JEE Main 2025 — 29 Jan Shift 1 (Previous Year Paper)

Let $A=[a_{ij}]=\begin{bmatrix}\log_5128 & \log_45\\ \log_58 & \log_425\end{bmatrix}$. If $A_{ij}$ is the cofactor of $a_{ij}$, $C_{ij}=\sum_{k=1}^{2}a_{ik}A_{jk}$, $1\le i, j\le2$, and $C=[C_{ij}]$, then 8|C| is equal to :

1. A.262
2. B.222
3. C.288
4. D.242✓

Correct answer: D

The integral $80\int_0^{\pi/4}\left(\frac{\sin\theta+\cos\theta}{9+16\sin2\theta}\right)d\theta$ is equal to :

1. A.$2\log_e3$
2. B.$4\log_e3$✓
3. C.$3\log_e4$
4. D.$6\log_e4$

Correct answer: B

Let the line x + y = 1 meet the circle $x^2+y^2=4$ at the points A and B. If the line perpendicular to AB and passing through the mid point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ADBC is equal to :

1. A.$3\sqrt{7}$
2. B.$\sqrt{14}$
3. C.$2\sqrt{14}$✓
4. D.$5\sqrt{7}$

Correct answer: C

Let $L_1:\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}$ and $L_2:\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}$ be two lines. Let $L_3$ be a line passing through the point (α, β, γ) and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $L_1$, then |5α − 11β − 8γ| equals :

1. A.20
2. B.18
3. C.25✓
4. D.16

Correct answer: C

Let $|z_1-8-2i|\le1$ and $|z_2-2+6i|\le2$, $z_1, z_2\in\mathbf{C}$. Then the minimum value of $|z_1-z_2|$ is :

1. A.13
2. B.10
3. C.3
4. D.7✓

Correct answer: D

Let the area of the region $\{(x, y): 2y\le x^2+3, y+|x|\le3, y\ge|x-1|\}$ be A. Then 6A is equal to :

1. A.18
2. B.14✓
3. C.16
4. D.12

Correct answer: B

The number of solutions of the equation $\left(\frac{9}{x}-\frac{9}{\sqrt{x}}+2\right)\left(\frac{2}{x}-\frac{7}{\sqrt{x}}+3\right)=0$ is :

1. A.4✓
2. B.3
3. C.1
4. D.2

Correct answer: A

Let the ellipse $E_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, a > b and $E_2: \frac{x^2}{A^2}+\frac{y^2}{B^2}=1$, A < B have same eccentricity $\frac{1}{\sqrt{3}}$. Let the product of their lengths of latus rectums be $\frac{32}{\sqrt{3}}$, and the distance between the foci of $E_1$ be 4. If $E_1$ and $E_2$ meet at A, B, C and D, then the area of the quadrilateral ABCD equals :

1. A.$\frac{24\sqrt{6}}{5}$✓
2. B.$\frac{18\sqrt{6}}{5}$
3. C.$\frac{12\sqrt{6}}{5}$
4. D.$6\sqrt{6}$

Correct answer: A

Let ABC be a triangle formed by the lines 7x − 6y + 3 = 0, x + 2y − 31 = 0 and 9x − 2y − 19 = 0. Let the point (h, k) be the image of the centroid of △ABC in the line 3x + 6y − 53 = 0. Then $h^2+k^2+hk$ is equal to :

1. A.47
2. B.37✓
3. C.36
4. D.40

Correct answer: B

Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}=2\hat{i}+7\hat{j}+3\hat{k}$. Let $L_1: \vec{r}=(-\hat{i}+2\hat{j}+\hat{k})+\lambda\vec{a}$, λ ∈ R and $L_2: \vec{r}=(\hat{j}+\hat{k})+\mu\vec{b}$, μ ∈ R be two lines. If the line $L_3$ passes through the point of intersection of $L_1$ and $L_2$, and is parallel to $\vec{a}+\vec{b}$, then $L_3$ passes through the point :

1. A.(2, 8, 5)
2. B.(5, 17, 4)
3. C.(−1, −1, 1)
4. D.(8, 26, 12)✓

Correct answer: D

Define a relation R on the interval $\left[0, \frac{\pi}{2}\right)$ by x R y if and only if $\sec^2x-\tan^2y=1$. Then R is :

