JEE Main 2025 — 23 Jan Shift 1 (Previous Year Paper)

Let $I(x)=\int\frac{dx}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $I(37)-I(24)=\frac{1}{4}\left(\frac{1}{b^{\frac{1}{13}}}-\frac{1}{c^{\frac{1}{13}}}\right)$, $b, c\in\mathbf{N}$, then $3(b+c)$ is equal to

1. A.26
2. B.40
3. C.39✓
4. D.22

Correct answer: C

Let $f(x)=\log_ex$ and $g(x)=\frac{x^4-2x^3+3x^2-2x+2}{2x^2-2x+1}$. Then the domain of $f\circ g$ is

1. A.$\mathbf{R}$✓
2. B.$[0, \infty)$
3. C.$(0, \infty)$
4. D.$[1, \infty)$

Correct answer: A

One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both the dice are thrown together, is

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

Correct answer: C

Let $\left|\frac{\bar{z}-i}{2\bar{z}+i}\right|=\frac{1}{3}$, $z\in\mathbf{C}$, be the equation of a circle with center at C. If the area of the triangle, whose vertices are at the points (0, 0), C and ($\alpha$, 0) is 11 square units, then $\alpha^2$ equals:

1. A.$\frac{81}{25}$
2. B.50
3. C.$\frac{121}{25}$
4. D.100✓

Correct answer: D

Let P be the foot of the perpendicular from the point Q(10, $-3$, $-1$) on the line $\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z+1}{-2}$. Then the area of the right angled triangle PQR, where R is the point (3, $-2$, 1), is

1. A.$\sqrt{30}$
2. B.$3\sqrt{30}$✓
3. C.$8\sqrt{15}$
4. D.$9\sqrt{15}$

Correct answer: B

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

1. A.-1020
2. B.-1200
3. C.-1080✓
4. D.-120

Correct answer: C

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is

1. A.36000✓
2. B.35000
3. C.34000
4. D.37000

Correct answer: A

Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC, divides the arc AC such that $\frac{\text{length of arc AB}}{\text{length of arc BC}}=\frac{1}{5}$, and $\vec{OC}=\alpha\vec{OA}+\beta\vec{OB}$, then $\alpha+\sqrt{2}(\sqrt{3}-1)\beta$ is equal to

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

Correct answer: C

The value of $\int_{e^2}^{e^4}\frac{1}{x}\left(\frac{e^{((\log_ex)^2+1)^{-1}}}{e^{((\log_ex)^2+1)^{-1}}+e^{((6-\log_ex)^2+1)^{-1}}}\right)dx$ is

1. A.$\log_e2$
2. B.1✓
3. C.2
4. D.$e^2$

Correct answer: B

Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be $\hat{i}+2\hat{j}+\hat{k}$, $\hat{i}+3\hat{j}-2\hat{k}$ and $2\hat{i}+\hat{j}-\hat{k}$ respectively. The altitude from the vertex D to the opposite face ABC meets the median line segment through A of the triangle ABC at the point E. If the length of AD is $\frac{\sqrt{110}}{3}$ and the volume of the tetrahedron is $\frac{\sqrt{805}}{6\sqrt{2}}$, then the position vector of E is

1. A.$\frac{1}{6}(12\hat{i}+12\hat{j}+\hat{k})$
2. B.$\frac{1}{2}(\hat{i}+4\hat{j}+7\hat{k})$
3. C.$\frac{1}{6}(7\hat{i}+12\hat{j}+\hat{k})$✓
4. D.$\frac{1}{12}(7\hat{i}+4\hat{j}+3\hat{k})$

Correct answer: C

If the system of equations $(\lambda-1)x+(\lambda-4)y+\lambda z=5$, $\lambda x+(\lambda-1)y+(\lambda-4)z=7$, $(\lambda+1)x+(\lambda+2)y-(\lambda+2)z=9$ has infinitely many solutions, then $\lambda^2+\lambda$ is equal to

1. A.10
2. B.12✓
3. C.6
4. D.20

Correct answer: B

If the line $3x-2y+12=0$ intersects the parabola $4y=3x^2$ at the points A and B, then at the vertex of the parabola, the line segment AB subtends an angle equal to

