JEE Main 2025 · 28 Jan 2025 · Shift 2

Q1.A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $10\pi \mathrm{rad}{\mathrm{s}}^{-1}$ about an axis through its centre and perpendicular to the disc. What is the protential difference …

Q2.A parallel plate capacitor of capacitance $1\mu \mathrm{F}$ is charged to a potential difference of 20 V . The distance between plates is $1\mu \mathrm{m}$. The energy density between plates of capacitor is :

Q3.Match List-I with List-II

List-I
(A) Angular Impulse
(B) Latent Heat
(C) Electrical resistivity
(D) Electromotive force

List-II
(I) $\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$
(II) $\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$
(II …

Q4.The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities will be :

Q5.The kinetic energy of translation of the molecules in 50 g of ${\mathrm{CO}}_2$ gas at $17^{\circ }\mathrm{C}$ is :

Q6.In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A . If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ' -2 ' then the radius of …

Q7.The frequency of revolution of the electron in Bohr's orbit varies with n , the principal quantum number as

Q8.Which of the following phenomena can not be explained by wave theory of light ?

Q9.The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between $\mathrm{t}=0$ to $\mathrm{t}=4\mathrm{s}$ ?

Q10.Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 $\mathrm{km}/\mathrm{s}$, the escape velocity in km/s from the planet will be :

Q11.Given below are two statements. One is labelled as
Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Knowing initial position ${\mathrm{x}}_0$ and initial momentum ${\mathrm{p}}_0$ is enough to determine the position and momentum at any time t for a simple ha …

Q12.A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is :

Q13.A body of mass 4 kg is placed on a plane at a point P having coordinate $(3,4)\mathrm{m}$. Under the action of force $\overrightarrow{\mathrm{F}}=(2\hat{\mathrm{i}}+3\hat{\mathrm{j}})\mathrm{N}$, it moves to a new point Q having coordinates $(6,10)\mathrm{m}$ in 4 sec . The …

Q14.An infinite wire has a circular bend of radius a, and carrying a current $I$ as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by :

Q15.A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

Q16.a 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?
(Given : density of water $=1000\mathrm{kg}{\mathrm{m}}^{-3}$ )

Q17.The magnetic field of an E.M. wave is given by
$\overrightarrow{\mathrm{B}}=\left(\frac{\sqrt{3}}{2}\hat{\mathrm{i}}+\frac{1}{2}\hat{\mathrm{j}}\right)30\sin \left[\omega \left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)\right]$ (S.I. Units)
The corresponding electric fiel …

Q18.A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be : (Take ' g ' as acceleration due to gravity)

Q19.A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time $\mathrm{t}=0$ with a constant velocity. If the induced EMF is E $\propto {\mathrm{t}}^{\mathrm{n}}$, then value o …

Q20.An electric dipole of dipole moment $6\times 10^{-6}\mathrm{Cm}$ is placed in uniform electric field of magnitude $10^6\mathrm{V}/\mathrm{m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole momen …

Q21.The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $7\times 10^6\mathrm{Pa}$, would be ______ ${\mathrm{mm}}^3$.
(Given bulk modulus of copper $=1.4\times 10^{11}{\mathrm{Nm}}^{-2}$ )

Q22.The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B , will be ______ A.

Q23.A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the ra …

Q1.consider the elementary reaction
$\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g})\to \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})$
If the volume of reaction mixture is suddenly reduced to $\frac{1}{3}$ of its initial volume, the reaction rate will become ' $x$ ' tim …

Q2.The amphoteric oxide among ${\mathrm{V}}_2{\mathrm{O}}_3,{\mathrm{V}}_2{\mathrm{O}}_4$ and ${\mathrm{V}}_2{\mathrm{O}}_5$ upon reaction with alkali leads to formation of an oxide anion. The oxidation state of V in the oxide anion is :