1. A.an equivalence relation✓
2. B.both reflexive and symmetric but not transitive
3. C.both reflexive and transitive but not symmetric
4. D.reflexive but neither symmetric not transitive

Correct answer: A

Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2 and 3 only, then the number of elements in the set P is :

1. A.158
2. B.173
3. C.161✓
4. D.164

Correct answer: C

Let $x_1, x_2, \ldots, x_{10}$ be ten observations such that $\sum_{i=1}^{10}(x_i-2)=30$, $\sum_{i=1}^{10}(x_i-\beta)^2=98$, β > 2, and their variance is $\frac{4}{5}$. If μ and $\sigma^2$ are respectively the mean and the variance of $2(x_1-1)+4\beta, 2(x_2-1)+4\beta, \ldots, 2(x_{10}-1)+4\beta$, then $\frac{\beta\mu}{\sigma^2}$ is equal to :

1. A.120
2. B.90
3. C.100✓
4. D.110

Correct answer: C

Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is :

1. A.84
2. B.108
3. C.90✓
4. D.122

Correct answer: C

The least value of n for which the number of integral terms in the Binomial expansion of $\left(\sqrt[3]{7}+\sqrt[12]{11}\right)^n$ is 183, is :

1. A.2196
2. B.2148
3. C.2184✓
4. D.2172

Correct answer: C

Let $\vec{a}=2\hat{i}-\hat{j}+3\hat{k}$, $\vec{b}=3\hat{i}-5\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}\times\vec{c}=\vec{c}\times\vec{b}$ and $(\vec{a}+\vec{c})\cdot(\vec{b}+\vec{c})=168$. Then the maximum value of $|\vec{c}|^2$ is :

1. A.77
2. B.154
3. C.462
4. D.308✓

Correct answer: D

Let y = y(x) be the solution of the differential equation $\cos x(\log_e(\cos x))^2dy+(\sin x-3y\sin x\log_e(\cos x))dx=0$, $x\in\left(0, \frac{\pi}{2}\right)$. If $y\left(\frac{\pi}{4}\right)=\frac{-1}{\log_e2}$, then $y\left(\frac{\pi}{6}\right)$ is equal to :

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

Correct answer: D

The value of $\lim_{n\to\infty}\left(\sum_{k=1}^{n}\frac{k^3+6k^2+11k+5}{(k+3)!}\right)$ is :

1. A.7/3
2. B.2
3. C.5/3✓
4. D.4/3

Correct answer: C

Let M and m respectively be the maximum and the minimum values of $f(x)=\begin{vmatrix}1+\sin^2x & \cos^2x & 4\sin4x\\ \sin^2x & 1+\cos^2x & 4\sin4x\\ \sin^2x & \cos^2x & 1+4\sin4x\end{vmatrix}$, x ∈ R. Then $M^4-m^4$ is equal to :

1. A.1215
2. B.1280✓
3. C.1295
4. D.1040

Correct answer: B

Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersects at the points A and B, then $(AB)^2$ is equal to :

1. A.96
2. B.392
3. C.384
4. D.192✓

Correct answer: D

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

Correct answer: 5

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is ______.

Correct answer: 1405

Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which $\lim_{x\to0^+}\left(x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\ldots+\left[\frac{p}{x}\right]\right)-x^2\left(\left[\frac{1}{x^2}\right]+\left[\frac{2^2}{x^2}\right]+\ldots+\left[\frac{9^2}{x^2}\right]\right)\right)\ge1$ is equal to ______.

Correct answer: 24

Let f : (0, ∞) → R be a twice differentiable function. If for some a ≠ 0, $\int_0^1f(\lambda x)d\lambda=af(x)$, f(1) = 1 and $f(16)=\frac{1}{8}$, then $16-f'\left(\frac{1}{16}\right)$ is equal to ______.

Correct answer: 112

Let $S=\{m\in\mathbf{Z}: A^{m^2}+A^m=3I-A^{-6}\}$, where $A=\begin{bmatrix}2 & -1\\ 1 & 0\end{bmatrix}$. Then n(S) is equal to ______.