1. A.$\tan^{-1}\left(\frac{4}{5}\right)$
2. B.$\tan^{-1}\left(\frac{11}{9}\right)$
3. C.$\tan^{-1}\left(\frac{9}{7}\right)$✓
4. D.$\frac{\pi}{2}-\tan^{-1}\left(\frac{3}{2}\right)$

Correct answer: C

If A, B, and $(\mathrm{adj}(A^{-1})+\mathrm{adj}(B^{-1}))$ are non-singular matrices of same order, then the inverse of $A(\mathrm{adj}(A^{-1})+\mathrm{adj}(B^{-1}))^{-1}B$, is equal to

1. A.$\frac{1}{|AB|}(\mathrm{adj}(B)+\mathrm{adj}(A))$✓
2. B.$AB^{-1}+A^{-1}B$
3. C.$\frac{AB^{-1}}{|A|}+\frac{BA^{-1}}{|B|}$
4. D.$\mathrm{adj}(B^{-1})+\mathrm{adj}(A^{-1})$

Correct answer: A

If $\frac{\pi}{2}\le x\le\frac{3\pi}{4}$, then $\cos^{-1}\left(\frac{12}{13}\cos x+\frac{5}{13}\sin x\right)$ is equal to

1. A.$x-\tan^{-1}\frac{4}{3}$
2. B.$x+\tan^{-1}\frac{4}{5}$
3. C.$x-\tan^{-1}\frac{5}{12}$✓
4. D.$x+\tan^{-1}\frac{5}{12}$

Correct answer: C

Let a curve $y=f(x)$ pass through the points (0, 5) and ($\log_e2$, k). If the curve satisfies the differential equation $2(3+y)e^{2x}dx-(7+e^{2x})dy=0$, then k is equal to

1. A.4
2. B.8✓
3. C.32
4. D.16

Correct answer: B

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is

1. A.40
2. B.44✓
3. C.48
4. D.52

Correct answer: B

Let the area of a $\triangle PQR$ with vertices P(5, 4), Q($-2$, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are O$\left(2, \frac{14}{5}\right)$ and C(c, d) respectively, then c + 2d is equal to

1. A.3✓
2. B.2
3. C.$\frac{7}{3}$
4. D.$\frac{8}{3}$

Correct answer: A

The value of $(\sin70^\circ)(\cot10^\circ\cot70^\circ-1)$ is

1. A.1✓
2. B.3/2
3. C.2/3
4. D.0

Correct answer: A

If the function $f(x)=\begin{cases}\frac{2}{x}\{\sin(k_1+1)x+\sin(k_2-1)x\}, & x<0\\ 4, & x=0\\ \frac{2}{x}\log_e\left(\frac{2+k_1x}{2+k_2x}\right), & x>0\end{cases}$ is continuous at x = 0, then $k_1^2+k_2^2$ is equal to

1. A.5
2. B.8
3. C.20
4. D.10✓

Correct answer: D

Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

1. A.8
2. B.10
3. C.9
4. D.7✓

Correct answer: D

The sum of all rational terms in the expansion of $\left(1+2^{1/3}+3^{1/2}\right)^6$ is equal to ______.

Correct answer: 612

If the area of the larger portion bounded between the curves $x^2+y^2=25$ and $y=|x-1|$ is $\frac{1}{4}(b\pi+c)$, $b, c\in\mathbf{N}$, then b + c is equal to ______.

Correct answer: 77

Let the circle C touch the line $x-y+1=0$, have the centre on the positive x-axis, and cut off a chord of length $\frac{4}{\sqrt{13}}$ along the line $-3x+2y=1$. Let H be the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$, whose one of the foci is the centre of C and the length of the transverse axis is the diameter of C. Then $2\alpha^2+3\beta^2$ is equal to ______.

Correct answer: 19

If the set of all values of a, for which the equation $5x^3-15x-a=0$ has three distinct real roots, is the interval ($\alpha$, $\beta$), then $\beta-2\alpha$ is equal to ______.

Correct answer: 30

If the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has equal roots, where a + c = 15 and $b=\frac{36}{5}$, then $a^2+c^2$ is equal to ______.

