JEE Main 2025 · 03 Apr 2025 · Shift 1

Q1.During the melting of a slab of ice at 273 K at atmospheric pressure :

Q2.Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area $0.5{\mathrm{m}}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the wate …

Q3.Choose the correct logic circuit for the given truth table having inputs A and B .

Q4.The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is :

Q5.A wire of length 25 m and cross-sectional area 0.5 mm^2 having resistivity of 2 x 10^-6 Ohm m is bent into a complete circle. The resistance between diametrically opposite points will be

Q6.Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
( $\mu =$ coefficient of friction between the two blocks) …

Q7.Which of the following curves possibly represent one-dimensional motion of a particle ?
(A) (see graph)
(B) (see graph)
(C) (see graph)
(D) (see graph)

Choose the correct answer from the options given below :

Q8.A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant ${\epsilon }_1$ and ${\epsilon }_2$, as shown in figures. The distance between the plates is d and area of each plate is A . If capacitance in first configuration and second config …

Q9.Match the LIST-I with LIST-II

Q10.A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

Q11.A piston of mass M is hung from a massless spring whose restoring force law goes as $\mathrm{F}=-{\mathrm{kx}}^3$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n ' moles o …

Q12.A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800{\mathrm{cm}}^3$ and temperature $27^{\circ }\mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200{\mathrm{cm}}^3$ is :
(Take …

Q13.Match the LIST-I with LIST-II

Choose the correct answer from the options given below :

Q14.The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10\mathrm{cm}$ is 120 V . The potential at the centre of shell, at a distance $\mathrm{r}=5\mathrm{cm}$ from centre, and at a distance $\mathrm{r}=15\mathrm{cm}$ from the c …

Q15.The work function of a metal is 3 eV . The color of the visible light that is required to cause emission of photoelectrons is

Q16.A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

Q17.A person measures mass of 3 different particles as $435.42\mathrm{g},226.3\mathrm{g}$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

Q18.The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is

Q19.The angle of projection of a particle is measured from the vertical axis as $\varphi$ and the maximum height reached by the particle is ${\mathrm{h}}_{\mathrm{m}}$. Here ${\mathrm{h}}_{\mathrm{m}}$ as function of $\varphi$ can be presented as

Q20.Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emerge …

Q21.Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4$ seconds. If the sides of the triangle are increased to length 2a and also t …

Q22.A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T . The magnetic force on the wire is ______ mN .

Q23.Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI . The value of $x$ is ______ .

Q24.A loop ABCDA , carrying current $\mathrm{I}=12\mathrm{A}$, is placed in a plane, consists of two semi-circular segments of radius ${\mathrm{R}}_1=6\pi \mathrm{m}$ and ${\mathrm{R}}_2=4\pi \mathrm{m}$. The magnitude of the resultant magnetic field at center O is …

Q25.In the figure shown below, a resistance of $150.4\Omega$ is connected in series to an ammeter A of resistance $240\Omega$. A shunt resistance of $10\Omega$ is connected in parallel with the ammeter. The reading of the ammeter is ______ mA.

Q1.Which of the following postulate of Bohr's model of hydrogen atom in not in agreement with quantum mechanical model of an atom ?

Q2.Given below are two statements

Statement I: The N-N single bond is weaker and longer than that of $\mathrm{P}-\mathrm{P}$ single bond
Statement II : Compounds of group 15 elements in $+3$ oxidation states readily undergo disproportionation reactions.
In the light of above statem …

Q3.Given below are two statements

Statement I : A catalyst cannot alter the equilibrium constant ( ${\mathrm{K}}_{\mathrm{c}}$ ) of the reaction, temperature remaining constant
Statement II : A homogenous catalyst can change the equilibrium composition of a system temperature remaini …

Q4.The metal ions that have the calculated spin only magnetic moment value of 4.9 B.M. are
A. ${\mathrm{Cr}}^{2+}$
B. ${\mathrm{Fe}}^{2+}$
C. ${\mathrm{Fe}}^{3+}$
D. ${\mathrm{Co}}^{2+}$
E. ${\mathrm{Mn}}^{3+}$

Choose the correct answer from the options given below

Q5.In a reaction $\mathrm{A}+\mathrm{B}\to \mathrm{C}$, initial concentrations of $A$ and $B$ are related as $[A{]}_0=8[B{]}_0$. The half lives of $A$ and $B$ are 10 min and 40 min . respectively. If they start to disappear at the same time, both following first order kinet …

Q6.Which of the following is the correct structure of L -fructose?

Q7.Identify the correct statements from the following
A. (see structures) are metamers
B. (see structures) are functional isomers
C. (see structures) are position isomers
D. (see structures) are homologous
Choose the correct answer from the options given below

Q8.Among $10^{-9}\mathrm{g}$ (each) of the following elements, which one will have the highest number of atoms?

