JEE Main 2025 · 07 Apr 2025 · Shift 2

Q1.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 air craft is made of metal which protects persons sitting inside from lightning-strikes.
Reason (R) : The electric field inside the cavi …

Q2.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 $\left({}_{29}^{64}\mathrm{Cu}\right)$ nucleus is greater than that of the carbon $\left({}_6^{12}\mathrm{C}\right)$ nuc …

Q3.The unit of $\sqrt{\frac{2I}{{ϵ}_{0}c}}$ is :
(I = intensity of an electromagnetic wave, $\mathrm{c}:$ speed of light)

Q4.The dimension of $\sqrt{\frac{{\mu }_0}{{ϵ}_0}}$ is equal to that of :
( ${\mu }_0=$ Vacuum permeability and ${ϵ}_0=$ Vacuum permittivity)

Q5.A photo-emissive substance is illuminated with a radiation of wavelength ${\lambda }_{\mathrm{i}}$ so that it releases electrons with de-Broglie wavelength ${\lambda }_{\mathrm{e}}$. The longest wavelength of radiation that can emit photoelectron is ${\lambda }_0$. Expression for …

Q6.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 thus areal velocity of planet is constant.
Reason (R) : For …

Q7.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 :
(Give : Molar mass of helium $=4\mathrm{g}/\mathrm{mol}$, Molar mass of argon $=40\mathrm{g}/\mathrm{mol}$ )

Q8.A capillary tube of radius 0.1 mm is partly dipped in water (surface tension $70\mathrm{dyn}/\mathrm{cm}$ 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 …

Q9.A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm , then the focal length of the mirror is ____ .

Q10.A dipole with two electric charges of $2\mu \mathrm{C}$ magnitude each, with separation distance $0.5\mu \mathrm{m}$, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference …

Q11.Consider the following logic circuit.

The output is $\mathrm{Y}=0$ when :

Q12.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 :

Q13.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 i …

Q14.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 …

Q15.Which one of the following forces cannot be expressed in terms of potential energy?

Q16.A helicopter flying horizontally with a speed of $360\mathrm{km}/\mathrm{h}$ 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 wa …

Q17.An object with mass 500 g moves along x -axis with speed $\mathrm{v}=4\sqrt{\mathrm{x}}\mathrm{m}/\mathrm{s}$. The force acting on the object is :

Q18.A transparent block A having refractive index $\mu =1.25$ is surrounded by another medium of refractive index $\mu =1.0$ as shown in figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in figure. What is the maximum value of …

Q19.A parallel plate capacitor has charge $5\times 10^{-6}\mathrm{C}$. 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 $4\times 10^{-6}$ C then the dielectric constant of the slab …

Q20.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.

Q21.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 : …

Q22.The electric field in a region is given by $\vec{E}=(2\hat{i}+4\hat{j}+6\hat{k})\times 10^3\mathrm{N}/\mathrm{C}$. The flux of the field through a rectangular surface parallel to $\mathrm{x}-\mathrm{z}$ plane is $6.0{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$. The area of t …

Q23.$M$ and $R$ be the mass and radius of a disc. A small disc of radius $R/3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the centre O and perpendicular to the plane of disc is …

Q24.Match List-I with List-II:
List-I: (A) Isothermal (B) Adiabatic (C) Isobaric (D) Isochoric
List-II: (I) W (work done) = 0 (II) Q (supplied heat) = 0 (III) ΔU (change in internal energy) ≠ 0 (IV) ΔU = 0
Choose the correct answer from the options given below:

Q1.Given below are two statements :

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

Statement (II) : Natural proteins are denatured by acids which convert the water so …

Q2.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 conta …

Q3.The hydration energies of ${\mathrm{K}}^{+}$ and ${\mathrm{Cl}}^{-}$ are -x and -y $\mathrm{kJ}/\mathrm{mol}$ respectively. If lattice energy of KCl is -z $\mathrm{kJ}/\mathrm{mol}$, then the heat of solution of KCl is :

Q4.$\mathrm{A}(\mathrm{g})\to \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ is a first order reaction.

The reaction was started with react …

Q5." P " is an optically active compound with molecular formula ${\mathrm{C}}_6{\mathrm{H}}_{12}\mathrm{O}$. 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 …

Q6.Choose the incorrect trend in the atomic radii (r) of the elements :

Q7.Match List-I with List-II
| (B) (see structure) | (II) (a) $\mathrm{NaOH},368\mathrm{K}$; (b) …

Q8.The correct statement amongst the following is :

Q9.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 ${\mathrm{x}}_{\mathrm{A}}$ and $x_B$ are the mole fraction of $A$ and $B$ in solution while $y_A$ and $y_B$ are the mole fraction …

Q10.' X ' is the number of acidic oxides among ${\mathrm{VO}}_2$, ${\mathrm{V}}_2{\mathrm{O}}_3,{\mathrm{CrO}}_3,{\mathrm{V}}_2{\mathrm{O}}_5$ and ${\mathrm{Mn}}_2{\mathrm{O}}_7$. The primary valency of cobalt in …

Q11.The descending order of basicity of following amines is :

