JEE Advanced 2025 · 18 May 2025 · Paper 2

Q1.A temperature difference can generate e.m.f. in some materials. Let $S$ be the e.m.f. produced per unit temperature difference between the ends of a wire, $\sigma$ the electrical conductivity and $\kappa$ the thermal conductivity of the material of the wire. Taking …

Q2.Two co-axial conducting cylinders of same length $\ell$ with radii $\sqrt{2}R$ and $2R$ are kept, as shown in Fig. 1. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielec …

Q3.As shown in the figures, a uniform rod $O{O}^{\prime }$ of length $l$ is hinged at the point $O$ and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top-end $(O^{\prime })$ of the rod, as show …

Q4.Consider a star of mass $m_2$ kg revolving in a circular orbit around another star of mass $m_1$ kg with $m_1\gg m_2$. The heavier star slowly acquires mass from the lighter star at a constant rate of $\gamma$ kg/s. In this transfer process, there is no other los …

Q5.A positive point charge of $10^{-8}$ C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved b …

Q6.Two identical concave mirrors each of focal length $f$ are facing each other as shown in the schematic diagram. The focal length $f$ is much larger than the size of the mirrors. A glass slab of thickness $t$ and refractive index $n_0$ is kept equidistant from the mirror …

Q7.Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of ${\sigma }_0$. The separation between any two consecutive sheets is 1 μm. The vario …

Q8.The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 1 …

Q9.A conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$. The sphere is rotating about an axis passing through its center with a uniform angular speed $\omega$. The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the sa …

Q10.A hydrogen atom, initially at rest in its ground state, absorbs a photon of frequency $v_1$ and ejects the electron with a kinetic energy of 10 eV. The electron then combines with a positron at rest to form a positronium atom in its ground state and simultaneously emits a pho …

Q11.An ideal monatomic gas of n moles is taken through a cycle $WXYZW$ consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic $V-T$ diagram. The volume of the gas at $W,X$ and $Y$ points are, 64 cm³, 125 cm³ and 250 cm³, respective …

Q12.A geostationary satellite above the equator is orbiting around the earth at a fixed distance $r_1$ from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance $r_2$ from the center o …

Q13.The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartm …

Q14.In a Young's double slit experiment, a combination of two glass wedges $A$ and $B$, having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The separation between the slits is $d=2$ mm and the shortest distance between …

Q15.A projectile of mass 200 g is launched in a viscous medium at an angle 60° with the horizontal, with an initial velocity of 270 m/s. It experiences a viscous drag force $\vec{F}=-c\vec{v}$ where the drag coefficient $c=0.1$ kg/s and $\vec{v}$ is the instantaneous velocity …

Q16.An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular am …

Q1.During sodium nitroprusside test of sulphide ion in an aqueous solution, one of the ligands coordinated to the metal ion is converted to

Q2.The complete hydrolysis of $\mathrm{ICl}$, ${\mathrm{ClF}}_3$ and ${\mathrm{BrF}}_5$, respectively, gives

Q3.Monocyclic compounds P, Q, R and S are the major products formed in the reaction sequences given below.

The product having the highest number of unsaturated carbon atom(s) is-

Q4.The correct reaction/reaction sequence that would produce a dicarboxylic acid as the major product is

Q5.The correct statements (s) about intermolecular forces is(are)

Q6.The compound(s) with P-H bond(s) is(are)

Q7.The correct statement(s) is(are)

Q8.For the reaction sequence given below, the correct statement(s) is(are)

Q9.The density (in $\mathrm{g}{\mathrm{cm}}^{-3}$) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is ____.

Use: Atomic mass of metal = 105.6 amu and Avogadro's constant $=6\times 10^{23}{\mathrm{mol}}^{-1}$

Q10.The solubility of barium iodate in an aqueous solution prepared by mixing 200 mL of 0.010 M barium nitrate with 100 mL of 0.10 M sodium iodate is $\mathbf{X}\times 10^{-6}\mathrm{mol}{\mathrm{dm}}^{-3}$. The value of $\mathbf{X}$ is ____.