Correct answer: 117

A light hollow cube of side length 10 cm and mass 10g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y\pi\times10^{-2}$ s, where the value of y is (Acceleration due to gravity, g = 10 $m/s^2$, density of water = $10^3\ kg/m^3$)

1. A.1
2. B.2✓
3. C.4
4. D.6

Correct answer: B

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

1. A.1.0 cm✓
2. B.2.0 cm
3. C.1.5 cm
4. D.0.5 cm

Correct answer: A

Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is 6 $\Omega$ B. Current in Ammeter is 1A C. Potential across AB is 4 Volts. D. Potential across CD is 4 Volts E. Total resistance of the circuit is 8 $\Omega$. Choose the correct answer from the options given below:

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

Correct answer: D

Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

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

Correct answer: D

A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$?

1. A.8
2. B.1/4✓
3. C.4
4. D.1/8

Correct answer: B

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness 'h' in terms of the angle of incidence 'i' and angle of refraction 'r', if the glass slab is placed in air medium?

1. A.$\frac{h\tan(i-r)}{\tan r}$
2. B.$\frac{h\cos(i-r)}{\sin r}$
3. C.h
4. D.$\frac{h\sin(i-r)}{\cos r}$✓

Correct answer: D

Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor R. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below:

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

Correct answer: B

A solid sphere of mass 'm' and radius 'r' is allowed to roll without slipping from the highest point of an inclined plane of length 'L' and makes an angle 30° with the horizontal. The speed of the particle at the bottom of the plane is $v_1$. If the angle of inclination is increased to 45° while keeping L constant. Then the new speed of the sphere at the bottom of the plane is $v_2$. The ratio $v_1^2:v_2^2$ is

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

Correct answer: B

Given a thin convex lens (refractive index $\mu_2$), kept in a liquid (refractive index $\mu_1$, $\mu_1<\mu_2$) having radii of curvatures $|R_1|$ and $|R_2|$. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

1. A.$\frac{\mu_1|R_1|\cdot|R_2|}{\mu_2(|R_1|+|R_2|)-\mu_1|R_2|}$✓
2. B.$\frac{(\mu_2+\mu_1)|R_1|}{(\mu_2-\mu_1)}$
3. C.$\frac{\mu_1|R_1|\cdot|R_2|}{\mu_2(2|R_1|+|R_2|)-\mu_1\sqrt{|R_1|\cdot|R_2|}}$
4. D.$\frac{\mu_1|R_1|\cdot|R_2|}{\mu_2(|R_1|+|R_2|)-\mu_1|R_1|}$

Correct answer: A

The position of a particle moving on x-axis is given by $x(t)=A\sin t+B\cos^2t+Ct^2+D$, where t is time. The dimension of $\frac{ABC}{D}$ is

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

Correct answer: D

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is ______ grams. (Latent heat of fusion of lead = $2.5\times10^4\ JKg^{-1}$ and specific heat capacity of lead = 125 $JKg^{-1}K^{-1}$)

1. A.10✓
2. B.15
3. C.5
4. D.20

Correct answer: A

Match the LIST-I with LIST-II. LIST-I: A. Pressure varies inversely with volume of an ideal gas. B. Heat absorbed goes partly to increase internal energy and partly to do work. C. Heat is neither absorbed nor released by a system. D. No work is done on or by a gas. LIST-II: I. Adiabatic process II. Isochoric process III. Isothermal process IV. Isobaric process. Choose the correct answer from the options given below:

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

Correct answer: C

The electric field of an electromagnetic wave in free space is $\vec{E}=57\cos[7.5\times10^6t-5\times10^{-3}(3x+4y)](4\hat{i}-3\hat{j})$ N/C. The associated magnetic field in Tesla is

1. A.$\vec{B}=-\frac{57}{3\times10^8}\cos[7.5\times10^6t-5\times10^{-3}(3x+4y)](\hat{k})$
2. B.$\vec{B}=\frac{57}{3\times10^8}\cos[7.5\times10^6t-5\times10^{-3}(3x+4y)](\hat{k})$
3. C.$\vec{B}=\frac{57}{3\times10^8}\cos[7.5\times10^6t-5\times10^{-3}(3x+4y)](5\hat{k})$
4. D.$\vec{B}=-\frac{57}{3\times10^8}\cos[7.5\times10^6t-5\times10^{-3}(3x+4y)](5\hat{k})$✓

Correct answer: D

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ______ km.