(A) (see structure)

(B) (see structure)

(C) (see structure)

(D) ${\mathrm{CH}}_3{\mathrm{NH}}_2$

(E) ${\left({\mathrm{CH}}_3\right)}_2\mathrm{NH}$

Choose the correct answer from the options given below :

Q12.Match List-I with List-II
| (B) …

Q13.Match List-I with List-II
| (D) …

Q14.In ${\mathrm{SO}}_2,{\mathrm{NO}}_2^{-}$ and ${\mathrm{N}}_3^{-}$ the hybridizations at the central atom are respectively :

Q15.The number of unpaired electrons responsible for the paramagnetic nature of the following complex species are respectively : …

Q16.The number of optically active products obtained from the complete ozonolysis of the given compound is :

Q17.Given below are two statements :

Statement (I) : (see structure A) is more polar than (see structure B)

Statement (II) : Boiling point of (see structure C) is lower than (see structure D) but it is more polar than (see structure E)

In the light of the above statements, choose …

Q18.The extra stability of half-filled subshell is due to
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electr …

Q19.The correct statements from the following are :
(A) ${\mathrm{Tl}}^{3+}$ is a powerful oxidising agent
(B) ${\mathrm{Al}}^{3+}$ does not get reduced easily
(C) Both ${\mathrm{Al}}^{3+}$ and ${\mathrm{Tl}}^{3+}$ are very stable in solution
(D) ${\mathrm{Tl}}^{+}$ is more stable than …

Q20.Given below are two statements :

1 M aqueous solution of each of $\mathrm{Cu}{\left({\mathrm{NO}}_3\right)}_2$, ${\mathrm{AgNO}}_3,{\mathrm{Hg}}_2{\left({\mathrm{NO}}_3\right)}_2;\mathrm{Mg}{\left({\mathrm{NO}}_3\right)}_2$ are electrolysed using inert electrodes,

Given : …

Q21.Only litre buffer solution was prepared by adding 0.10 mol each of ${\mathrm{NH}}_3$ and ${\mathrm{NH}}_4\mathrm{Cl}$ in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is $\_\_\_\_$ $\times 10^{-2}$,(Nearest integer)
(Given : …

Q22.In Dumas' method 292 mg of an organic compound released 50 mL of nitrogen gas ( ${\mathrm{N}}_2$ ) at 300 K temperature and 715 mm Hg pressure. The percentage composition of ' N ' in the organic compound is $\_\_\_\_$ % (Nearest integer)
(Aqueous tension at …

Q23.Butane reacts with oxygen to produce carbon dioxide and water following the equation given below
${\mathrm{C}}_4{\mathrm{H}}_{10}(\mathrm{g})+\frac{13}{2}{\mathrm{O}}_2(\mathrm{g})\to 4{\mathrm{CO}}_2(\mathrm{g})+5{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$
If 174.0 kg o …

Q24.The number of paramagnetic metal complex species among ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+},{\left[\mathrm{Co}{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3\right]}^{3-}$, …

Q25.Identify the structure of the final product (D) in the following sequence of the reactions :

(see reaction scheme)

Total number of ${\mathrm{sp}}^2$ hybridised carbon atoms in product D is.

Q1.If the orthocentre of the triangle formed by the lines $\mathrm{y}=\mathrm{x}+1,\mathrm{y}=4\mathrm{x}-8$ and $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ is at $(3,-1)$, then $\mathrm{m}-\mathrm{c}$ is :

Q2.Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that $\frac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1$. Then $\frac{|\vec{a}+\vec{b}{|}^2}{|\vec{a}{|}^2}$ is :

Q3.Let
$\mathrm{A}=\{(\alpha ,\beta )\in \mathbf{R}\times \mathbf{R}:|\alpha -1|\le 4$ and $|\beta -5|\le 6\}$
and
$B=\left\{(\alpha ,\beta )\in \mathbf{R}\times \mathbf{R}:16(\alpha -2{)}^2+9(\beta -6{)}^2\le 144\right\}$.
Then

Q4.If the range of the function $f(x)=\frac{5-x}{x^2-3x+2}$, $x\ne 1,2$, is $(-\infty ,\alpha ]\cup [\beta ,\infty )$, then ${\alpha }^2+{\beta }^2$ is equal to :

Q5.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 $\frac{\mathrm{m}}{\mathrm{n}},\gcd (\mathrm{m},\mathrm{n})=1$, then …

Q6.Let a random variable X take values $0,1,2,3$ with $\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)=\mathrm{p},\mathrm{P}(\mathrm{X}=2)=\mathrm{P}(\mathrm{X}=3)$ and $\mathrm{E}\left({\mathrm{X}}^2\right)=2\mathrm{E}(\mathrm{X})$. Then the value of $8\mathrm{p}-1$ is …

Q7.If the area of the region
$\left\{(\mathrm{x},\mathrm{y}):1+{\mathrm{x}}^2\le \mathrm{y}\le \min \{\mathrm{x}+7,11-3\mathrm{x}\}\right\}$ is A , then 3 A is equal to

Q8.Let $f:\mathbf{R}\to \mathbf{R}$ be a polynomial function of degree four having extreme values at $\mathrm{x}=4$ and $\mathrm{x}=5$.