Q3.Match List-I with List-II

List-I (Saccharides):
(A) Sucrose
(B) Maltose
(C) Lactose
(D) Amylopectin

List-II (Glycosidic-linkages found):
(I) $\alpha$ 1-4
(II) $\alpha 1-4$ and $\alpha 1-6$
(III) $\alpha 1-\beta 2$
(IV) $\beta 1-4$

Choose the correct answer from the o …

Q4.Identify product $[\mathrm{A}],[\mathrm{B}]$ and $[\mathrm{C}]$ in the following reaction sequence :

Q5.Arrange the following in increasing order of solubility product :
$\mathrm{Ca}(\mathrm{OH}{)}_2,\mathrm{AgBr},\mathrm{PbS},\mathrm{HgS}$

Q6.The purification method based on the following physical transformation is :

Q7.Identify correct conversion during acidic hydrolysis from the following :
(A) starch gives galactose.
(B) cane sugar gives equal amount of glucose and fructose.
(C) milk sugar gives glucose and galactose.
(D) amylopectin gives glucose and fructose.
(E) amylose gives only glucose. …

Q8.An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path $\mathrm{A}\to \mathrm{B}\to \mathrm{C}\to \mathrm{D}\to \mathrm{A}$ as shown in the three cases above.

Choose the …

Q9.The product B formed in the following reaction sequence is :

Q10.Concentrated nitric acid is labelled as $75\%$ by mass. The volume in mL of the solution which contains 30 g of nitric acid is ____ .
Given : Density of nitric acid solution is $1.25\mathrm{g}/\mathrm{mL}$

Q11.Match List-I with List-II.

List-I (Complex):
(A) ${\left[{\mathrm{CoF}}_6\right]}^{3-}$
(B) ${\left[{\mathrm{NiCl}}_4\right]}^{2-}$
(C) ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$
(D) ${\left[\mathrm{Ni}(\mathrm{CN}{)}_4\right]}^{2-}$

List-II (Hybridisatio …

Q12.The total number of compounds from below when treated with hot ${\mathrm{KMnO}}_4$ giving benzoic acid is :

Q13.Given below are two statements :

Statement (I): According to the Law of Octaves, the elements were arranged in the increasing order of their atomic number.

Statement (II) : Meyer observed a periodically repeated pattern upon plotting physical properties of certain elements agai …

Q14.For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth?

Q15.Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?
(A) $1\mathrm{s}<2\mathrm{p}<3\mathrm{d}<4\mathrm{s}$
(B) $1\mathrm{s}<2\mathrm{s}=2\mathrm{p}<3\mathrm{s}=3\mathrm{p}$
(C) …

Q16.Identify correct statements :
(A) Primary amines do not give diazonium salts when treated with ${\mathrm{NaNO}}_2$ in acidc condition.
(B) Aliphatic and aromatic primary amines on heating wth ${\mathrm{CHCl}}_3$ and ethanolic KOH form carbylamines.
(C) Secondary and tertiary amin …

Q17.Given below are two statements :

Statement (I) :
(see structures)
and
(see structure)
isomeric compounds.

Statement (II) :
(see structure)
and
(see structure)
are functional group isomers.

In the light of the above statements, choose the correct answer from the options given b …

Q18.Identify the inorganic sulphides that are yellow in colour :
(A) $({\mathrm{NH}}_4{)}_2\mathrm{S}$
(B) PbS
(C) CuS
(D) ${\mathrm{As}}_2{\mathrm{S}}_3$
(E) ${\mathrm{As}}_2{\mathrm{S}}_5$

Choose the correct answer from the options given below :

Q19.The spin only magnetic moment ($\mu$) value (B.M.) of the compound with strongest oxidising power among ${\mathrm{Mn}}_2{\mathrm{O}}_3$, TiO and VO is ____ B.M. (Nearest integer).

