JEE Main 4 April 2025 Shift 2 Question Paper

Question 1

Let $a>0$. If the function $f(x)=6x^3-45ax^2+108a^2x+1$ attains its local maximum and minimum values at the points $x_1$ and $x_2$ respectively such that $x_1x_2=54$, then $a+x_1+x_2$ is equal to:

Accepted Answer

(B) 18

Answer

(A) 15

Answer

(C) 24

Answer

(D) 13

Question 2

Let $f$ be a differentiable function on $\mathbb{R}$ such that $f(2)=1$, $f'(2)=4$. Let $\lim_{x	o0}\left(\dfrac{f(2+x)}{f(2)}ight)^{3/x}=e^{\alpha}$. Then the number of times the curve $y=4x^3-4x^2-4(\alpha-7)x-\alpha$ meets x-axis is:

Accepted Answer

(A) 2

Answer

(B) 1

Answer

(C) 0

Answer

(D) 3

Question 3

The sum of the infinite series $\cot^{-1}\left(\dfrac{7}{4}\right)+\cot^{-1}\left(\dfrac{19}{4}\right)+\cot^{-1}\left(\dfrac{39}{4}\right)+\cot^{-1}\left(\dfrac{67}{4}\right)+\dots$ is:

Accepted Answer

(D) $\dfrac{\pi}{2}-	an^{-1}\left(\dfrac{1}{2}ight)$

Answer

(A) $\dfrac{\pi}{2}+	an^{-1}\left(\dfrac{1}{2}ight)$

Answer

(B) $\dfrac{\pi}{2}-\cot^{-1}\left(\dfrac{1}{2}\right)$

Answer

(C) $\dfrac{\pi}{2}+\cot^{-1}\left(\dfrac{1}{2}\right)$

Question 4

Let $A=\{-3,-2,-1,0,1,2,3\}$ and $R$ be a relation on $A$ defined by $xRy$ if and only if $2x-y\in\{0,1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to:

Accepted Answer

(B) 17

Answer

(A) 18

Answer

(C) 15

Answer

(D) 16

Question 5

Let the product of $\omega_1=(8+i)\sin	heta+(7+4i)\cos	heta$ and $\omega_2=(1+8i)\sin	heta+(4+7i)\cos	heta$ be $\alpha+i\beta$, $i=\sqrt{-1}$. Let $p$ and $q$ be the maximum and minimum values of $\alpha+\beta$ respectively. Then $p+q$ is equal to:

Accepted Answer

(B) 130

Answer

(A) 140

Answer

(C) 160

Answer

(D) 150

Question 6

Let the values of $p$, for which the shortest distance between the lines $\dfrac{x+1}{3}=\dfrac{y}{4}=\dfrac{z}{5}$ and $\vec{r}=(p\hat{i}+2\hat{j}+\hat{k})+\lambda(2\hat{i}+3\hat{j}+4\hat{k})$ is $\dfrac{1}{\sqrt6}$, be $a, b$, $(a<b)$. Then the length of the latus rectum of the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is:

Accepted Answer

(C) $\dfrac{2}{3}$

Answer

(A) 9

Answer

(B) $\dfrac{3}{2}$

Answer

(D) 18

Question 7

The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at distances $\sqrt2$ and $2\sqrt2$ units from the origin, respectively. If the point $(1,k)$ lies on the parabola, then a possible value of $k$ is:

Accepted Answer

(B) 9

Answer

(A) 4

Answer

(C) 3

Answer

(D) 8

Question 8

Let the domains of the functions $f(x)=\log_4\log_3\log_7\left(8-\log_2(x^2+4x+5)\right)$ and $g(x)=\sin^{-1}\left(\dfrac{7x+10}{x-2}\right)$ be $(\alpha,\beta)$ and $[\gamma,\delta]$, respectively. Then $\alpha^2+\beta^2+\gamma^2+\delta^2$ is equal to:

Accepted Answer

(A) 15

Answer

(B) 13

Answer

(C) 16

Answer

(D) 14

Question 9

A line passing through the point $A(-2,0)$, touches the parabola $P:y^2=x-2$ at the point $B$ in the first quadrant. The area of the region bounded by the line $AB$, parabola $P$ and the x-axis, is:

Accepted Answer

(C) $\dfrac{8}{3}$

Answer

(A) $\dfrac{7}{3}$

Answer

(B) 2

Answer

(D) 3

Question 10

Let the sum of the focal distances of the point $P(4,3)$ on the hyperbola $H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ be $8\sqrt{\dfrac{5}{3}}$. If for $H$, the length of the latus rectum is $l$ and the product of the focal distances of the point $P$ is $m$, then $9l^2+6m$ is equal to:

Accepted Answer

(C) 185

Answer

(A) 184

Answer

(B) 186

Answer

(D) 187

Question 11

Let the matrix $A=\begin{bmatrix}1&0&0\1&0&1\0&1&0\end{bmatrix}$ satisfy $A^n=A^{n-2}+A^2-I$ for $n\ge3$. Then the sum of all the elements of $A^{50}$ is:

Accepted Answer

(A) 53

Answer

(B) 52

Answer

(C) 39

Answer

(D) 44

Question 12

If the sum of the first 20 terms of the series $\dfrac{4\cdot1}{4+3\cdot1^2+1^4}+\dfrac{4\cdot2}{4+3\cdot2^2+2^4}+\dfrac{4\cdot3}{4+3\cdot3^2+3^4}+\dots$ is $\dfrac{m}{n}$, where $m$ and $n$ are coprime, then $m+n$ is equal to:

Accepted Answer

(C) 421

Answer

(A) 423

Answer

(B) 420

Answer

(D) 422

Question 13

If $1^2\binom{15}{1}+2^2\binom{15}{2}+3^2\binom{15}{3}+\dots+15^2\binom{15}{15}=2^m\cdot3^n\cdot5^k$, where $m,n,k\in\mathbb{N}$, then $m+n+k$ is equal to:

Accepted Answer

(A) 19

Answer

(B) 21

Answer

(C) 18

Answer

(D) 15

Question 14

Let for two distinct values of $p$ the lines $y=x+p$ touch the ellipse $E:\dfrac{x^2}{4^2}+\dfrac{y^2}{3^2}=1$ at the points $A$ and $B$. Let the line $y=x$ intersect $E$ at the points $C$ and $D$. Then the area of the quadrilateral $ABCD$ is equal to:

Accepted Answer

(B) 24

Answer

(A) 36

Answer

(C) 48

Answer

(D) 20

Question 15

Consider two sets $A$ and $B$, each containing three numbers in A.P. Let the sum and the product of the elements of $A$ be 36 and $p$ respectively and the sum and the product of the elements of $B$ be 36 and $q$ respectively. Let $d$ and $D$ be the common differences of the APs in $A$ and $B$ respectively such that $D=d+3$, $d>0$. If $\dfrac{p+q}{p-q}=\dfrac{19}{5}$, then $p-q$ is equal to:

Accepted Answer

(D) 540

Answer

(A) 600

Answer

(B) 450

Answer

(C) 630

Question 16

If a curve $y=y(x)$ passes through the point $\left(1,\dfrac{\pi}{2}\right)$ and satisfies the differential equation $(7x^4\cot y-e^x\operatorname{cosec}y)\dfrac{dx}{dy}=x^5$, $x\ge1$, then at $x=2$, the value of $\cos y$ is:

Accepted Answer

(C) $\dfrac{2e^2-e}{128}$

Answer

(A) $\dfrac{2e^2-e}{64}$

Answer

(B) $\dfrac{2e^2+e}{64}$

Answer

(D) $\dfrac{2e^2+e}{128}$

Question 17

The centre of a circle $C$ is at the centre of the ellipse $E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, $a>b$. Let $C$ pass through the foci $F_1$ and $F_2$ of $E$ such that the circle $C$ and the ellipse $E$ intersect at four points. Let $P$ be one of these four points. If the area of the triangle $PF_1F_2$ is 30 and the length of the major axis of $E$ is 17, then the distance between the foci of $E$ is:

Accepted Answer

(B) 13

Answer

(A) 26

Answer

(C) 12

Answer

(D) $\dfrac{13}{2}$

Question 18

Let $f(x)+2f\left(\dfrac{1}{x}\right)=x^2+5$ and $2g(x)-3g\left(\dfrac{1}{2}\right)=x$, $x>0$. If $\alpha=\displaystyle\int_1^2 f(x)\,dx$, and $\beta=\displaystyle\int_1^2 g(x)\,dx$, then the value of $9\alpha+\beta$ is:

Accepted Answer

(D) 11

Answer

(A) 1

Answer

(B) 0

Answer

(C) 10

Question 19

Let $A$ be the point of intersection of the lines $L_1:\dfrac{x-7}{1}=\dfrac{y-5}{0}=\dfrac{z-3}{-1}$ and $L_2:\dfrac{x-1}{3}=\dfrac{y+3}{4}=\dfrac{z+7}{5}$. Let $B$ and $C$ be the points on the lines $L_1$ and $L_2$ respectively such that $AB=AC=\sqrt{15}$. Then the square of the area of the triangle $ABC$ is:

Accepted Answer

(A) 54

Answer

(B) 63

Answer

(C) 57

Answer

(D) 60

Question 20

Let the mean and the standard deviation of the observation $2, 3, 3, 4, 5, 7, a, b$ be 4 and $\sqrt2$ respectively. The mean deviation about the mode of these observations is:

Accepted Answer

(A) 1

Answer

(B) $\dfrac{3}{4}$

Answer

(C) 2

Answer

(D) $\dfrac{1}{2}$

Question 21

If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\displaystyle\sum_{k=1}^{n}\left(\alpha^k+\dfrac{1}{\alpha^k}\right)^2=20$, then $n$ is equal to ______.

Accepted Answer

11

Question 22

If $\displaystyle\int\dfrac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^{9}}\,dx=\dfrac{1}{m}\left(\left(\sqrt{1+x^2}+x\right)^{n}\left(n\sqrt{1+x^2}-x\right)\right)+C$, where $C$ is the constant of integration and $m,n\in\mathbb{N}$, then $m+n$ is equal to ______.

Accepted Answer

379

Question 23

A card from a pack of 52 cards is lost. From the remaining 51 cards, $n$ cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\dfrac{11}{50}$, then $n$ is equal to ______.

Accepted Answer

2

Question 24

Let $m$ and $n$, $(m<n)$ be two 2-digit numbers. Then the total number of pairs $(m,n)$, such that $\gcd(m,n)=6$, is ______.

Accepted Answer

64

Question 25

Let the three sides of a triangle ABC be given by the vectors $2\hat{i}-\hat{j}+\hat{k}$, $\hat{i}-3\hat{j}-5\hat{k}$ and $3\hat{i}-4\hat{j}-4\hat{k}$. Let G be the centroid of the triangle ABC. Then $6\left(|AG|^2+|BG|^2+|CG|^2\right)$ is equal to ______.

Accepted Answer

164

Question 26

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents the time dependent mass of P, Q and R?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 27

There are 'n' number of identical electric bulbs, each is designed to draw a power p independently from the mains supply. They are now joined in series across the main supply. The total power drawn by the combination is:

Accepted Answer

(C) $\dfrac{p}{n}$

Answer

(A) $np$

Answer

(B) $\dfrac{p}{n^2}$

Answer

(D) $p$

Question 28

Consider a rectangular sheet of solid material of length $\ell=9$ cm and width $d=4$ cm. The coefficient of linear expansion is $\alpha=3.1	imes10^{-5}\ K^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $m=0.1$ kg and the specific heat capacity $C_v=900\ J\,kg^{-1}K^{-1}$. If the amount of heat supplied to the material is $8.1	imes10^2$ J then change in area of the rectangular sheet is:

Accepted Answer

(A) $2.0	imes10^{-5}\ m^2$

Answer

(B) $2.0	imes10^{-3}\ m^2$

Answer

(C) $6.0	imes10^{-5}\ m^2$

Answer

(D) $4.0	imes10^{-5}\ m^2$

Question 29

Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(A) Both Statement I and Statement II are correct

Answer

(B) Statement I is incorrect but Statement II is correct

Answer

(D) Both Statement I and Statement II are incorrect

Question 30

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^7$ N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $	heta$ of the rod axis from its original position is: (shear moduli, $G=10^{10}\ N/m^2$)

Accepted Answer

(A) $\dfrac{1}{160\pi}$

Answer

(B) $\dfrac{1}{4\pi}$

Answer

(C) $\dfrac{1}{40\pi}$

Answer

(D) $\dfrac{1}{2\pi}$

Question 31

From the combination of resistors with resistance values $R_1=R_2=R_3=5\ \Omega$ and $R_4=10\ \Omega$, which of the following combination is the best circuit to get an equivalent resistance of $6\ \Omega$?