Element : Pb, Po, Pr and Pt

Q9.Which of the following statements are correct?
A. The process of the addition an electron to a neutral gaseous atom is always exothermic
B. The process of removing an electron from an isolated gaseous atom is always endothermic
C. The $1^{\text{st }}$ ionization energy of the bo …

Q10.Which of the following properties will change when system containing solution 1 will become solution 2 ?

Q11.Number of molecules from below which cannot give ioddoform reaction is :
Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol

Q12.Identify [A], [B], and [C], respectively in the following reaction sequence :

Q13.In the following reactions, which one is NOT correct?

Q14.The correct order of the complexes ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_5\left({\mathrm{H}}_2\mathrm{O}\right)\right]}^{3+}$ (A), ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ (B), ${\left[\mathrm{Co}(\mathrm{CN}{)}_6\right]}^{3-}$ (C) and …

Q15.In the following system,
${\mathrm{PCl}}_5(\mathrm{g})\rightleftharpoons {\mathrm{PCl}}_3(\mathrm{g})+{\mathrm{Cl}}_2(\mathrm{g})$ at equilibrium, upon addition of xenon gas at constant $T\&p$, the concentration of

Q16.2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is :
(Given : Ebullioscopic constant of water $=0.52\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$ )

Q17.Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis ?

Q18.The least acidic compound, among the following is:

Q19.Correct order of limiting molar conductivity for cations in water at 298 K is :

Q20.During estimation of nitrogen by Dumas' method of compound X (0.42 g):

_____ mL of ${\mathrm{N}}_2$ gas will be liberated at STP. (nearest integer)
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$: C: 12, H: 1, N : 14)

Q21.0.5 g of an organic compound on combustion gave 1.46 g of ${\mathrm{CO}}_2$ and 0.9 g of ${\mathrm{H}}_2\mathrm{O}$. The percentage of carbon in the compound is _____. (Nearest integer)
[Given : Molar mass (in $\mathrm{g}{\mathrm{mol}}^{-1}$ ) C: 12, H: 1, O : 16]

Q22.The number of optical isomers exhibited by the iron complex (A) obtained from the following reaction is _____.
FeCl3 + KOH + H2C2O4 -> A

Q23.Given : …

Q24.Consider the following reactions
$\mathrm{A}+\mathrm{NaCl}+{\mathrm{H}}_2{\mathrm{SO}}_4\to {\mathrm{CrO}}_2{\mathrm{Cl}}_2+$ Side Products
Little
amount …

Q1.Let A be a matrix of order $3\times 3$ and $|\mathrm{A}|=5$. If $|2\mathrm{adj}(3\mathrm{A}\mathrm{adj}(2\mathrm{A}))|=2^{\alpha }\cdot 3^{\beta }\cdot 5^{\gamma }$ where $\alpha ,\beta ,\gamma \in \mathrm{N}$, then $\alpha +\beta +\gamma$ is equal to

Q2.Let a line passing through the point $(4,1,0)$ intersect the line $L_1:\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $\mathrm{A}(\alpha ,\beta ,\gamma )$ and the line ${\mathrm{L}}_2:x-6=y=-z+4$ at the point $\mathrm{B}(\mathrm{a},\mathrm{b},\mathrm{c})$. …

Q3.Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt{3}x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2+3x-1=0$. If $P_n={\alpha }^n+{\beta }^n$ and $Q_n={\gamma }^n+{\delta }^n$, then …

Q4.The sum of all rational terms in the expansion of $(2+\sqrt{3}{)}^8$ is

Q5.Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$. Let $\mathrm{R}$ be a relation on A defined by xRy if and only if $0\le x^2+2y\le 4$. Let $\ell$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relati …

Q6.A line passing through the point $\mathrm{P}(\sqrt{5},\sqrt{5})$ intersects the ellipse $\frac{{\mathrm{x}}^2}{36}+\frac{{\mathrm{y}}^2}{25}=1$ at $A$ and $B$ such that $(PA)\cdot (PB)$ is maximum. Then $5(P{A}^2+P{B}^2)$ is equal to:

Q7.The sum $1+3+11+25+45+71+\dots$ upto 20 terms, is equal to

Q8.If the domain of the function $f(x)={\log }_e\left(\frac{2x-3}{5+4x}\right)+{\sin }^{-1}\left(\frac{4+3x}{2-x}\right)$ is $[\alpha ,\beta )$, then ${\alpha }^2+4\beta$ is equal to

