JEE Advanced 2025 · 18 May 2025 · Paper 1

Q1.The center of a disk of radius $r$ and mass $m$ is attached to a spring of spring constant $k$, inside a ring of radius $R>r$ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical …

Q2.In a scattering experiment, a particle of mass $2m$ collides with another particle of mass $m$, which is initially at rest. Assuming the collision to be perfectly elastic, the maximum angular deviation $\theta$ of the heavier particle, as shown in the figure, in radians is …

Q3.A conducting square loop initially lies in the $XZ$ plane with its lower edge hinged along the $X$-axis. Only in the region $y\ge 0$, there is a time dependent magnetic field pointing along the $Z$-direction, $\vec{B}(t)=B_0(\cos \omega t)\hat{K}$, where $B_0$ …

Q4.Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $D$ of a tube. The measured value of $D$ is:

Q5.A conducting square loop of side $L$, mass $M$ and resistance $R$ is moving in the $XY$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y\ge 0$ has a uniform magnetic field, $\vec{B}=B_{0}k$. The magnetic field is zero everywhere else. At ti …

Q6.Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm, 0.05 mm, and $6.0\mu \mathrm{m}$, respectively. Which of the following option(s) give(s) the volume of the strip in ${\mathrm{cm}}^3$ with correct significant figures:

Q7.Consider a system of three connected strings, $S_1,S_2$ and $S_3$ with uniform linear mass densities $\mu \mathrm{kg}/\mathrm{m}$, $4\mu \mathrm{kg}/\mathrm{m}$ and $16\mu \mathrm{kg}/\mathrm{m}$, respectively, as shown in the figure. $S_1$ and …

Q8.A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height $y$ (in m) of the elevator, from the ground, with time $t$ (in s) is given by $y=8\left[1+\sin \left(\frac{2\pi t}{T}\right)\right]$, w …

Q9.A cube of unit volume contains $35\times 10^7$ photons of frequency $10^{15}\mathrm{Hz}$. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is …

Q10.Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures ${\mathrm{T}}_{\mathrm{P}}$ and ${\mathrm{T}}_{\mathrm{Q}}$, respectively, with ${\mathrm{T}}_{\mathrm{Q}}<{\mathrm{T}}_{\mathrm{P}}$, as shown in Fig. 1. The radia …

Q11.A solid glass sphere of refractive index $n=\sqrt{3}$ and radius $R$ contains a spherical air cavity of radius $\frac{\mathrm{R}}{2}$, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index $n=1$ ) remains inside …

Q12.A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{bd}{D}=m\lambda$, where $b$ is the slit width, $D$ the shortest distance between the slit and the screen, $d$ the distance between the $m^{\text{th }}$ diffractio …

Q13.Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$, a neutron having thermal energy $k_{\mathrm{B}}T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by …

Q14.List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $p$, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance $2r$ apart a …

Q15.A circuit with an electrical load having impedance $Z$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $V(t)=300\sin (400t)\mathrm{V}$, where $t$ is time in s. List-I shows various options for the load. The possible currents …

Q16.List-I shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-II.
Choose the option that describes the correct match between the entries in List-I to those in List-II.

| List-I | | List- …

Q1.The heating of ${\mathrm{NH}}_4{\mathrm{NO}}_2$ at $60-70^{\circ }\mathrm{C}$ and ${\mathrm{NH}}_4{\mathrm{NO}}_3$ at $200-250^{\circ }\mathrm{C}$ is associated with the formation of nitrogen containing compounds $\mathbf{X}$ and $\mathbf{Y}$, respectively. $\mathbf{X}$ and …

Q2.The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

Q3.One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

Q4.Consider the depicted hydrogen (H) in the hydrocarbons given below. The most acidic hydrogen (H) is

Q5.Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the INCORRECT statement(s) is(are)

Q6.The pair(s) of diamagnetic ions is(are)

Q7.For the reaction sequence given below, the correct statement(s) is(are)

(In the options, X is any atom other than carbon and hydrogen, and it is different in P, Q and R)

Q8.In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to ${\mathrm{Cr}}^{3+}$. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of ${\mathrm{Cr}}^{3+}$ is ____.

Use: 1 Faraday $=96500\mathrm{C}{\mathrm{mol}}^{-1}$

Q9.At 25°C, the concentration of ${\mathrm{H}}^{+}$ ions in $1.00\times 10^{-3}\mathrm{M}$ aqueous solution of a weak monobasic acid having acid dissociation constant $\left(K_a\right)=4.00\times 10^{-11}$ is $\mathbf{X}\times 10^{-7}\mathrm{M}$. The value of …

Q10.Molar volume $\left(V_m\right)$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio (in $\mathrm{mol}{\mathrm{dm}}^{-3}$) of the coefficient of $V_m^2$ to the coefficient of $V_m$ for …

Q11.Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ____.

