JEE Main 7 April 2025 Shift 2 Question Paper

Question 1

If the orthocentre of the triangle formed by the lines $y=x+1$, $y=4x-8$ and $y=mx+c$ is at $(3,-1)$, then $m-c$ is:

Accepted Answer

(A) 0

Answer

(B) $-2$

Answer

(C) 4

Answer

(D) 2

Question 2

Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that $\dfrac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1$. Then $\dfrac{|\vec{a}+\vec{b}|^2}{|\vec{a}|^2}$ is:

Accepted Answer

(C) $2+\sqrt{2}$

Answer

(A) $2+4\sqrt{2}$

Answer

(B) $1+\sqrt{2}$

Answer

(D) $4+2\sqrt{2}$

Question 3

Let $A=\{(\alpha,\beta)\in\mathbb{R}	imes\mathbb{R}:|\alpha-1|\le 4 	ext{ and } |\beta-5|\le 6\}$ and $B=\{(\alpha,\beta)\in\mathbb{R}	imes\mathbb{R}:16(\alpha-2)^2+9(\beta-6)^2\le 144\}$. Then

Accepted Answer

(A) $B\subset A$

Answer

(B) $A\cup B=\{(x,y):-4\le x\le 4,\ -1\le y\le 11\}$

Answer

(C) neither $A\subset B$ nor $B\subset A$

Answer

(D) $A\subset B$

Question 4

If the range of the function $f(x)=\dfrac{5-x}{x^2-3x+2}$, $x
e 1,2$, is $(-\infty,\alpha]\cup[\beta,\infty)$, then $\alpha^2+\beta^2$ is equal to:

Accepted Answer

(D) 194

Answer

(A) 190

Answer

(B) 192

Answer

(C) 188

Question 5

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is $\dfrac{m}{n}$, $\gcd(m,n)=1$, then $n^2-m^2$ is equal to:

Accepted Answer

(A) 80

Answer

(B) 60

Answer

(C) 72

Answer

(D) 64

Question 6

Let a random variable $X$ take values $0,1,2,3$ with $P(X=0)=P(X=1)=p$, $P(X=2)=P(X=3)$ and $E(X^2)=2E(X)$. Then the value of $8p-1$ is:

Accepted Answer

(B) 2

Answer

(A) 0

Answer

(C) 1

Answer

(D) 3

Question 7

If the area of the region $\{(x,y):1+x^2\le y\le \min\{x+7,\ 11-3x\}\}$ is $A$, then $3A$ is equal to:

Accepted Answer

(A) 50

Answer

(B) 49

Answer

(C) 46

Answer

(D) 47

Question 8

Let $f:\mathbb{R}	o\mathbb{R}$ be a polynomial function of degree four having extreme values at $x=4$ and $x=5$. If $\lim\limits_{x	o 0}\dfrac{f(x)}{x^2}=5$, then $f(2)$ is equal to:

Accepted Answer

(B) 10

Answer

(A) 12

Answer

(C) 8

Answer

(D) 14

Question 9

The number of solutions of the equation $\cos 2	heta\,\cos\dfrac{	heta}{2}+\cos\dfrac{5	heta}{2}=2\cos^3\dfrac{5	heta}{2}$ in $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}ight]$ is:

Accepted Answer

(A) 7

Answer

(B) 5

Answer

(C) 6

Answer

(D) 9

Question 10

Let $a_n$ be the $n^{th}$ term of an A.P. If $S_n=a_1+a_2+a_3+\dots+a_n=700$, $a_6=7$ and $S_7=7$, then $a_n$ is equal to:

Accepted Answer

(C) 64

Answer

(A) 56

Answer

(B) 65

Answer

(D) 70

Question 11

Let the locus of $z\in\mathbb{C}$, such that $\mathrm{Re}\left(\dfrac{z-1}{2z+i}\right)+\mathrm{Re}\left(\dfrac{\bar{z}-1}{2\bar{z}-i}\right)=2$, is a circle of radius $r$ and center $(a,b)$, then $\dfrac{15ab}{r^2}$ is equal to:

Accepted Answer

(C) 18

Answer

(A) 24

Answer

(B) 12

Answer

(D) 16

Question 12

Let the length of a latus rectum of an ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ be 10. If its eccentricity is the minimum value of the function $f(t)=t^2+t+\dfrac{11}{12}$, $t\in\mathbb{R}$, then $a^2+b^2$ is equal to:

Accepted Answer

(B) 126

Answer

(A) 125

Answer

(C) 120

Answer

(D) 115

Question 13

Let $y=y(x)$ be the solution of the differential equation $(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x$, $y(0)=1$. Then $\displaystyle\int_{-3}^{3} y(x)\,dx$ is:

Accepted Answer

(A) 24

Answer

(B) 36

Answer

(C) 30

Answer

(D) 18

Question 14

If the equation of the line passing through the point $\left(0,-\dfrac{1}{2},0\right)$ and perpendicular to the lines $\vec{r}=\lambda(\hat{i}+a\hat{j}+b\hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}-6\hat{k})+\mu(-b\hat{i}+a\hat{j}+5\hat{k})$ is $\dfrac{x-1}{-2}=\dfrac{y+4}{d}=\dfrac{z-c}{-4}$, then $a+b+c+d$ is equal to:

Accepted Answer

(B) 14

Answer

(A) 10

Answer

(C) 13

Answer

(D) 12

Question 15

Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular polygon $P$ of $n$ sides and $q$ be the number of all quadrilaterals that can be formed by joining the vertices of $P$. If $p+q=126$, then the eccentricity of the ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{n}=1$ is:

Accepted Answer

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

Answer

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

Answer

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

Answer

(C) $\dfrac{\sqrt{7}}{4}$

Question 16

Consider the lines $L_1:x-1=y-2=z$ and $L_2:x-2=y=z-1$. Let the feet of the perpendiculars from the point $P(5,1,-3)$ on the lines $L_1$ and $L_2$ be $Q$ and $R$ respectively. If the area of the triangle $PQR$ is $A$, then $4A^2$ is equal to:

Accepted Answer

(B) 147

Answer

(A) 139

Answer

(C) 151

Answer

(D) 143

Question 17

The number of real roots of the equation $x|x-2|+3|x-3|+1=0$ is:

Accepted Answer

(C) 1

Answer

(A) 4

Answer

(B) 2

Answer

(D) 3

Question 18

Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\dfrac{x^2}{b^2}+\dfrac{y^2}{25}=1$ and the hyperbola $\dfrac{x^2}{16}-\dfrac{y^2}{b^2}=1$, respectively. If $b<5$ and $e_1e_2=1$, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is:

Accepted Answer

(B) $\dfrac{3}{5}$

Answer

(A) $\dfrac{4}{5}$

Answer

(C) $\dfrac{\sqrt{7}}{4}$

Answer

(D) $\dfrac{\sqrt{3}}{2}$

Question 19

Let the system of equations $x+5y-z=1$, $4x+3y-3z=7$, $24x+y+\lambda z=\mu$; $\lambda,\mu\in\mathbb{R}$, have infinitely many solutions. Then the number of the solutions of this system, if $x,y,z$ are integers and satisfy $7\le x+y+z\le 77$, is

Accepted Answer

(A) 3

Answer

(B) 6

Answer

(C) 5

Answer

(D) 4

Question 20

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is:

Accepted Answer

(D) 757

Answer

(A) 760

Answer

(B) 755

Answer

(C) 750

Question 21

If the function $f(x)=\dfrac{	an(	an x)-\sin(\sin x)}{	an x-\sin x}$ is continuous at $x=0$, then $f(0)$ is equal to __________.

Accepted Answer

2

Question 22

If $\displaystyle\int\left(\dfrac{1}{x}+\dfrac{1}{x^3}\right)\left(3x^{-24}+x^{-26}\right)^{1/23}dx=-\dfrac{\alpha}{3(\alpha+1)}\left(3x^{\beta}+x^{\gamma}\right)^{\frac{\alpha+1}{\alpha}}+C$, $x>0$, $(\alpha,\beta,\gamma\in\mathbb{Z})$, where $C$ is the constant of integration, then $\alpha+\beta+\gamma$ is equal to __________.

