JEE Main 2025 · 08 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 : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.

Reason R : Electrostatic …

Q2.A rod of linear mass density '$\lambda$' and length '$L$' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

Q3.A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $\mathrm{P}\times 10^{11}{\mathrm{Nm}}^{-2}$, where the value …

Q4.Electric charge is transferred to an irregular metallic disk as shown in figure. If ${\sigma }_1,{\sigma }_2,{\sigma }_3$ and ${\sigma }_4$ are charge densities at given points then, choose the correct answer from the options given below:
(A) …

Q5.Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.
(Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$, specific heat of water $=4200\mathrm{J}/(\mathrm{kg}\mathrm{K})$)

Q6.A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be

Q7.An infinitely long wire has uniform linear charge density $\lambda =2\mathrm{nC}/\mathrm{m}$. The net flux through a Gaussian cube of side length $\sqrt{3}\mathrm{cm}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, w …

Q8.The output voltage in the following circuit is (Consider ideal diode case)

Q9.Two metal spheres of radius $R$ and $3R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes ${\sigma }_1$ and ${\sigma }_2$, respectively. The ratio …

Q10.A quantity Q is formulated as ${\mathrm{X}}^{-2}{\mathrm{Y}}^{+\frac{3}{2}}{\mathrm{Z}}^{-\frac{2}{5}}$. $X$, $Y$ and $Z$ are independent parameters which have fractional errors of $0.1,0.2$ and 0.5, respectively in measurement. The maximum fractional error of $Q$ is

Q11.A monoatomic gas having $\gamma =\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to ${\left(\frac{1}{8}\right)}^{\text{th }}$ of its initial volume. The ratio of final pressure and initial pressure is: ($\gamma$ is the ratio of spe …

Q12.A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is

Q13.Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is ${\mathrm{v}}_1$, …

Q14.Figure shows a current carrying square loop ABCD of edge length is 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is $2r$, then the magnitude of the resultant magnetic field at centre of the square loop is

Q15.A body of mass 2 kg moving with velocity of ${\overrightarrow{\mathrm{v}}}_{\mathrm{in}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}{\mathrm{ms}}^{-1}$ enters into a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ …

Q16.Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are the total flying times of first and second ball, resp …

Q17.The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, ${\mathrm{y}}_1(\mathrm{x},\mathrm{t})=4\sin (\mathrm{kx}-\omega \mathrm{t})$ and $y_2(x,t)=2\sin \left(kx-\omega t+\frac{2\pi }{3}\right)$, are:
(Take the angular frequ …

Q18.In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case

Q19.For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

Q20.A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is $200\mathrm{N}/\mathrm{m}$. The block is pushed such …

Q21.An electron is released from rest near an infinite non-conducting sheet of uniform charge density '$-\sigma$'. The rate of change of de-Broglie wavelength associated with the electron varies inversely as ${\mathrm{n}}^{\text{th}}$ power of time. The numerical value of $n$ is ______ …

Q22.A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8{\mathrm{cm}}^3$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take $1\mathrm{atm}=10^5\mathrm{Pa}$)

Q23.Space between the plates of a parallel plate capacitor of plate area $4{\mathrm{cm}}^2$ and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in par …

Q24.A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of $25\pi \mathrm{Nm}$ for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ______ m.

Q25.A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balan …

Q1.In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2(s)$, respectively. The ratio $t_1/t_2$ will :

Q2.$\mathrm{A}\underset{\text{ (ii) }{\mathrm{H}}_3{\mathrm{O}}^{+}}{\overset{\text{(i) }\mathrm{NaOH}}{\to }}\mathrm{B}\underset{\text{ (ii) }{\mathrm{H}}_2{\mathrm{SO}}_4,\Delta }{\overset{\text{ (i) }\mathrm{EtOH}}{\to }}\mathrm{C}$
'A' shows positive Lassaign's test for N and its molar mass i …

Q3.Choose the correct set of reagents for the following conversion.