Q20.Consider the following data :

Heat of formation of ${\mathrm{CO}}_2(\mathrm{g})=-393.5\mathrm{kJ}{\mathrm{mol}}^{-1}$
Heat of formation of ${\mathrm{H}}_2\mathrm{O}(\mathrm{l})=-286.0\mathrm{kJ}{\mathrm{mol}}^{-1}$
Heat of combustion of benzene …

Q21.Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12.

The current in Amperes used for the given electrolysis is ____. (Nearest integer).

Q22.A group 15 element forms $\mathrm{d}\pi -\mathrm{d}\pi$ bond with transition metals. It also forms hydride, which is a strongest base among the hydrides of other group members that form $\mathrm{d}\pi -\mathrm{d}\pi$ bond. The atomic number of the element is ____.

Q23.Total number of molecules/species from following which will be paramagnetic is ____.
${\mathrm{O}}_2,{\mathrm{O}}_2^{+},{\mathrm{O}}_2^{-},\mathrm{NO},{\mathrm{NO}}_2,\mathrm{CO},{\mathrm{K}}_2[{\mathrm{NiCl}}_4]$, …

Q1.Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and $\mathrm{Bag}{\mathrm{B}}_3$ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that t …

Q2.Let $\mathrm{A},\mathrm{B},\mathrm{C}$ be three points in xy -plane, whose position vector are given by $\sqrt{3}\hat{i}+\hat{j},\hat{i}+\sqrt{3}\hat{j}$ and $a\hat{\mathrm{i}}+(1-\mathrm{a})\hat{\mathrm{j}}$ respectively with respect to the origin O . If the distance of t …

Q3.If the components of $\overrightarrow{\mathrm{a}}=\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}$ along and perpendicular to $\vec{b}=3\hat{i}+\hat{j}-\hat{k}$ respectively, are $\frac{16}{11}(3\hat{i}+\hat{j}-\hat{k})$ and …

Q4.If $\alpha +\mathrm{i}\beta$ and $\gamma +\mathrm{i}\delta$ are the roots of ${\mathrm{x}}^2-(3-2\mathrm{i})\mathrm{x}-(2\mathrm{i}-2)=0,\mathrm{i}=\sqrt{-1}$, then $\alpha \gamma +\beta \delta$ is equal to :

Q5.If the midpoint of a chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ is $(\sqrt{2},4/3)$, and the length of the chord is $\frac{2\sqrt{\alpha }}{3}$, then $\alpha$ is :

Q6.Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S , one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is :

Q7.Let $f$ be a real valued continuous function defined on the positive real axis such that $\mathrm{g}(\mathrm{x})={\int }_0^{\mathrm{x}}\mathrm{t}f(\mathrm{t})\mathrm{dt}$. If $\mathrm{g}\left({\mathrm{x}}^3\right)={\mathrm{x}}^6+{\mathrm{x}}^7$, then value of …

Q8.The square of the distance of the point $\left(\frac{15}{7},\frac{32}{7},7\right)$ from the line $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ in the direction of the vector $\hat{i}+4\hat{j}+7\hat{k}$ is :

Q9.The area of the region bounded by the curves $\mathrm{x}\left(1+{\mathrm{y}}^2\right)=1$ and ${\mathrm{y}}^2=2\mathrm{x}$ is :

Q10.Let $\mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}}& -2\\ 0& 1\end{array}\right]$ and $\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right],\theta >0$. If …

Q11.If $f(\mathrm{x})=\int \frac{1}{{\mathrm{x}}^{1/4}\left(1+{\mathrm{x}}^{1/4}\right)}\mathrm{dx},f(0)=-6$, then $f(1)$ is equal to :

Q12.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ be a twice differentiable function such that $f(2)=1$. If $\mathrm{F}(\mathrm{x})=\mathrm{x}f(\mathrm{x})$ for all $\mathrm{x}\in \mathrm{R}$, ${\int }_0^{2}x{F}^{\prime }(x)dx=6$ and …