1. A.6
2. B.3
3. C.12✓
4. D.9

Correct answer: C

The electric flux is $\phi=\alpha\sigma+\beta\lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\frac{\alpha}{\beta}\right)$ represents

1. A.area
2. B.displacement✓
3. C.electric field
4. D.charge

Correct answer: B

Regarding self-inductance: A. The self-inductance of the coil depends on its geometry. B. Self-inductance does not depend on the permeability of the medium. C. Self-induced e.m.f. opposes any change in the current in a circuit. D. Self-inductance is electromagnetic analogue of mass in mechanics. E. Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:

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

Correct answer: B

A sub-atomic particle of mass $10^{-30}$ kg is moving with a velocity $2.21\times10^6$ m/s. Under the matter wave consideration, the particle will behave closely like ______. (h = $6.63\times10^{-34}$ J.s)

1. A.Gamma rays
2. B.X-rays✓
3. C.Visible radiation
4. D.Infra-red radiation

Correct answer: B

A spherical surface of radius of curvature R, separates air from glass (refractive index = 1.5). The centre of curvature is in the glass medium. A point object 'O' placed in air on the optic axis of the surface, so that its real image is formed at 'I' inside glass. The line OI intersects the spherical surface at P and PO = PI. The distance PO equals to

1. A.1.5 R
2. B.3 R
3. C.2 R
4. D.5 R✓

Correct answer: D

A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

1. A.$\frac{a}{r}\sim3$✓
2. B.$\frac{a}{r}\sim20$
3. C.$\frac{a}{r}\sim10$
4. D.$\frac{a}{r}\sim0.5$

Correct answer: A

Consider a moving coil galvanometer (MCG): A. The torsional constant in moving coil galvanometer has dimentions $[ML^2T^{-2}]$ B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C. If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles. D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:

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

Correct answer: D

A force $f=x^2y\hat{i}+y^2\hat{j}$ acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4m, 2m) is ______ Joule (round off to the nearest integer)

Correct answer: 152

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A}=2\hat{i}+3n\hat{j}+2\hat{k}$ and $\vec{B}=2\hat{i}-2\hat{j}+4p\hat{k}$, respectively. If both the vectors are at right angle to each other, the value of $n^{-1}$ is ______.

Correct answer: 3

An ideal gas initially at 0°C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamic process is ______ K.

Correct answer: 273

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 $\Omega$, the value of the current in the circuit will be ______ A.

Correct answer: 3

Given below are two statements: Statement I: In Lassaigne's test, the covalent organic molecules are transformed into ionic compounds. Statement II: The sodium fusion extract of an organic compound having N and S gives prussian blue colour with $FeSO_4$ and $Na_4[Fe(CN)_6]$. In the light of the above statements, choose the correct answer from the options given below

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

Correct answer: C

$FeO_4^{2-}\xrightarrow{+2.0\,V}Fe^{3+}\xrightarrow{0.8\,V}Fe^{2+}\xrightarrow{-0.5\,V}Fe^0$. In the above diagram, the standard electrode potentials are given in volts (over the arrow). The value of $E^\ominus_{FeO_4^{2-}/Fe^{2+}}$ is

1. A.2.1 V
2. B.1.2 V
3. C.1.4 V
4. D.1.7 V✓

Correct answer: D

Which among the following react with Hinsberg's reagent? A. Aniline ($C_6H_5NH_2$) B. N,N-Dimethylaniline ($C_6H_5N(CH_3)_2$) C. $CH_3-NH_2$ D. $N(CH_3)_3$ E. Diphenylamine ($C_6H_5-NH-C_6H_5$). Choose the correct answer from the options given below:

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

Correct answer: D

The incorrect statement among the following is

1. A.$PH_3$ shows lower proton affinity than $NH_3$.
2. B.$PF_3$ exists but $NF_5$ does not.
3. C.$NO_2$ can dimerise easily.
4. D.$SO_2$ can act as an oxidizing agent, but not as a reducing agent.✓

Correct answer: D

What amount of bromine will be required to convert 2 g of phenol into 2,4,6-tribromophenol? (Given molar mass in g $mol^{-1}$ of C, H, O, Br are 12, 1, 16, 80 respectively)

1. A.20.44 g
2. B.6.0 g
3. C.4.0 g
4. D.10.22 g✓

Correct answer: D

The major product of the following reaction is: $CH_3CH_2CH=O\xrightarrow[\text{reflux}]{\text{excess HCHO, alkali}}$ ?