Accepted Answer

19

Question 23

For $t>-1$, let $\alpha_t$ and $\beta_t$ be the roots of the equation $\left((t+2)^{1/7}-1ight)x^2+\left((t+2)^{1/6}-1ight)x+\left((t+2)^{1/21}-1ight)=0$. If $\lim\limits_{t	o -1^+}\alpha_t=a$ and $\lim\limits_{t	o -1^+}\beta_t=b$, then $72(a+b)^2$ is equal to __________.

Accepted Answer

98

Question 24

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be $2a$ and $2b$, respectively, and one focus and the corresponding directrix of this hyperbola be $(-5,0)$ and $5x+9=0$, respectively. If the product of the focal distances of a point $\left(\alpha,2\sqrt{5}\right)$ on the hyperbola is $p$, then $4p$ is equal to __________.

Accepted Answer

189

Question 25

The sum of the series $2	imes 1	imes{}^{20}C_4-3	imes 2	imes{}^{20}C_5+4	imes 3	imes{}^{20}C_6-5	imes 4	imes{}^{20}C_7+\dots+18	imes 17	imes{}^{20}C_{20}$, is equal to __________.

Accepted Answer

34

Question 26

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The outer body of an aircraft is made of metal which protects persons sitting inside from lightning-strikes.
Reason (R): The electric field inside the cavity enclosed by a conductor is zero.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(A) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer

(B) (A) is correct but (R) is not correct

Answer

(C) Both (A) and (R) are correct but (R) is not correct explanation of (A)

Answer

(D) (A) is not correct but (R) is correct

Question 27

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The density of the copper $\left({}^{64}_{29}\mathrm{Cu}\right)$ nucleus is greater than that of the carbon $\left({}^{12}_{6}\mathrm{C}\right)$ nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(B) (A) is not correct but (R) is correct

Answer

(A) (A) is correct but (R) is not correct

Answer

(C) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer

(D) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Question 28

The unit of $\sqrt{\dfrac{2I}{\epsilon_0\,c}}$ is: ($I$ = intensity of an electromagnetic wave, $c$ = speed of light)

Accepted Answer

(D) $NC^{-1}$

Answer

(A) Vm

Answer

(B) NC

Answer

(C) Nm

Question 29

The dimension of $\sqrt{\dfrac{\mu_0}{\epsilon_0}}$ is equal to that of: ($\mu_0$ = vacuum permeability and $\epsilon_0$ = vacuum permittivity)

Accepted Answer

(D) Resistance

Answer

(A) Voltage

Answer

(B) Capacitance

Answer

(C) Inductance

Question 30

A photo-emissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$. The longest wavelength of radiation that can emit photoelectron is $\lambda_0$. Expression for de-Broglie wavelength is given by: ($m$ = mass of the electron, $h$ = Planck's constant and $c$ = speed of light)

Accepted Answer

(A) $\lambda_e=\sqrt{\dfrac{h}{2mc\left(\frac{1}{\lambda_i}-\frac{1}{\lambda_0}\right)}}$

Answer

(B) $\lambda_e=\sqrt{\dfrac{h\lambda_0}{2mc}}$

Answer

(C) $\lambda_e=\dfrac{h}{\sqrt{2mc\left(\frac{1}{\lambda_i}-\frac{1}{\lambda_0}\right)}}$

Answer

(D) $\lambda_e=\sqrt{\dfrac{h\lambda_i}{2mc}}$

Question 31

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and areal velocity of planet is constant.
Reason (R): For a central force field the angular momentum is constant.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(A) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer

(B) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Answer

(C) (A) is correct but (R) is not correct

Answer

(D) (A) is not correct but (R) is correct

Question 32

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Given: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Accepted Answer

(D) 1 : 1

Answer

(A) 1 : 10

Answer

(B) 10 : 1

Answer

(C) $1:\sqrt{10}$

Question 33

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass-water contact angle $\simeq 0^\circ$) with $30^\circ$ inclined with vertical. The length of water risen in the capillary is __________ cm. (Take $g=9.8$ m/s$^2$)

Accepted Answer

(A) $\dfrac{82}{5}$

Answer

(B) $\dfrac{57}{2}$

Answer

(C) $\dfrac{71}{5}$

Answer

(D) $\dfrac{68}{5}$

Question 34

A mirror is used to produce an image with magnification of $\dfrac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is __________.