Use: Universal gas constant $(\mathrm{R})=8.3\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$; Atomic mass (in amu): …

Q12.The monomer $(\mathbf{X})$ involved in the synthesis of Nylon 6,6 gives positive carbylamine test. If 10 moles of $\mathbf{X}$ are analyzed using Dumas method, the amount (in grams) of nitrogen gas evolved is ____.

Use: Atomic mass of N (in amu) = 14

Q13.The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of $\mathbf{S}$ produced is ____.

Use: Atomic mass (in amu): …

Q14.The correct match of the group reagents in List-I for precipitating the metal ion given in List-II from solutions, is
| …

Q15.The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match each entry in List-I with the appropriate entry in List-II and choose the correct options.

List-I
(P) Stephen reaction
(Q) Sandmeyer reaction
(R) Hoffma …

Q16.Match the compounds in List-I with the appropriate observations in List-II and choose the correct option.

List-I
(P) (see structure)
(Q) (see structure)
(R) (see structure)
(S) (see structure)

List-II
(1) Reaction with phenyl diazonium salt gives yellow dye.
(2) Reaction with n …

Q1.Let $\mathbb{R}$ denote the set of all real numbers. Let $a_{\mathrm{i}},b_{\mathrm{i}}\in \mathbb{R}$ for $\mathrm{i}\in \{1,2,3\}$.
Define the functions $f:\mathbb{R}\to \mathbb{R},g:\mathbb{R}\to \mathbb{R}$, and …

Q2.Three students $S_1,S_2$ and $S_3$ are given a problem to solve. Consider the following events :
$U:$ At least one of $S_1,S_2$ and $S_3$ can solve the problem,
$V:S_1$ can solve the problem, given that neither ${\mathrm{S}}_2$ nor …

Q3.Let $\mathbb{R}$ denote the set of all real numbers. Define the function $f:\mathbb{R}\to \mathbb{R}$ by

Then which one o …

Q4.Consider the matrix

Let the transpose of a matrix $X$ be denoted by ${\mathrm{X}}^T$. Then the number of 3 × 3 invertible matrices Q with integer entries, such that …

Q5.Let $L_1$ be the line of intersection of the planes given by the equations

Let $L_2$ be the line passing through the point $P(2,-1,3)$ and parallel to $L_1$. Let $M$ denote the plane given by the equation …

Q6.Let $\mathbb{N}$ denote the set of all natural numbers, and $\mathbb{Z}$ denote the set of all integers. Consider the functions $f:\mathbb{N}\to \mathbb{Z}$ and $g:\mathbb{Z}\to \mathbb{N}$ defined by …

Q7.Let $\mathbb{R}$ denote the set of all real numbers. Let $z_1=1+2i$ and $z_2=3i$ be two complex numbers, where $i=\sqrt{-1}$. Let

Then which of the fo …

Q8.Let the set of all relations $R$ on the set $\{a,b,c,d,e,f\}$, such that $R$ is reflexive and symmetric, and $R$ contains exactly 10 elements, be denoted by $S$.
Then the number of elements in $S$ is ____.

Q9.For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\overrightarrow{0}$ denote the zero vector. Let $P,Q$ and $R$ be three distinct points in the $XY$-plane. Let $S$ be a point inside the tr …

Q10.Let $S$ be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2 . For example, 2210222 is in $S$, but 0210222 is NOT in $S$.

Then the number of elements $x$ in $S$ such that at least one the digits 0 and 1 appears exactly twice in $x$, is …

Q11.Let $\alpha$ and $\beta$ be the real numbers such that

Then the value of $\alpha +\beta$ is ____.

Q12.Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to \mathbb{R}$ be a function such that $f(x)>0$ for all $x\in \mathbb{R}$, and $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb{R}$.

Let the real numbers …

Q13.For all $x>0$, let $y_1(x),y_2(x)$, and $y_3(x)$ be the functions satisfying …

Q14.Consider the following frequency distribution :

Suppose that the sum of the frequencies is 19 and the median of this frequency distribution …

Q15.Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let $[x]$ denote the greatest integer less than or equal to $x$. Let $n$ denote a natural number.
Match each entry in List-I to the correct entry in List-II and choose the correct option.

| | L …

Q16.Let $\vec{w}=\hat{i}+\hat{j}-2\hat{k}$, and $\overrightarrow{\mathrm{u}}$ and $\overrightarrow{\mathrm{v}}$ be two vectors such that $\vec{u}\times \vec{v}=\vec{w}$ and $\vec{v}\times \vec{w}=\vec{u}$. Let $\alpha ,\beta ,\gamma$ and $t$ be real numbers such that …