1. A.$CH_3-C(=CH_2)-CH=O$
2. B.$CH_3-C(CH_2OH)_3$✓
3. C.$CH_3-CH_2-CH_2-OH$
4. D.$CH_3-CH(CH_2OH)-CH=O$

Correct answer: B

The complex that shows Facial - Meridional isomerism is:

1. A.$[Co(NH_3)_4Cl_2]^+$
2. B.$[Co(en)_3]^{3+}$
3. C.$[Co(NH_3)_3Cl_3]$✓
4. D.$[Co(en)_2Cl_2]^+$

Correct answer: C

Match the LIST-I with LIST-II. LIST-I (Classification of molecules based on octet rule): A. Molecules obeying octet rule B. Molecules with incomplete octet C. Molecules with incomplete octet with odd electron D. Molecules with expanded octet. LIST-II (Example): I. NO, $NO_2$ II. $BCl_3$, $AlCl_3$ III. $H_2SO_4$, $PCl_5$ IV. $CCl_4$, $CO_2$. 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-I, D-III✓
3. C.A-III, B-II, C-I, D-IV
4. D.A-II, B-IV, C-III, D-I

Correct answer: B

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this? Given : Rydberg constant $R_H=10^5\ cm^{-1}$, h = $6.6\times10^{-34}$ J s, c = $3\times10^8$ m/s)

1. A.Balmer series, $\infty\to2$
2. B.Paschen series, $5\to3$
3. C.Paschen series, $\infty\to3$✓
4. D.Lyman series, $\infty\to1$

Correct answer: C

$2.8\times10^{-3}$ mol of $CO_2$ is left after removing $10^{21}$ molecules from its 'x' mg sample. The mass of $CO_2$ taken initially is Given: $N_A=6.02\times10^{23}\ mol^{-1}$

1. A.196.2 mg✓
2. B.98.3 mg
3. C.48.2 mg
4. D.150.4 mg

Correct answer: A

The correct set of ions (aqueous solution) with same colour from the following is:

1. A.$Sc^{3+}$, $Ti^{3+}$, $Cr^{2+}$
2. B.$V^{2+}$, $Cr^{3+}$, $Mn^{3+}$✓
3. C.$Ti^{4+}$, $V^{4+}$, $Mn^{2+}$
4. D.$Zn^{2+}$, $V^{3+}$, $Fe^{3+}$

Correct answer: B

The correct stability order of the following species/molecules is: p = cyclopropenyl anion (three-membered ring with one C=C and a − charge); q = cyclopentadienyl anion (five-membered ring with two C=C, a − charge and an H on the charged carbon); r = cyclooctatetraene (eight-membered ring with four C=C).

1. A.r > q > p
2. B.p > q > r
3. C.q > r > p✓
4. D.q > p > r

Correct answer: C

Match the LIST-I with LIST-II. LIST-I (Name reaction): A. Swarts reaction B. Sandmeyer's reaction C. Wurtz Fittig reaction D. Finkelstein reaction. LIST-II (Product obtainable): I. Ethyl benzene II. Ethyl iodide III. Cyanobenzene IV. Ethyl fluoride. Choose the correct answer from the options given below:

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

Correct answer: D

Given below are two statements: Statement I: Fructose does not contain an aldehydic group but still reduces Tollen's reagent Statement II: In the presence of base, fructose undergoes rearrangement to give glucose. 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: A

The element that does not belong to the same period of the remaining elements (modern periodic table) is:

1. A.Osmium
2. B.Palladium✓
3. C.Iridium
4. D.Platinum

Correct answer: B

Which of the following happens when $NH_4OH$ is added gradually to the solution containing 1M $A^{2+}$ and 1M $B^{3+}$ ions? Given : $K_{sp}[A(OH)_2]=9\times10^{-10}$ and $K_{sp}[B(OH)_3]=27\times10^{-18}$ at 298 K.