Accepted Answer

(C) 10.7 cm

Answer

(A) 10 cm

Answer

(B) 12.7 cm

Answer

(D) 15 cm

Question 35

A dipole with two electric charges of 2 μC magnitude each, with separation distance 0.5 μm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates with a potential difference of 5 V applied. Separation between the plates is 0.5 mm. If the dipole is rotated by $30^\circ$ from the axis, it tends to realign in the direction due to a torque. The value of torque is:

Accepted Answer

(A) $5	imes10^{-9}$ Nm

Answer

(B) $5	imes10^{-3}$ Nm

Answer

(C) $2.5	imes10^{-12}$ Nm

Answer

(D) $2.5	imes10^{-9}$ Nm

Question 36

Consider the following logic circuit. The output is $Y=0$ when:

Accepted Answer

(A) A = 1 and B = 1

Answer

(B) A = 0 and B = 1

Answer

(C) A = 1 and B = 0

Answer

(D) A = 0 and B = 0

Question 37

Match the LIST-I (Mechanical quantity) with LIST-II (Dimensional formula). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

The equation of a wave travelling on a string is $y=\sin[20\pi x+10\pi t]$, where $x$ and $t$ are distance and time in SI units. The minimum distance between two points having the same oscillating speed is:

Accepted Answer

(A) 5.0 cm

Answer

(B) 20 cm

Answer

(C) 10 cm

Answer

(D) 2.5 cm

Question 39

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Refractive index of glass is higher than that of air.
Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(C) (A) is correct but (R) is not correct

Answer

(A) (A) is not correct but (R) is correct

Answer

(B) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer

(D) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Question 40

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Magnetic monopoles do not exist.
Reason (R): Magnetic field lines are continuous and form closed loops.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(C) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer

(A) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Answer

(B) (A) is correct but (R) is not correct

Answer

(D) (A) is not correct but (R) is correct

Question 41

Which one of the following forces cannot be expressed in terms of potential energy?

Accepted Answer

(C) Frictional force

Answer

(A) Coulomb's force

Answer

(B) Gravitational force

Answer

(D) Restoring force

Question 42

Match the LIST-I (Thermodynamic process) with LIST-II (Characteristic). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 43

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is: (use acceleration due to gravity $g=10$ m/s$^2$ and neglect air resistance)

Accepted Answer

(D) $2\sqrt{2}$ km

Answer

(A) $2\sqrt{5}$ km

Answer

(B) 4 km

Answer

(C) 7.2 km

Question 44

An object with mass 500 g moves along x-axis with speed $v=4\sqrt{x}$ m/s. The force acting on the object is:

Accepted Answer

(D) 4 N

Answer

(A) 8 N

Answer

(B) 5 N

Answer

(C) 6 N

Question 45

A transparent block A having refractive index $\mu=1.25$ is surrounded by another medium of refractive index $\mu=1.0$ as shown in the figure. A light ray is incident on the flat face of the block with incident angle $	heta$ as shown in the figure. What is the maximum value of $	heta$ for which light suffers total internal reflection at the top surface of the block?

Accepted Answer

(C) $\sin^{-1}(3/4)$

Answer

(A) $	an^{-1}(4/3)$

Answer

(B) $	an^{-1}(3/4)$

Answer

(D) $\cos^{-1}(3/4)$

Question 46

A parallel plate capacitor has charge $5	imes10^{-8}$ C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4	imes10^{-8}$ C then the dielectric constant of the slab is __________.

Accepted Answer

5

Question 47

An inductor of reactance 100 $\Omega$, a capacitor of reactance 50 $\Omega$, and a resistor of resistance 50 $\Omega$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is __________ W.

Accepted Answer

1

Question 48

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are: $\dfrac{L_A}{L_B}=\dfrac{1}{2}$, $\dfrac{r_A}{r_B}=2$ and $\dfrac{K_A}{K_B}=\dfrac{1}{2}$. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of the rods' interface is __________ K, when equilibrium is established.