If ${\lim }_{\mathrm{x}\to 0}\frac{f(\mathrm{x})}{{\mathrm{x}}^2}=5$, then $f(2)$ is equal to :

Q9.The number of solutions of the equation
$\cos 2\theta \cos \frac{\theta }{2}+\cos \frac{5\theta }{2}=2{\cos }^3\frac{5\theta }{2}$ in $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$ is :

Q10.Let $a_n$ be the $n^{\text{th }}$ term of an A.P.

If ${\mathrm{S}}_{\mathrm{n}}={\mathrm{a}}_1+{\mathrm{a}}_2+{\mathrm{a}}_3+\dots .+{\mathrm{a}}_{\mathrm{n}}=700,{\mathrm{a}}_6=7$ and ${\mathrm{S}}_7=7$, then ${\mathrm{a}}_{\mathrm{n}}$ is equal to :

Q11.If the locus of $z\in \mathrm{C}$, such that

is a circle of radius $r$ and center $(a,b)$ then $\frac{15ab}{r^2}$ is equal to :

Q12.Let the length of a latus rectum of an ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ be 10 . If its eccentricity is the minimum value of the function $f(\mathrm{t})={\mathrm{t}}^2+\mathrm{t}+\frac{11}{12}$, …

Q13.Let $y=y(x)$ be the solution of the differential equation $\left(x^2+1\right)y^{\prime }-2xy=\left(x^4+2x^2+1\right)\cos x$, $\mathrm{y}(0)=1$. Then ${\int }_{-3}^3\mathrm{y}(\mathrm{x})\mathrm{dx}$ is :

Q14.If the equation of the line passing through the point $\left(0,-\frac{1}{2},0\right)$ and perpendicular to the lines $\overrightarrow{\mathrm{r}}=\lambda (\hat{\mathrm{i}}+\mathrm{a}\hat{\mathrm{j}}+\mathrm{b}\hat{\mathrm{k}})$ and …

Q15.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 $\mathrm{p}+\mathrm{q}=126$, then the eccentricity of the ellipse …

Q16.Consider the lines ${\mathrm{L}}_1:\mathrm{x}-1=\mathrm{y}-2=\mathrm{z}$ and ${\mathrm{L}}_2:\mathrm{x}-2=\mathrm{y}=\mathrm{z}-1$. Let the feet of the perpendiculars from the point $\mathrm{P}(5,1,-3)$ on the lines ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ be Q and R res …

Q17.The number of real roots of the equation $\mathrm{x}|\mathrm{x}-2|+3|\mathrm{x}-3|+1=0$ is :

Q18.Let ${\mathrm{e}}_1$ and ${\mathrm{e}}_2$ be the eccentricities of the ellipse $\frac{x^2}{b^2}+\frac{y^2}{25}=1$ and the hyperbola $\frac{x^2}{16}-\frac{y^2}{b^2}=1$, respectively. If $\mathrm{b}<5$ and ${\mathrm{e}}_1{\mathrm{e}}_2=1$, then the eccentri …

Q19.Let the system of equations
$\mathrm{x}+5\mathrm{y}-\mathrm{z}=1$
$4\mathrm{x}+3\mathrm{y}-3\mathrm{z}=7$
$24\mathrm{x}+\mathrm{y}+\lambda \mathrm{z}=\mu$
$\lambda ,\mu \in \mathrm{R}$, have infinitely many solutions. Then the number of the solutions of this system, …

Q20.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 :

Q21.If the function $f(\mathrm{x})=\frac{\tan (\tan \mathrm{x})-\sin (\sin \mathrm{x})}{\tan \mathrm{x}-\sin \mathrm{x}}$ is continuous at $\mathrm{x}=0$, then $f(0)$ is equal to ______.

Q22.If $\int \left(\frac{1}{\mathrm{x}}+\frac{1}{{\mathrm{x}}^3}\right)\left(\sqrt[23]{3{\mathrm{x}}^{-24}+{\mathrm{x}}^{-26}}\right)\mathrm{dx}$

$(\alpha ,\beta ,\gamma \in Z)$, …

Q23.For $\mathrm{t}>-1$, let ${\alpha }_{\mathrm{t}}$ and ${\beta }_{\mathrm{t}}$ be the roots of the equation $\left((t+2{)}^{\frac{1}{7}}-1\right)x^2+\left((t+2{)}^{\frac{1}{6}}-1\right)x+\left((t+2{)}^{\frac{1}{21}}-1\right)=0$.

If …

Q24.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 $5\mathrm{x}+9=0$, respectively. If the product of the focal distances of a point …

Q25.The sum of the series
$2\times 1\times {}^{20}{\mathrm{C}}_4-3\times 2\times {}^{20}{\mathrm{C}}_5+4\times 3\times {}^{20}{\mathrm{C}}_6-5\times 4\times {}^{20}{\mathrm{C}}_7+\dots +18\times 17\times {}^{20}{\mathrm{C}}_{20}$, is equal to