Q4.1, 2-dibromocyclooctane …

Q5.Given below are two statements :
Statement I: A homolepitc octahedral complex, formed using monodentate ligands, will not show stereoisomerism.
Statement II : cis- and trans- platin are heteroleptic complexes of Pd.
In the light of the above statements, choose the correct answer …

Q6.The atomic number of the element from the following with lowest $1^{\text{st }}$ ionisation enthalpy is:

Q7.Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

Q8.$\mathrm{HA}(\mathrm{aq})\rightleftharpoons {\mathrm{H}}^{+}(\mathrm{aq})+{\mathrm{A}}^{-}(\mathrm{aq})$
The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is $0.20^{\circ }\mathrm{C}$.
The dissociation constant for the acid is
Given : …

Q9.What is the correct IUPAC name of (see structure) ?

Q10.The correct decreasing order of spin only magnetic moment values (BM) of ${\mathrm{Cu}}^{+},{\mathrm{Cu}}^{2+},{\mathrm{Cr}}^{2+}$ and ${\mathrm{Cr}}^{3+}$ ions is :

Q11.Which one of the following reactions will not lead to the desired ether formation in major proportion? (iso-Bu $\Rightarrow$ isobutyl, sec-Bu $\Rightarrow$ sec-butyl, nPr $\Rightarrow$ n-propyl, ${}^{\mathrm{t}}\mathrm{Bu}\Rightarrow$ tert-butyl, Et $\Rightarrow$ ethyl)

Q12.On combustion 0.210 g of an orgainc compound containing C , H and O gave 0.127 g H₂O and 0.307 g CO₂. The percentages of hydrogen and oxygen in the given organic compound respectively are:

Q13.(see structure)

Choose the correct option for structures of A and B, respectively.

Q14.Correct statements for an element with atomic number 9 are
A. There can be 5 electrons for which $m_s=+\frac{1}{2}$ and 4 electrons for which $m_s=-\frac{1}{2}$
B. There is only one electron in $p_z$ orbital
C. The last electron goes to orbital with $n=2$ and $l=1$

1. The sum …

Q15.The number of species from the following that are involved in ${\mathrm{sp}}^3{\mathrm{d}}^2$ hybridization is
$[\mathrm{Co}({\mathrm{NH}}_3{)}_6{]}^{3+}$, ${\mathrm{SF}}_6$, $[{\mathrm{CrF}}_6{]}^{3-}$, $[{\mathrm{CoF}}_6{]}^{3-}$, $[\mathrm{Mn}(\mathrm{CN}{)}_6{]}^{3-}$ and $[{\mathrm{MnCl}}_6{]}^{3-}$

Q16.When (see structure) undergoes intramolecular aldol condensation, the major product formed is:

Q17.Given below are two statements:

Statement I: ${\mathrm{H}}_2\mathrm{Se}$ is more acidic than ${\mathrm{H}}_2\mathrm{Te}$.
Statement II: ${\mathrm{H}}_2\mathrm{Se}$ has higher bond enthalpy for dissociation than ${\mathrm{H}}_2\mathrm{Te}$.

In the light of the above statements, choose t …

Q18.Resonance in ${\mathrm{X}}_2\mathrm{Y}$ can be represented as

(see structure)

The enthalpy of formation of ${\mathrm{X}}_2\mathrm{Y}$ ($\mathrm{X}\equiv \mathrm{X}(\mathrm{g})+\frac{1}{2}\mathrm{Y}=\mathrm{Y}(\mathrm{g})\to {\mathrm{X}}_2\mathrm{Y}(\mathrm{g})$) is 80 kJ mo …

Q19.The energy of an electron in first Bohr orbit of H-atom is -13.6 eV. The magnitude of energy value of electron in the first excited state of ${\mathrm{Be}}^{3+}$ is _____ eV. (nearest integer value)

Q20.20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value)
(Given: Na=23, I=127, Ag=108, N=14, O=16 g mol⁻¹)

Q21.The equilibrium constant for decomposition of ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$

${\mathrm{H}}_2\mathrm{O}(\mathrm{g})\rightleftharpoons {\mathrm{H}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})$ ($\Delta G^{\circ }=92.34$ kJ mol⁻¹) is $8.0\times 10^{-3}$ at 2300 K and tot …