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 32

A metallic ring is uniformly charged as shown in the figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to "O" is "E" is magnitude. What would be the magnitude of electric field at "O" due to arc ABC?

Accepted Answer

(B) $\sqrt2\,E$

Answer

(A) $2E$

Answer

(C) $\dfrac{E}{2}$

Answer

(D) Zero

Question 33

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa):

Accepted Answer

(B) 6

Answer

(A) 4.4

Answer

(C) 24

Answer

(D) 18

Question 34

An object is kept at rest at a distance of $3R$ above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M = mass of earth, G = Universal gravitational constant)

Accepted Answer

(A) $\sqrt{\dfrac{GM}{2R}}$

Answer

(B) $\sqrt{\dfrac{GM}{R}}$

Answer

(C) $\sqrt{\dfrac{3GM}{R}}$

Answer

(D) $\sqrt{\dfrac{2GM}{R}}$

Question 35

Three parallel plate capacitors $C_1$, $C_2$ and $C_3$ each of capacitance 5 $\mu$F are connected as shown in the figure. The effective capacitance between points A and B, when the space between the parallel plates of $C_1$ capacitor is filled with a dielectric medium having dielectric constant of 4, is:

Accepted Answer

(C) $9\ \mu F$

Answer

(A) $22.5\ \mu F$

Answer

(B) $7.5\ \mu F$

Answer

(D) $30\ \mu F$

Question 36

The displacement x versus time t graph is shown below. (A) The average velocity during 0 to 3 s is 10 m/s. (B) The average velocity during 3 to 5 s is 0 m/s. (C) The instantaneous velocity at t = 2 s is 5 m/s. (D) The average velocity during 5 to 7 s and instantaneous velocity at t = 6.5 s are zero. (E) The average velocity from t = 0 to t = 9 s is zero. Choose the correct answer from the options given below:

Accepted Answer

(D) (B), (C), (E) only

Answer

(A) (A), (D), (E) only

Answer

(B) (B), (C), (D) only

Answer

(C) (B), (D), (E) only

Question 37

A wheel is rolling on a plane surface. The speed of a particle at the highest point of the rim is 8 m/s. The speed of the particle on the rim of the wheel at the same level as the centre of the wheel, will be:

Accepted Answer

(A) $4\sqrt2$ m/s

Answer

(B) 8 m/s

Answer

(C) 4 m/s

Answer

(D) $8\sqrt2$ m/s

Question 38

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm):

Accepted Answer

(B) 0.002

Answer

(A) 0.001

Answer

(C) 0.0005

Answer

(D) 0.0025

Question 39

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle $45^\circ$ with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is: (work done by the applied force)

Accepted Answer

(C) 245 J

Answer

(A) 970 J

Answer

(B) 735 J

Answer

(D) 490 J

Question 40

Two polarisers $P_1$ and $P_2$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $P_3$ is inserted in between $P_1$ and $P_2$ at the particular angle between them. The transmitted intensity of the light passing through all three polarisers is maximum. The angle between the polarisers $P_1$ and $P_3$ is:

Accepted Answer

(A) $\dfrac{\pi}{4}$

Answer

(B) $\dfrac{\pi}{6}$

Answer

(C) $\dfrac{\pi}{8}$

Answer

(D) $\dfrac{\pi}{3}$

Question 41

Consider a n-type semiconductor in which $n_e$ and $n_h$ are number of electrons and holes, respectively. (A) Holes are minority carriers. (B) The dopant is a pentavalent atom. (C) $n_e n_h 
e n_i^2$ (where $n_i$ is number of electrons or holes in semiconductor when it is in intrinsic form). (D) $n_e n_h \ge n_i^2$. (E) The holes are not generated due to the donors. Choose the correct answer from the options given below:

Accepted Answer

(C) (A), (B), (E) only

Answer

(A) (A), (C), (D) only

Answer

(B) (A), (C), (E) only

Answer

(D) (A), (B), (C) only

Question 42

Match List-I (Process) with List-II (First-law relation). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 43

Displacement of a wave is expressed as $x(t)=5\cos\left(628t+\dfrac{\pi}{2}\right)$ m. The wavelength of the wave when its velocity is 300 m/s is:

Accepted Answer

(B) 3 m

Answer

(A) 1.5 m

Answer

(C) 0.5 m

Answer

(D) 0.33 m

Question 44

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

Accepted Answer

(B) 7.5 cm

Answer

(A) 45 cm

Answer

(C) 22.5 cm

Answer

(D) 15 cm

Question 45

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $[M^P\,L^Q\,T^A]$. The value of P and Q are:

Accepted Answer

(D) $0, -1$

Answer

(A) 1, 0

Answer

(B) $-1, 1$

Answer

(C) $1, -1$

Question 46

A particle of charge 1.6 $\mu$C and mass 16 $\mu$g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to the magnetic field. The time required for the particle to return to original location for the first time is ______ s. ($\pi=3.14$)

Accepted Answer

10

Question 47

A solid sphere with uniform density and radius R is rotating with constant angular velocity $\omega_1$ about its diameter. After some time during the rotation its mass starts losing at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius becomes $R/2$ is $x\omega_1$. The value of x is ______.

Accepted Answer

32

Question 48

If an optical medium possesses a relative permeability of $\dfrac{10}{\pi}$ and relative permittivity of $\dfrac{1}{0.0885}$, then the velocity of light is greater in vacuum than in this medium by ______ times. ($\mu_0=4\pi	imes10^{-7}$ H/m, $\varepsilon_0=8.85	imes10^{-12}$ F/m, $c=3	imes10^8$ m/s)

Accepted Answer

6

Question 49

In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the double slit pattern is replaced with a single slit of width equal to that of each slit, then the width of 20 maxima of double slit is ______ times the width of central maxima of single slit. (take x-value is ______)

Accepted Answer

15

Question 50

An inductor of self inductance 1 H connected in series with a resistor of $100\pi\ \Omega$ and an AC supply of $100\pi$ volt, 50 Hz. Maximum current flowing in the circuit is ______ A.

Accepted Answer

1

Question 51

The correct order of basicity for the following molecules is:

Accepted Answer

(D) $R > Q > P$

Answer

(A) $P > Q > R$

Answer

(B) $R > P > Q$

Answer

(C) $Q > P > R$

Question 52

The incorrect relationship in the following pairs in relation to ionisation enthalpies is:

Accepted Answer

(D) $Mn^{2+} < Fe^{2+}$

Answer

(A) $Mn^+ < Cr^+$

Answer

(B) $Mn^{2+} < Mn^+$

Answer

(C) $Fe^{2+} < Fe^{3+}$

Question 53

Which among the following compounds give yellow solid when reacted with NaOI/NaOH?

Accepted Answer

(B) (A) and (C) Only

Answer

(A) (B), (C) and (E) Only

Answer

(C) (C) and (D) Only

Answer

(D) (A), (C) and (D) Only

Question 54

A dipeptide, "x" on complete hydrolysis gives "y" and "z". "y" on treatment with aq. $HNO_2$ produces lactic acid. On the other hand "z" on heating gives the following cyclic molecule. Based on the information given, the dipeptide X is:

Accepted Answer

(B) alanine-glycine

Answer

(A) valine-glycine

Answer

(C) valine-leucine

Answer

(D) alanine-alanine

Question 55

In which pairs, the first ion is more stable than the second?

Accepted Answer

(B) (A) & (B) only

Answer

(A) (B) & (D) only

Answer

(C) (B) & (C) only

Answer

(D) (A) & (C) only

Question 56

Given below are two statements: Statement (I): Alcohols are formed when alkyl chlorides are treated with aqueous potassium hydroxide by elimination reaction. Statement (II): In alcoholic potassium hydroxide, alkyl chlorides form alkenes by abstracting the hydrogen from the $\beta$-carbon. In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(B) Statement I is incorrect but Statement II is correct

Answer

(A) Both Statement I and Statement II are incorrect

Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(D) Both Statement I and Statement II are correct

Question 57

Given below are two statements: Statement (I): Molal depression constant $K_f$ is given by $\dfrac{M_1 R T_f}{\Delta S_{fus}}$, where symbols have their usual meaning. Statement (II): $K_f$ for benzene is less than the $K_f$ for water. In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(D) Statement I is correct but Statement II is incorrect

Answer

(A) Statement I is incorrect but Statement II is correct

Answer

(B) Both Statement I and Statement II are incorrect

Answer

(C) Both Statement I and Statement II are correct

Question 58

The IUPAC name of the following compound is:

Accepted Answer

(D) Hept-1-en-6-yn-4-ol

Answer

(A) 4-Hydroxyhept-1-en-6-yne

Answer

(B) 4-Hydroxyhept-6-en-1-yne

Answer

(C) Hept-6-en-1-yn-4-ol

Question 59

Match List-I (Separation of) with List-II (Separation Technique). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 60

A toxic compound "A" when reacted with NaCN in aqueous acidic medium yields an edible cooking component and food preservative "B". "B" is converted to "C" by diborane and can be used as an additive to petrol to reduce emission. "C" upon reaction with oleum at $140^\circ C$ yields an inhalable anaesthetic "D". Identify "A", "B", "C" and "D", respectively.

Accepted Answer

(C) Methanol; acetic acid; ethanol; diethyl ether

Answer

(A) Methanol; formaldehyde; methyl chloride; chloroform

Answer

(B) Ethanol; acetonitrile; ethylamine; ethylene

Answer

(D) Acetaldehyde; 2-hydroxypropanoic acid; propanoic acid; dipropyl ether

Question 61

The correct order of $[FeF_6]^{3-}$, $[CoF_6]^{3-}$, $[Ni(CO)_4]$ and $[Ni(CN)_4]^{2-}$ complex species based on the number of unpaired electrons present is:

Accepted Answer

(D) $[FeF_6]^{3-} > [CoF_6]^{3-} > [Ni(CN)_4]^{2-} = [Ni(CO)_4]$

Answer

(A) $[FeF_6]^{3-} > [CoF_6]^{3-} > [Ni(CN)_4]^{2-} > [Ni(CO)_4]$

Answer

(B) $[Ni(CN)_4]^{2-} > [FeF_6]^{3-} > [CoF_6]^{3-} > [Ni(CO)_4]$

Answer

(C) $[CoF_6]^{3-} > [FeF_6]^{3-} > [Ni(CO)_4] > [Ni(CN)_4]^{2-}$

Question 62

Consider the given data: (a) $HCl(g) + 10H_2O(l) \rightarrow HCl.10H_2O$, $\Delta H = -69.01\ kJ\,mol^{-1}$; (b) $HCl(g) + 40H_2O(l) \rightarrow HCl.40H_2O$, $\Delta H = -72.79\ kJ\,mol^{-1}$. Choose the correct statement:

Accepted Answer

(B) The heat of solution depends on the amount of solvent.

Answer

(A) Dissolution of gas in water is an endothermic process

Answer

(C) The heat of dilution for the $HCl.10H_2O$ to $HCl.40H_2O$ is $3.78\ kJ\,mol^{-1}$.

Answer

(D) The heat of formation of HCl solution is represented by both (a) and (b)

Question 63

Consider the ground state of chromium atom $(Z = 24)$. How many electrons are with Azimuthal quantum number $l = 1$ and $l = 2$ respectively?

Accepted Answer

(C) 12 and 5

Answer

(A) 12 and 4

Answer

(B) 16 and 4

Answer

(D) 16 and 5

Question 64

Given below are two statements: Statement (I): The first ionisation enthalpy of group 14 elements is higher than the corresponding elements of group 13. Statement (II): Melting points and boiling points of group 13 elements are in general much higher than the corresponding elements of group 14. In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(A) Statement I is correct but Statement II is incorrect

Answer

(B) Statement I is incorrect but Statement II is correct

Answer

(C) Both Statement I and Statement II are incorrect

Answer

(D) Both Statement I and Statement II are correct

List-I (Process)	List-II (First-law relation)
A.Isobaric	I. $\Delta Q=\Delta W$
B.Isochoric	II. $\Delta Q=\Delta U$
C.Adiabatic	III. $\Delta Q=$ zero
D.Isothermal	IV. $\Delta Q=\Delta U+P\Delta V$

List-I (Separation of)	List-II (Separation Technique)
A.Aniline from aniline-water mixture	I.Simple distillation
B.Glycerol from spent-lye in soap industry	II.Fractional distillation
C.Different fractions of crude oil in petroleum industry	III.Distillation at reduced pressure
D.Chloroform-Aniline mixture	IV.Steam distillation

JEE Main 4 April 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 4 April 2025 Shift 2

Chemistry — JEE Main 4 April 2025 Shift 2

Mathematics — JEE Main 4 April 2025 Shift 2

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