Q9.If ${\sum }_{\mathrm{r}=1}^9\left(\frac{\mathrm{r}+3}{2^{\mathrm{r}}}\right)\cdot {}^9{\mathrm{C}}_{\mathrm{r}}=\alpha {\left(\frac{3}{2}\right)}^9-\beta$, where $\alpha ,\beta \in \mathrm{N}$, then $(\alpha +\beta {)}^2$ is equal to

Q10.The number of solutions of the equation $2x+3\tan x=\pi$, $x\in [-2\pi ,2\pi ]-\left\{\pm \frac{\pi }{2},\pm \frac{3\pi }{2}\right\}$ is

Q11.If $y(x)=\left|\begin{array}{ccc}\sin x& \cos x& \sin x+\cos x+1\\ 27& 28& 27\\ 1& 1& 1\end{array}\right|$, $x\in \mathbb{R}$, then $\frac{d^{2}y}{d{x}^2}+y$ is equal to

Q12.Let g be a differentiable function such that ${\int }_0^{\mathrm{x}}\mathrm{g}(\mathrm{t})\mathrm{dt}=\mathrm{x}-{\int }_0^{\mathrm{x}}\mathrm{tg}(\mathrm{t})\mathrm{dt}$, $\mathrm{x}\ge 0$ and let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ satisfy the differential equation …

Q13.A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines
${\mathrm{L}}_1:2\mathrm{x}+\mathrm{y}+6=0$ and ${\mathrm{L}}_2:4\mathrm{x}+2\mathrm{y}-\mathrm{p}=0,\mathrm{p}>0$, at the points A and B , respectively. I …

Q14.Let $z\in C$ be such that $\frac{z^2+3i}{z-2+i}=2+3i$. Then the sum of all possible values of $z^2$ is

Q15.Let $f(x)=\int {\mathrm{x}}^3\sqrt{3-{\mathrm{x}}^2}\mathrm{dx}$. If $5f(\sqrt{2})=-4$, then $f(1)$ is equal to

Q16.Let $a_1,a_2,a_3,\dots$ be a G. P. of increasing positive numbers. If ${\mathrm{a}}_3{\mathrm{a}}_5=729$ and ${\mathrm{a}}_2+{\mathrm{a}}_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to

Q17.Let the domain of the function
$f(\mathrm{x})={\log }_2{\log }_4{\log }_6\left(3+4\mathrm{x}-{\mathrm{x}}^2\right)$ be $(\mathrm{a},\mathrm{b})$. If …

Q18.The radius of the smallest circle which touches the parabolas $\mathrm{y}={\mathrm{x}}^2+2$ and $\mathrm{x}={\mathrm{y}}^2+2$ is

Q19.Let $f(\mathrm{x})=\{\begin{array}{lll}(1+\mathrm{ax}{)}^{1/\mathrm{x}}& ,& \mathrm{x}<0\\ 1+\mathrm{b}& ,& \mathrm{x}=0\\ \frac{(\mathrm{x}+4{)}^{1/2}-2}{(\mathrm{x}+\mathrm{c}{)}^{1/3}-2}& ,& \mathrm{x}>0\end{array}$
be continuous at $\mathrm{x}=0$. Then …

Q20.Line ${\mathrm{L}}_1$ passes through the point $(1,2,3)$ and is parallel to z -axis. Line ${\mathrm{L}}_2$ passes through the point ( $\lambda$, 5, 6) and is parallel to y -axis. Let for $\lambda ={\lambda }_1,{\lambda }_2,{\lambda }_2<{\lambda }_1$, the shortest distance …

Q21.All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by ${\mathrm{W}}_{\mathrm{n}}$. Let the probability $\mathrm{P}\left({\mathrm{W}}_{\mathrm{n}}\right)$ o …

Q22.Let the product of the focal distances of the point $\mathrm{P}(4,2\sqrt{3})$ on the hyperbola $\mathrm{H}:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ be 32. Let the length of the conjugate axis of H be p and the length of its latus rectu …

Q23.Let $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=3\hat{i}+2\hat{j}-\hat{k},\vec{c}=\lambda \hat{j}+\mu \hat{k}$ and $\hat{d}$ be a unit vector such that $\vec{a}\times \hat{d}=\vec{b}\times \hat{d}$ and $\vec{c}\cdot \hat{d}=1$, If $\overrightarrow{\mathrm{c}}$ is pe …

Q24.If the number of seven-digit numbers, such that the sum of their digits is even, is $m\cdot n\cdot 10^{\mathrm{n}}$; $m,n\in \{1,2,3,\dots ,9\}$, then $m+n$ is equal to

Q25.The area of the region bounded by the curve $y=\max \{|x|,x|x-2|\}$, then x-axis and the lines $x=-2$ and $x=4$ is equal to ______.