Q22.Consider the following half cell reaction
${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}(\mathrm{aq})+6{\mathrm{e}}^{-}+14{\mathrm{H}}^{+}(\mathrm{aq})\to 2{\mathrm{Cr}}^{3+}(\mathrm{aq})+7{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$
The reaction was conducted with the ratio of …

Q23.Match the LIST-I with LIST-II:
LIST-I (Reagent): A. Sodium bicarbonate solution B. Neutral ferric chloride C. Ceric ammonium nitrate D. Alkaline KMnO₄
LIST-II (Functional Group detected): I. Double bond/unsaturation II. Carboxylic acid III. Phenolic -OH IV. Alcoholic -OH …

Q24.Match the LIST-I with LIST-II:
LIST-I (Complex/Species): A. [Ni(CO)₄] B. [Ni(CN)₄]²⁻ C. [NiCl₄]²⁻ D. [MnBr₄]²⁻
LIST-II (Shape & magnetic moment): I. Tetrahedral, 2.8 BM II. Square planar, 0 BM III. Tetrahedral, 0 BM IV. Tetrahedral, 5.9 BM
Choose the correct answer from …

Q1.Let the values of $\lambda$ for which the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-\lambda }{3}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{6}}$ be ${\lambda }_1$ and ${\lambda }_2$. Then the radius of the circle pa …

Q2.Let $\alpha$ be a solution of $x^2+x+1=0$, and for some a and b in $\mathbb{R},\left[\begin{array}{lll}4& a& b\end{array}\right]\left[\begin{array}{ccc}1& 16& 13\\ -1& -1& 2\\ -2& -14& -8\end{array}\right]=\left[\begin{array}{lll}0& 0& 0\end{array}\right]$. If …

Q3.Let the function $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{3}+\frac{3}{\mathrm{x}}+3,\mathrm{x}\ne 0$ be strictly increasing in $\left(-\infty ,{\alpha }_1\right)\cup \left({\alpha }_2,\infty \right)$ and strictly decreasing in …

Q4.If A and B are two events such that $\mathrm{P}(\mathrm{A})=0.7$, $\mathrm{P}(\mathrm{B})=0.4$ and $\mathrm{P}(\mathrm{A}\cap \overline{\mathrm{B}})=0.5$, where $\overline{\mathrm{B}}$ denotes the complement of B, then …

Q5.If $\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\dots \infty =\frac{{\pi }^4}{90}$,
$\frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\dots =\alpha$,
$\frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\dots \infty =\beta$,
then $\frac{\alpha }{\beta }$ is equal to

Q6.The sum of the squares of the roots of $|x-2{|}^2+|x-2|-2=0$ and the squares of the roots of $x^2-2|x-3|-5=0$, is

Q7.Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle $\alpha$ with the positive x-axis and the equations of its diagonals are $(\sqrt{3}+1)x+(\sqrt{3}-1)y=0$ and $(\sqrt{3}-1)x-(\sqrt{3}+1)y+8\sqrt{3}=0$. Then …

Q8.Let $f(x)$ be a positive function and
$I_1={\int }_{-\frac{1}{2}}^{1}2xf(2x(1-2x))dx$ and $I_2={\int }_{-1}^{2}f(x(1-x))dx$.
Then the value of $\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}$ is equal to

Q9.Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-\hat{k}$. Let $\hat{c}$ be a unit vector in the plane of the vectors $\vec{a}$ and $\vec{b}$ and be perpendicular to $\vec{a}$. Then such a vector $\hat{c}$ is

Q10.Let the ellipse $3x^2+p{y}^2=4$ pass through the centre $C$ of the circle $x^2+y^2-2x-4y-11=0$ of radius r. Let ${\mathrm{f}}_1,{\mathrm{f}}_2$ be the focal distances of the point C on the ellipse. Then $6{\mathrm{f}}_1{\mathrm{f}}_2-\mathrm{r}$ is equal to

Q11.The integral ${\int }_{-1}^{\frac{3}{2}}\left(\left|{\pi }^2\mathrm{x}\sin (\pi \mathrm{x})\right|\right)\mathrm{dx}$ is equal to