Correct answer: 2

Consider $I_1$ and $I_2$ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If $L_1$ = self inductance of coil 1, $M_{12}$ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be

1. A.$\varepsilon_1=-L_1\frac{dI_1}{dt}+M_{12}\frac{dI_2}{dt}$
2. B.$\varepsilon_1=-L_1\frac{dI_1}{dt}-M_{12}\frac{dI_1}{dt}$
3. C.$\varepsilon_1=-L_1\frac{dI_1}{dt}-M_{12}\frac{dI_2}{dt}$✓
4. D.$\varepsilon_1=-L_1\frac{dI_2}{dt}-M_{12}\frac{dI_1}{dt}$

Correct answer: C

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate 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.Both (A) and (R) are true and (R) is the correct explanation of (A)✓
3. C.(A) is false but (R) is true
4. D.(A) is true but (R) is false

Correct answer: B

For the circuit shown above, equivalent GATE is : [A and B feed a NAND gate; A and B also feed a NOR gate; the NAND and NOR outputs feed a final NAND gate giving Y]

1. A.AND gate
2. B.NOT gate
3. C.OR gate✓
4. D.NAND gate

Correct answer: C

An electric dipole of mass m, charge q, and length $l$ is placed in a uniform electric field $\vec{E}=E_0\hat{i}$. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

1. A.$2\pi\sqrt{\frac{ml}{2qE_0}}$✓
2. B.$\frac{1}{2\pi}\sqrt{\frac{ml}{2qE_0}}$
3. C.$2\pi\sqrt{\frac{ml}{qE_0}}$
4. D.$\frac{1}{2\pi}\sqrt{\frac{2ml}{qE_0}}$

Correct answer: A

Match List - I with List - II. List - I: (A) Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (B) Electric field at distance r > 0 from a uniformly charged infinite plane sheet with surface charge density σ. (C) Electric field outside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ. List - II: (I) $\sigma/\epsilon_0$ (II) $\sigma/2\epsilon_0$ (III) 0 (IV) $\frac{\sigma}{\epsilon_0r^2}$. Choose the correct answer from the options given below :

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

Correct answer: C

The fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at the depth of 2.5 km below the sea level is ______ %. Given, the Bulk modulus of water = 2 × $10^9$ N $m^{-2}$, density of water = $10^3$ kg $m^{-3}$, acceleration due to gravity = g = 10 m $s^{-2}$.

1. A.1.5
2. B.1.75
3. C.1.25✓
4. D.1.0

Correct answer: C

Let u and v be the distances of the object and the image from a lens of focal length f. The correct graphical representation of u and v for a convex lens when |u| > f, is

1. A.Curve: v large near the asymptote u = f and decreasing as |u| increases (concave-down branch starting high at the dashed line)
2. B.Straight line rising towards the dashed line
3. C.Curve: v rising steeply as u approaches the dashed asymptote (u = f) from larger |u|, flattening for large |u| (rectangular-hyperbola branch)✓
4. D.U-shaped curve with vertical rises at both ends

Correct answer: C

If λ and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be

1. A.1/K vs λ: straight line through origin
2. B.1/K vs λ: decreasing curve
3. C.1/K vs λ: rising concave-down curve
4. D.1/K vs λ: rising concave-up curve (parabola through origin)✓

Correct answer: D

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum. Reason (R) : Mass of a photon is zero. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: B

Two projectiles are fired with same initial speed from same point on ground at angles of (45° − α) and (45° + α), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

1. A.$\frac{1-\tan\alpha}{1+\tan\alpha}$
2. B.$\frac{1-\sin2\alpha}{1+\sin2\alpha}$✓
3. C.$\frac{1+\sin\alpha}{1-\sin\alpha}$
4. D.$\frac{1+\sin2\alpha}{1-\sin2\alpha}$

Correct answer: B

The expression given below shows the variation of velocity (v) with time (t), $v=At^2+\frac{Bt}{C+t}$. The dimension of ABC is :

1. A.$[M^0L^2T^{-3}]$✓
2. B.$[M^0L^1T^{-3}]$
3. C.$[M^0L^2T^{-2}]$
4. D.$[M^0L^1T^{-2}]$

Correct answer: A

As shown below, bob A of a pendulum having massless string of length 'R' is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)

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

Correct answer: D

A body of mass 'm' connected to a massless and unstretchable string goes in verticle circle of radius 'R' under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is $n\sqrt{gR}$, where, n ≥ 1, then ratio of kinetic energy of the body at bottom to that at top of the circle is