1. A.$A(OH)_2$ will precipitate before $B(OH)_3$
2. B.$A(OH)_2$ and $B(OH)_3$ will precipitate together
3. C.$B(OH)_3$ will precipitate before $A(OH)_2$✓
4. D.Both $A(OH)_2$ and $B(OH)_3$ do not show precipitation with $NH_4OH$

Correct answer: C

The d– electronic configuration of an octahedral Co(II) complex having magnetic moment of 3.95 BM is:

1. A.$e^4t_2^3$
2. B.$t_{2g}^6e_g^1$
3. C.$t_{2g}^3e_g^0$
4. D.$t_{2g}^5e_g^2$✓

Correct answer: D

Ice at −5°C is heated to become vapor with temperature of 110°C at atmospheric pressure. The entropy change associated with this process can be obtained from

1. A.$\int_{268K}^{273K}\frac{C_{p,m}}{T}dT+\frac{\Delta H_{m,fusion}}{T_f}+\frac{\Delta H_{m,vaporisation}}{T_b}+\int_{273K}^{373K}\frac{C_{p,m}dT}{T}+\int_{373K}^{383K}\frac{C_{p,m}dT}{T}$✓
2. B.$\int_{268K}^{383K}C_pdT+\frac{\Delta H_{melting}}{273}+\frac{\Delta H_{boiling}}{373}$
3. C.$\int_{268K}^{273K}C_{p,m}dT+\frac{\Delta H_{m,fusion}}{T_f}+\frac{\Delta H_{m,vaporisation}}{T_b}+\int_{273K}^{373K}C_{p,m}dT+\int_{373K}^{383K}C_{p,m}dT$
4. D.$\int_{268K}^{383K}C_pdT+\frac{q_{rev}}{T}$

Correct answer: A

Propane molecule on chlorination under photochemical condition gives two di-chloro products, "x" and "y". Amongst "x" and "y", "x" is an optically active molecule. How many tri-chloro products (consider only structural isomers) will be obtained from "x" when it is further treated with chlorine under the photochemical condition?

1. A.3✓
2. B.4
3. C.2
4. D.5

Correct answer: A

$CrCl_3\cdot xNH_3$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558°C. Assuming 100% ionisation of this complex and coordination number of Cr is 6, the complex will be (Given $K_f$ = 1.86 K kg $mol^{-1}$)

1. A.$[Cr(NH_3)_3Cl_3]$
2. B.$[Cr(NH_3)_5Cl]Cl_2$✓
3. C.$[Cr(NH_3)_4Cl_2]Cl$
4. D.$[Cr(NH_3)_6]Cl_3$

Correct answer: B

If 1 mM solution of ethylamine produces pH = 9, then the ionization constant ($K_b$) of ethylamine is $10^{-x}$. The value of x is ______ (nearest integer). [The degree of ionization of ethylamine can be neglected with respect to unity.]

Correct answer: 7

The standard enthalpy and standard entropy of decomposition of $N_2O_4$ to $NO_2$ are 55.0 kJ $mol^{-1}$ and 175.0 J/K/mol respectively. The standard free energy change for this reaction at 25°C in J $mol^{-1}$ is ______ (Nearest integer)

Correct answer: 2850

During "S" estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. The percentage of Sulphur in the given compound is ______ %. (Given molar mass in g $mol^{-1}$ of Ba : 137, S : 32, O : 16)

Correct answer: 40

Consider the following sequence of reactions to produce major product (A): 3-Nitrotoluene (m-nitrotoluene) $\xrightarrow{\text{i) } Br_2, Fe;\ \text{ii) Sn, HCl;\ iii) } NaNO_2, HCl, 273K;\ \text{iv) } H_3PO_2, H_2O}$ (A) Major Product. Molar mass of product (A) is ______ g $mol^{-1}$. (Given molar mass in g $mol^{-1}$ of C : 12, H: 1, O :16, Br : 80, N : 14, P:31)