Q13.For positive integers $n$, if $4a_n=\left(n^2+5n+6\right)$ and ${\mathrm{S}}_{\mathrm{n}}={\sum }_{\mathrm{k}=1}^{\mathrm{n}}\left(\frac{1}{{\mathrm{a}}_{\mathrm{k}}}\right)$, then the value of $507{\mathrm{S}}_{2025}$ is :

Q14.Let $f:[0,3]\to \mathrm{A}$ be defined by
$f(\mathrm{x})=2{\mathrm{x}}^3-15{\mathrm{x}}^2+36\mathrm{x}+7$ and $\mathrm{g}:[0,\infty )\to \mathrm{B}$ be defined by $\mathrm{g}(\mathrm{x})=\frac{{\mathrm{x}}^{2025}}{{\mathrm{x}}^{2025}+1}$. If both the functions ar …

Q15.Let $[\mathrm{x}]$ denote the greatest integer less than or equal to x . Then domain of $f(\mathrm{x})={\sec }^{-1}(2[\mathrm{x}]+1)$ is :

Q16.If ${\sum }_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi }{4}+(r-1)\frac{\pi }{6}\right)\sin \left(\frac{\pi }{4}+\frac{r\pi }{6}\right)}\right\}=a\sqrt{3}+b$, $\mathrm{a},\mathrm{b}\in \mathbf{Z}$, then ${\mathrm{a}}^2+{\mathrm{b}}^2$ is equal to :

Q17.Two equal sides of an isosceles triangle are along $-x+2y=4$ and $x+y=4$. If $m$ is the slope of its third side, then the sum, of all possible distinct values of m , is :

Q18.Let the coefficients of three consecutive terms ${\mathrm{T}}_{\mathrm{r}}$, ${\mathrm{T}}_{\mathrm{r}+1}$ and ${\mathrm{T}}_{\mathrm{r}+2}$ in the binomial expansion of $(\mathrm{a}+\mathrm{b}{)}^{12}$ be in a G.P. and let p be the number of all possible values of r . Let q be the sum o …

Q19.If A and B are the points of intersection of the circle $x^2+y^2-8x=0$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ and a point $P$ moves on the line $2x-3y+4=0$, then the centroid of $△PAB$ lies on the line :

Q20.Let $f:\mathbf{R}-\{0\}\to (-\infty ,1)$ be a polynomial of degree 2 , satisfying $f(\mathrm{x})f\left(\frac{1}{\mathrm{x}}\right)=f(\mathrm{x})+f\left(\frac{1}{\mathrm{x}}\right)$. If $f(\mathrm{K})=-2\mathrm{K}$, then the sum of squares of all possible values of …

Q21.The number of natural numbers, between 212 and 999, such that the sum of their digits is 15 , is

Q22.Let $f(\mathrm{x})={\lim }_{\mathrm{n}\to \infty }{\sum }_{\mathrm{r}=0}^{\mathrm{n}}\left(\frac{\tan \left(\mathrm{x}/2^{\mathrm{r}+1}\right)+{\tan }^3\left(\mathrm{x}/2^{\mathrm{r}+1}\right)}{1-{\tan }^2\left(\mathrm{x}/2^{\mathrm{r}+1}\right)}\right)$.

Then …

Q23.The interior angles of a polygon with n sides, are in an A.P. with common difference $6^{\circ }$. If the largest interior angle of the polygon is $219^{\circ }$, then n is equal to

Q24.Let A and B be the two points of intersection of the line $\mathrm{y}+5=0$ and the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $d$ denotes the distance between A and B , and a denotes the area of $△\mathrm{SAB}$, where S is the focus o …

Q25.If $y=y(x)$ is the solution of the differential equation,
$\sqrt{4-x^2}\frac{dy}{dx}=\left({\left({\sin }^{-1}\left(\frac{x}{2}\right)\right)}^2-y\right){\sin }^{-1}\left(\frac{x}{2}\right)$,
$-2\le x\le 2,y(2)=\left(\frac{{\pi }^2-8}{4}\right)$, then $y^2(0)$ is equal to …