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

Correct answer: A

The workdone in an adiabatic change in an ideal gas depends upon only :

1. A.change in its temperature✓
2. B.change in its specific heat
3. C.change in its pressure
4. D.change in its volume

Correct answer: A

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire\'s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

1. A.[a/4, 3a/2]
2. B.[a/4, 2a]
3. C.[a/2, 3a]
4. D.[a/2, 2a]✓

Correct answer: D

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance. Reason (R) : A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation. In the light of the above statements, choose the most appropriate 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: C

The pair of physical quantities not having same dimensions is :

1. A.Surface tension and impulse✓
2. B.Torque and energy
3. C.Pressure and Young's modulus
4. D.Angular momentum and Planck's constant

Correct answer: A

A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$. Magnetic flux φ and induced emf ε across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are :

1. A.φ = 0, ε = 0
2. B.φ = AB, ε = 0
3. C.φ = AB, ε = NABω
4. D.φ = 0, ε = NABω✓

Correct answer: D

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged. Reason (R) : By using the choke coil, the voltage across the tube is reduced by a factor $\left(R/\sqrt{R^2+\omega^2L^2}\right)$, where ω is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: D

A container of fixed volume contains a gas at 27° C. To double the pressure of the gas, the temperature of gas should be raised to ______ °C.

Correct answer: 327

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank, is ______ cm. (Take g = 10 m/s²)

Correct answer: 2000

In a hydraulic lift, the surface area of the input piston is 6 $cm^2$ and that of the output piston is 1500 $cm^2$. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ.

Correct answer: 5

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F}=\hat{i}-\hat{j}+\hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

Correct answer: 2

Two light beams fall on a transparent material block at point 1 and 2 with angle $\theta_1$ and $\theta_2$, respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, d = $4\sqrt{3}$ cm and $\theta_1=\theta_2=\cos^{-1}\left(\frac{n_2}{2n_1}\right)$, where refractive index of the block $n_2$ > refractive index of the outside medium $n_1$, then the thickness of the block is ______ cm.

Correct answer: 6

Match List - I with List - II. List - I (Structure): (A) $H_3C-CH_2-CH(C_2H_5)-CH_2-CH(CH_3)-C_2H_5$ (B) $(CH_3)_2C(C_3H_7)_2$ (C) skeletal: $CH_2=C(CH_3)-CH=CH-CH_3$... [drawn as a branched diene] (D) skeletal: $CH_2=CH-CH_2-CH(CH_3)_2$. List - II (IUPAC Name): (I) 4-Methylpent-1-ene (II) 3-Ethyl-5-methylheptane (III) 4,4-Dimethylheptane (IV) 2-Methyl-1,3-pentadiene. Choose the correct answer from the options given below :

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

Correct answer: C

The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed ?

1. A.A small decrease in molar conductivity is observed at infinite dilution.
2. B.Molar conductivity decreases sharply with increase in concentration.✓
3. C.A small increase in molar conductivity is observed at infinite dilution.
4. D.Molar conductivity increases sharply with increase in concentration.

Correct answer: B

In the following substitution reaction : 3,4-dibromonitrobenzene (Br at C-1 para to $NO_2$... i.e. 1,2-dibromo-4-nitrobenzene) $\xrightarrow{C_2H_5ONa/C_2H_5OH}$ P. Product 'P' formed is :

1. A.1-Bromo-2-ethoxy-4-nitrobenzene (OEt meta to NO2)
2. B.1,2-Diethoxy-4-nitrobenzene
3. C.2-Bromo-1-ethoxy-4-nitrobenzene (OEt para to NO2)✓
4. D.1,2-Dibromo-4-ethoxybenzene (NO2 replaced)

Correct answer: C

Match List - I with List - II. List - I (Carbohydrate): (A) Amylose (B) Cellulose (C) Glycogen (D) Amylopectin. List - II (Linkage Source): (I) β-$C_1$-$C_4$, plant (II) α-$C_1$-$C_4$, animal (III) α-$C_1$-$C_4$, α-$C_1$-$C_6$, plant (IV) α-$C_1$-$C_4$, plant. Choose the correct answer from the options given below :