Use: Solubility product consta …

Q11.Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from $10\mathrm{mg}{\mathrm{g}}^{-1}$ and $16\mathrm{mg}{\mathrm{g}}^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be …

Q12.Consider a reaction $A+R\to$ Product. The rate of this reaction is measured to be $k[A][R]$. At the start of the reaction, the concentration of $R,[R{]}_0$, is 10-times the concentration of $A,[A{]}_0$. The reaction can be considered to be a pseudo first order reaction w …

Q13.At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density $=1.00\mathrm{g}{\mathrm{cm}}^{-3}$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule …

Q14.An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is $\frac{\mathbf{X}}{\mathbf{F}}\times 10^3$ volts, where $\mathbf{F}$ is the Faraday constant. The value of $\mathbf{X}$ is ____.

Use : Standard Gibbs energi …

Q15.The sum of the spin only magnetic moment values (in B.M.) of ${\left[\mathrm{Mn}(\mathrm{Br}{)}_6\right]}^{3-}$ and ${\left[\mathrm{Mn}(\mathrm{CN}{)}_6\right]}^{3-}$ is ____.

Q16.A linear octasaccharide (molar mass $=1024\mathrm{g}{\mathrm{mol}}^{-1}$) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The amount of 2-deoxyribose formed is $58.26\%(\mathrm{w}/\mathrm{w})$ of the total amount of the monosaccharid …

Q1.Let $x_0$ be the real number such that $e^{x_0}+x_0=0$. For a given real number $\alpha$, define

for all real numbers $x$.
Then which one of the following statements is TRUE?

Q2.Let $\mathbb{R}$ denote the set of all real numbers. Then the area of the region

is

Q3.The total number of real solutions of the equation

is
(Here, the inverse trigonometric functions ${\sin }^{-1}x$ and ${\tan }^{-1}x$ assume values in …

Q4.Let $S$ denote the locus of the point of intersection of the pair of lines

where $\alpha$ varies over the set of non-zero real numbers. Let $T$ be the tangent to $S$ passing through the …

Q5.Let $I=\left(\begin{array}{ll}1& 0\\ 0& 1\end{array}\right)$ and $P=\left(\begin{array}{ll}2& 0\\ 0& 3\end{array}\right)$. Let $Q=\left(\begin{array}{ll}\mathrm{x}& \mathrm{y}\\ \mathrm{z}& 4\end{array}\right)$ for some non-zero real numbers $x,y$, and $z$, fo …

Q6.Let $S$ denote the locus of the mid-points of those chords of the parabola $y^2=x$, such that the area of the region enclosed between the parabola and the chord is $\frac{4}{3}$. Let $R$ denote the region lying in the first quadrant, enclosed by the parabola $y^2=x$ …

Q7.Let $P\left(x_1,y_1\right)$ and $Q\left(x_2,y_2\right)$ be two distinct points on the ellipse

such that $y_1>0$, and $y_2>0$. Let C denote the circle $x^2+y^2=9$, and $M$ be the point ( 3,0 ).
Suppose the line …

Q8.Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to \mathbb{R}$ be defined by

Then which of the following statements …

Q9.Let $y(x)$ be the solution of the differential equation

satisfying $y(1)=0$. Then the value of $2\frac{(y(e){)}^2}{y\left(e^2\right)}$ is ____.

Q10.Let $a_0,a_1,\dots .,a_{23}$ be real numbers such that

for every real number $x$. let $a_r$ be the largest among the numbers $a_j$ for $0\le j\le 23$.
The the value of $r$ is ____.

Q11.A factory has a total of three manufacturing units, $M_1,M_2$, and $M_3$, which produce bulbs independent of each other. The units $M_1,M_2$, and $M_3$ produce bulbs in the proportions of 2: 2: 1, respectively. It is known that 20% of the bulbs produced in …

Q12.Consider the vectors

For two distinct positive real numbers $\alpha$ and $\beta$, define …

Q13.For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi <\arg (z)\le \pi$. Let $\omega$ be the cube root of unity for which $0<\arg (\omega )<\pi$. Let

Then the …

Q14.Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to \mathbb{R}$ and $g:\mathbb{R}\to (0,4)$ be functions defined by

Define the composite function …

Q15.Let

Then the value of

is ____.

Q16.If

then the value of $\sqrt{7}\tan \left(\frac{2\alpha \sqrt{7}}{\pi }\right)$ is ____.
(Here, the inverse trigonometric function ${\tan }^{-1}x$ assumes values in …