Accepted Answer

360

Question 49

The electric field in a region is given by $\vec{E}=\left(2\hat{i}+4\hat{j}+6\hat{k}ight)	imes10^{3}$ N/C. The flux of the field through a rectangular surface parallel to the x-z plane is $6.0$ Nm$^2$C$^{-1}$. The area of the surface is __________ cm$^2$.

Accepted Answer

15

Question 50

Let M and R be the mass and radius of a disc. A small disc of radius $\dfrac{R}{3}$ is removed from the bigger disc as shown in the figure. The moment of inertia of the remaining part of the bigger disc about an axis AB passing through the centre O and perpendicular to the plane of the disc is $\dfrac{4}{x}MR^2$. The value of x is __________.

Accepted Answer

9

Question 51

Given below are two statements:

Statement (I): On hydrolysis, oligo peptides give rise to fewer number of α-amino acids while proteins give rise to a large number of β-amino acids.

Statement (II): Natural proteins are denatured by acids which convert the water soluble form of fibrous proteins to their water insoluble form.

In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(C) Both statement I and statement II are incorrect

Answer

(A) Both statement I and statement II are correct

Answer

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

Answer

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

Question 52

Mixture of 1 g each of chlorobenzene, aniline and benzoic acid is dissolved in 50 mL ethyl acetate and placed in a separating funnel. 5 M NaOH (30 mL) was added in the same funnel. The funnel was shaken vigorously and then kept aside. The ethyl acetate layer in the funnel contains:

Accepted Answer

(D) chlorobenzene and aniline

Answer

(A) benzoic acid

Answer

(B) benzoic acid and aniline

Answer

(C) benzoic acid and chlorobenzene

Question 53

The hydration energies of $K^+$ and $Cl^-$ are $-x$ and $-y$ kJ/mol respectively. If lattice energy of KCl is $-z$ kJ/mol, then the heat of solution of KCl is:

Accepted Answer

(C) $z-(x+y)$

Answer

(A) $+x-y-z$

Answer

(B) $x+y+z$

Answer

(D) $-z-(x+y)$

Question 54

$A(g)\rightarrow B(g)+C(g)$ is a first order reaction. The reaction was started with reactant A only. The total pressure of the system is $P_t$ at time $t$ and $P_\infty$ at the end of the reaction ($t=\infty$). Which of the following expression is correct for the rate constant $k$?

Accepted Answer

(C) $k=\dfrac{1}{t}\ln\dfrac{P_\infty}{2(P_\infty-P_t)}$

Answer

(A) $k=\dfrac{1}{t}\ln\dfrac{2(P_\infty-P_t)}{P_t}$

Answer

(B) $k=\dfrac{1}{t}\ln\dfrac{P_\infty}{P_t}$

Answer

(D) $k=\dfrac{1}{t}\ln\dfrac{P_\infty}{(P_\infty-P_t)}$

Question 55

"P" is an optically active compound with molecular formula $C_6H_{12}O$. When "P" is treated with 2,4-dinitrophenylhydrazine, it gives a positive test. However, in presence of Tollens reagent, "P" gives a negative test. Predict the structure of "P".

Accepted Answer

(B) $CH_3{-}CO{-}CH(CH_2CH_3){-}CH_3$

Answer

(A) $CH_3{-}CO{-}CH_2{-}CH_2{-}CH_2{-}CH_3$

Answer

(C) $H{-}CO{-}CH_2{-}CH(CH_2CH_3){-}CH_3$

Answer

(D) $CH_3{-}CO{-}CH_2{-}CH(CH_3){-}CH_3$

Question 56

Choose the incorrect trend in the atomic radii (r) of the elements:

Accepted Answer

(B) $r_{Mg}<r_{Al}$

Answer

(A) $r_{Br}<r_K$

Answer

(C) $r_{Rb}<r_{Cs}$

Answer

(D) $r_{At}<r_{Cs}$

Question 57

Match the LIST-I (Conversion) with LIST-II (Reagents and conditions used). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 58

The correct statement amongst the following is:

Accepted Answer

(D) $\Delta_f H^{\ominus}_{500}$ is zero for $O_2$(g)

Answer

(A) The term 'standard state' implies that the temperature is $0^\circ$C

Answer

(B) The standard state of pure gas is the pure gas at a pressure of 1 bar and temperature 273 K

Answer

(C) $\Delta_f H^{\ominus}_{298}$ is zero for O(g)

Question 59

Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $x_A$ and $x_B$ are the mole fraction of A and B in solution while $y_A$ and $y_B$ are the mole fraction of A and B in vapour phase then:

Accepted Answer

(C) $\dfrac{x_A}{x_B}>\dfrac{y_A}{y_B}$

Answer

(A) $\dfrac{x_A}{x_B}<\dfrac{y_A}{y_B}$

Answer

(B) $\dfrac{x_A}{x_B}=\dfrac{y_A}{y_B}$

Answer

(D) $(x_A-y_A)<(x_B-y_B)$

Question 60

'X' is the number of acidic oxides among $VO_2$, $V_2O_3$, $CrO_3$, $V_2O_5$ and $Mn_2O_7$. The primary valency of cobalt in $[Co(H_2NCH_2CH_2NH_2)_3]_2(SO_4)_3$ is Y. The value of X + Y is:

Accepted Answer

(A) 5

Answer

(B) 4

Answer

(C) 2

Answer

(D) 3

Question 61

The descending order of basicity of the following amines is:

Accepted Answer

(B) E > D > B > A > C

Answer

(A) B > E > D > A > C

Answer

(C) E > D > A > B > C

Answer

(D) E > A > D > C > B

Question 62

Match the LIST-I (Complex) with LIST-II (Primary and secondary valency). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

Match the LIST-I (Binary solution) with LIST-II (Property). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

In $SO_2$, $NO_2^-$ and $N_3^-$ the hybridizations at the central atom are respectively:

Accepted Answer

(A) $sp^2$, $sp^2$ and $sp$

Answer

(B) $sp^2$, $sp$ and $sp$

Answer

(C) $sp^2$, $sp^2$ and $sp^2$

Answer

(D) $sp$, $sp^2$ and $sp$

LIST-I (Mechanical quantity)	LIST-II (Dimensional formula)
A.Mass density	I. $[ML^2T^{-3}]$
B.Impulse	II. $[MLT^{-1}]$
C.Power	III. $[ML^2T^0]$
D.Moment of inertia	IV. $[ML^{-3}T^0]$

LIST-I (Thermodynamic process)	LIST-II (Characteristic)
A.Isothermal	I. $\Delta W$ (work done) $=0$
B.Adiabatic	II. $\Delta Q$ (supplied heat) $=0$
C.Isobaric	III. $\Delta U$ (change in internal energy) $\ne 0$
D.Isochoric	IV. $\Delta U=0$

LIST-I (Conversion)	LIST-II (Reagents and conditions used)
A.see figure	I.Warm, $H_2O$
B.see figure	II.(a) NaOH, 368 K; (b) $H_3O^+$
C.see figure	III.(a) NaOH, 443 K; (b) $H_3O^+$
D.see figure	IV.(a) NaOH, 623 K, 300 atm; (b) $H_3O^+$

LIST-I (Complex)	LIST-II (Primary and secondary valency)
A. $[Co(en)_2Cl_2]Cl$	I.3, 6
B. $[Pt(NH_3)_2Cl(NO_2)]$	II.3, 4
C. $Hg[Co(SCN)_4]$	III.2, 6
D. $[Mg(EDTA)]^{2-}$	IV.2, 4

LIST-I (Binary solution)	LIST-II (Property)
A.Solution of chloroform and acetone	I.Minimum boiling azeotrope
B.Solution of ethanol and water	II.Dimerizes
C.Solution of benzene and toluene	III.Maximum boiling azeotrope
D.Solution of acetic acid in benzene	IV. $\Delta V_{mix}=0$

JEE Main 7 April 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 7 April 2025 Shift 2

Chemistry — JEE Main 7 April 2025 Shift 2

Mathematics — JEE Main 7 April 2025 Shift 2

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