1. A.(A)-(II), (B)-(III), (C)-(I), (D)-(IV)
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

At temperature T, compound $AB_{2(g)}$ dissociates as $AB_{2(g)}\rightleftharpoons AB_{(g)}+\frac{1}{2}B_{2(g)}$ having degree of dissociation x (small compared to unity). The correct expression for x in terms of $K_p$ and p is

1. A.$\sqrt[3]{\frac{2K_p}{p}}$
2. B.$\sqrt[3]{\frac{2K_p^2}{p}}$✓
3. C.$\sqrt{K_p}$
4. D.$\sqrt[4]{\frac{2K_p}{p}}$

Correct answer: B

The product (P) formed in the following reaction is : ethyl 3-acetyl-5-formylbenzoate $\xrightarrow{Zn-Hg/HCl}$ Product (P)

1. A.Ethyl 3-acetyl-5-(hydroxymethyl)benzoate
2. B.Ethyl 3-(2-hydroxyethyl)-5-(hydroxymethyl)benzoate
3. C.1,3,5-substituted benzene with CH2CH2OH, CH2OH and CH2OH
4. D.Ethyl 3-ethyl-5-methylbenzoate✓

Correct answer: D

The steam volatile compounds among the following are : (A) o-nitrophenol (B) o-nitroaniline (C) m-aminophenol (D) p-aminophenol. 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.(A), (B) and (C) Only

Correct answer: A

The reaction $A_2+B_2\to2AB$ follows the mechanism $A_2\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}}A+A$ (fast), $A+B_2\xrightarrow{k_2}AB+B$ (slow), $A+B\to AB$ (fast). The overall order of the reaction is :

1. A.3
2. B.1.5✓
3. C.2
4. D.2.5

Correct answer: B

The correct option with order of melting points of the pairs (Mn, Fe), (Tc, Ru) and (Re, Os) is :

1. A.Fe < Mn, Ru < Tc and Os < Re
2. B.Mn < Fe, Tc < Ru and Os < Re✓
3. C.Fe < Mn, Ru < Tc and Re < Os
4. D.Mn < Fe, Tc < Ru and Re < Os

Correct answer: B

An element 'E' has the ionisation enthalpy value of 374 kJ $mol^{-1}$. 'E' reacts with elements A, B, C and D with electron gain enthalpy values of −328, −349, −325 and −295 kJ $mol^{-1}$, respectively. The correct order of the products EA, EB, EC and ED in terms of ionic character is :

1. A.EA > EB > EC > ED
2. B.EB > EA > EC > ED✓
3. C.ED > EC > EB > EA
4. D.ED > EC > EA > EB

Correct answer: B

Match List - I with List - II. List - I (Complex): (A) $[MnBr_4]^{2-}$ (B) $[FeF_6]^{3-}$ (C) $[Co(C_2O_4)_3]^{3-}$ (D) $[Ni(CO)_4]$. List - II (Hybridisation & Magnetic characters): (I) $d^2sp^3$ & diamagnetic (II) $sp^3d^2$ & paramagnetic (III) $sp^3$ & diamagnetic (IV) $sp^3$ & paramagnetic. Choose the correct answer from the options given below :

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

Correct answer: D

The correct increasing order of stability of the complexes based on $\Delta_o$ value is : I. $[Mn(CN)_6]^{3-}$ II. $[Co(CN)_6]^{4-}$ III. $[Fe(CN)_6]^{4-}$ IV. $[Fe(CN)_6]^{3-}$

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

Correct answer: B

Choose the correct statements. (A) Weight of a substance is the amount of matter present in it. (B) Mass is the force exerted by gravity on an object. (C) Volume is the amount of space occupied by a substance. (D) Temperatures below 0°C are possible in Celsius scale, but in Kelvin scale negative temperature is not possible. (E) Precision refers to the closeness of various measurements for the same quantity. 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), (D) and (E) Only
4. D.(C), (D) and (E) Only✓

Correct answer: D

If $a_0$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom ? [n : any integer]

1. A.$\frac{2a_0}{n\pi}$
2. B.$\frac{4n}{\pi a_0}$
3. C.$\frac{4\pi a_0}{n}$
4. D.$\frac{8\pi a_0}{n}$✓

Correct answer: D

1.24 g of $AX_2$ (molar mass 124 g $mol^{-1}$) is dissolved in 1 kg of water to form a solution with boiling point of 100.0156°C, while 25.4 g of $AY_2$ (molar mass 250 g $mol^{-1}$) in 2 kg of water constitutes a solution with a boiling point of 100.0260°C. $K_b(H_2O)$ = 0.52 K kg $mol^{-1}$. Which of the following is correct ?

