}}=1.51$ V, $E^\circ_{Cr^{3+}/Cr}=-0.74$ V, the strongest reducing agent is :

1. A.$MnO_4^-$
2. B.$Mn^{2+}$
3. C.$Cl^-$
4. D.Cr✓

Correct answer: D

The successive 5 ionisation energies of an element are 800, 2427, 3658, 25024 and 32824 kJ/mol, respectively. By using the above values predict the group in which the above element is present :

1. A.Group 13✓
2. B.Group 4
3. C.Group 2
4. D.Group 14

Correct answer: A

For reaction Aniline $\to$ 2-Bromoaniline (Major). The correct order of set of reagents for the above conversion is :

1. A.$Ac_2O$, $Br_2$, $H_2O(\Delta)$, NaOH
2. B.$H_2SO_4$, $Ac_2O$, $Br_2$, $H_2O(\Delta)$, NaOH✓
3. C.$Ac_2O$, $H_2SO_4$, $Br_2$, NaOH
4. D.$Br_2|FeBr_3$, $H_2O(\Delta)$, NaOH

Correct answer: B

Find the compound 'A' from the following reaction sequences. A $\xrightarrow{\text{aqua-regia}}$ B $\xrightarrow{\text{(1) } KNO_2|NH_4OH;\ \text{(2) AcOH}}$ yellow ppt

1. A.NiS
2. B.ZnS
3. C.MnS
4. D.CoS✓

Correct answer: D

The elemental composition of a compound is 54.2% C, 9.2% H and 36.6% O. If the molar mass of the compound is 132 g $mol^{-1}$, the molecular formula of the compound is : [Given : The relative atomic mass of C : H : O = 12 : 1 : 16]

1. A.$C_4H_8O_2$
2. B.$C_6H_{12}O_6$
3. C.$C_4H_9O_3$
4. D.$C_6H_{12}O_3$✓

Correct answer: D

Which of the following mixing of 1M base and 1M acid leads to the largest increase in temperature ?

1. A.30 mL $CH_3COOH$ and 30 mL NaOH
2. B.45 mL $CH_3COOH$ and 25 mL NaOH
3. C.30 mL HCl and 30 mL NaOH✓
4. D.50 mL HCl and 20 mL NaOH

Correct answer: C

Match List - I with List - II. List - I (Transition metal ion): (A) $Ti^{3+}$ (B) $V^{2+}$ (C) $Ni^{2+}$ (D) $Sc^{3+}$. List - II (Spin only magnetic moment (B.M.)): (I) 3.87 (II) 0.00 (III) 1.73 (IV) 2.84. Choose the correct answer from the options given below :

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

Correct answer: A

Identify correct statement/s : (A) $-OCH_3$ and $-NHCOCH_3$ are activating group. (B) −CN and −OH are meta directing group. (C) −CN and $-SO_3H$ are meta directing group. (D) Activating groups act as ortho - and para directing groups. (E) Halides are activating groups. Choose the correct answer from the options given below :

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

Correct answer: B

Consider a complex reaction taking place in three steps with rate constants $k_1$, $k_2$ and $k_3$ respectively. The overall rate constant k is given by the expression $k=\sqrt{\frac{k_1k_3}{k_2}}$. If the activation energies of the three steps are 60, 30 and 10 kJ $mol^{-1}$ respectively, then the overall energy of activation in kJ $mol^{-1}$ is ______. (Nearest integer)

Correct answer: 20

The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is ______.

Correct answer: 4

In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr). The percentage of Bromine in the organic compound is ______ $\times10^{-1}$% (Nearest integer). (Given : Molar mass of Ag is 108 and Br is 80 g $mol^{-1}$)

Correct answer: 255

The hydrocarbon (X) with molar mass 80 g $mol^{-1}$ and 90% carbon has ______ degree of unsaturation.

Correct answer: 3

The observed and normal molar masses of compound $MX_2$ are 65.6 and 164 respectively. The percent degree of ionisation of $MX_2$ is ______%. (Nearest integer)

Correct answer: 75