Q12.A line passing through the point $\mathrm{P}(\mathrm{a},0)$ makes an acute angle $\alpha$ with the positive x-axis. Let this line be rotated about the point P through an angle $\frac{\alpha }{2}$ in the clock-wise direction. If in the new position, the slope of the line is …

Q13.There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

Q14.Let $\mathrm{A}=\left\{\theta \in [0,2\pi ]:1+10\mathrm{Re}\left(\frac{2\cos \theta +\mathrm{i}\sin \theta }{\cos \theta -3\mathrm{i}\sin \theta }\right)=0\right\}$. Then ${\sum }_{\theta \in \mathrm{A}}{\theta }^2$ is equal to

Q15.Let $\mathrm{A}=\{0,1,2,3,4,5\}$. Let R be a relation on A defined by $(x,y)\in R$ if and only if max $\{\mathrm{x},\mathrm{y}\}\in \{3,4\}$. Then among the statements
$({\mathrm{S}}_1)$ : The number of elements in R is 18, and
$({\mathrm{S}}_2)$ : The relation R is symmetric …

Q16.The number of integral terms in the expansion of ${\left(5^{\frac{1}{2}}+7^{\frac{1}{8}}\right)}^{1016}$ is

Q17.Let $\mathrm{f}(\mathrm{x})=\mathrm{x}-1$ and $\mathrm{g}(\mathrm{x})={\mathrm{e}}^{\mathrm{x}}$ for $\mathrm{x}\in \mathbb{R}$. If $\frac{dy}{dx}=\left(e^{-2\sqrt{x}}g(f(f(x)))-\frac{y}{\sqrt{x}}\right),y(0)=0$, then $y(1)$ is :-

Q18.The value of ${\cot }^{-1}\left(\frac{\sqrt{1+{\tan }^2(2)}-1}{\tan (2)}\right)-{\cot }^{-1}\left(\frac{\sqrt{1+{\tan }^2\left(\frac{1}{2}\right)}+1}{\tan \left(\frac{1}{2}\right)}\right)$ is equal to

Q19.Let $\mathrm{A}=\left[\begin{array}{ccc}2& 2+\mathrm{p}& 2+\mathrm{p}+\mathrm{q}\\ 4& 6+2\mathrm{p}& 8+3\mathrm{p}+2\mathrm{q}\\ 6& 12+3\mathrm{p}& 20+6\mathrm{p}+3\mathrm{q}\end{array}\right]$. If …

Q20.Given below are two statements :
Statement I :
${\lim }_{x\to 0}\left(\frac{{\tan }^{-1}x+{\log }_e\sqrt{\frac{1+x}{1-x}}-2x}{x^5}\right)=\frac{2}{5}$
Statement II : …

Q21.Let the area of the bounded region $\left\{(\mathrm{x},\mathrm{y}):0\le 9\mathrm{x}\le {\mathrm{y}}^2,\mathrm{y}\ge 3\mathrm{x}-6\right\}$ be A . Then 6 A is equal to ______

Q22.Let the domain of the function $f(x)={\cos }^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha ,\beta ]$ and the domain of $g(x)={\log }_2\left(2-6{\log }_{27}(2x+5)\right)$ be $(\gamma ,\delta )$. Then $|7(\alpha +\beta )+4(\gamma +\delta )|$ is equal to ______

Q23.Let the area of the triangle formed by the lines $\mathrm{x}+2=\mathrm{y}-1=\mathrm{z}$, $\frac{\mathrm{x}-3}{5}=\frac{\mathrm{y}}{-1}=\frac{\mathrm{z}-1}{1}$ and $\frac{\mathrm{x}}{-3}=\frac{\mathrm{y}-3}{3}=\frac{\mathrm{z}-2}{1}$ be A . Then ${\mathrm{A}}^2$ is equal to ______

Q24.The product of the last two digits of $(1919{)}^{1919}$ is

Q25.Let $r$ be the radius of the circle, which touches x-axis at point ($\mathrm{a},0$), $\mathrm{a}<0$ and the parabola ${\mathrm{y}}^2=9\mathrm{x}$ at the point $(4,6)$. Then r is equal to ______