1. A.$AX_2$ is completely unionised while $AY_2$ is fully ionised.
2. B.$AX_2$ and $AY_2$ (both) are completely unionised.
3. C.$AX_2$ and $AY_2$ (both) are fully ionised.
4. D.$AX_2$ is fully ionised while $AY_2$ is completely unionised.✓

Correct answer: D

500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are : Given : R = 8.3 J $K^{-1}$ $mol^{-1}$

1. A.378 K and 300 J
2. B.368 K and 500 J
3. C.378 K and 500 J
4. D.348 K and 300 J✓

Correct answer: D

The standard reduction potential values of some of the p-block ions are given below. Predict the one with the strongest oxidising capacity.

1. A.$E^\ominus_{Al^{3+}/Al}$ = −1.66 V
2. B.$E^\ominus_{Sn^{4+}/Sn^{2+}}$ = +1.15 V
3. C.$E^\ominus_{Tl^{3+}/Tl}$ = +1.26 V
4. D.$E^\ominus_{Pb^{4+}/Pb^{2+}}$ = +1.67 V✓

Correct answer: D

Given below are two statements : Statement (I) : The radii of isoelectronic species increases in the order. $Mg^{2+}<Na^+<F^-<O^{2-}$ Statement (II) : The magnitude of electron gain enthalpy of halogen decreases in the order. Cl > F > Br > I. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: A

Total number of nucleophiles from the following is : $NH_3$, PhSH, $(H_3C)_2S$, $H_2C=CH_2$, $\overset{\ominus}{O}H$, $H_3O^\oplus$, $(CH_3)_2CO$, $(CH_3)_2C=NCH_3$

1. A.5✓
2. B.4
3. C.6
4. D.7

Correct answer: A

For a Mg | $Mg^{2+}$(aq) || $Ag^+$(aq) | Ag the correct Nernst Equation is :

1. A.$E_{cell}=E^\circ_{cell}-\frac{RT}{2F}\ln\frac{[Ag^+]}{[Mg^{2+}]}$
2. B.$E_{cell}=E^\circ_{cell}-\frac{RT}{2F}\ln\frac{[Ag^+]^2}{[Mg^{2+}]}$
3. C.$E_{cell}=E^\circ_{cell}+\frac{RT}{2F}\ln\frac{[Ag^+]^2}{[Mg^{2+}]}$✓
4. D.$E_{cell}=E^\circ_{cell}-\frac{RT}{2F}\ln\frac{[Mg^{2+}]}{[Ag^+]}$

Correct answer: C

The sum of sigma (σ) and pi (π) bonds in Hex-1,3-dien-5-yne is ______.

Correct answer: 15

Given below are some nitrogen containing compounds: p-nitroaniline, benzylamine ($C_6H_5CH_2NH_2$), acetanilide ($C_6H_5NHCOCH_3$), aniline. Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume ______ mg of HCl. (Given molar mass in g $mol^{-1}$ C : 12, H : 1, O : 16, Cl : 35.5)

Correct answer: 341

If $A_2B$ is 30% ionised in an aqueous solution, then the value of van't Hoff factor (i) is ______ × $10^{-1}$.

Correct answer: 16

The molar mass of the water insoluble product formed from the fusion of chromite ore ($FeCr_2O_4$) with $Na_2CO_3$ in presence of $O_2$ is ______ g $mol^{-1}$.

Correct answer: 160

2-(Hydroxymethyl)cyclopentan-1-ol $\xrightarrow{CrO_3\ (excess)}$ P $\xrightarrow{\text{one mole ethylene glycol}, H^+}$ Q $\xrightarrow{\text{(1) } CH_3MgI\text{ in ether; (2) } H_3O^+}$ R $\xrightarrow{\text{(1) } NaBH_4\text{ reduction; (2) } H_2O}$ 'S'. 0.1 mole of compound 'S' will weigh ______ g. (Given molar mass in g $mol^{-1}$ C : 12, H : 1, O : 16)

Correct answer: 13