JEE Main 2025 · 29 Jan 2025 · Shift 2

Q1.The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

Q2.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason …

Q3.An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density ${\sigma }_0$. Choose the correct option from the following. …

Q4.In an experiment with photoelectric effect, the stopping potential.

Q5.A point charge causes an electric flux of $-2\times 10^4{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :

(Given …

Q6.A poly-atomic molecule ( ${\mathrm{C}}_{\mathrm{V}}=3\mathrm{R},{\mathrm{C}}_{\mathrm{P}}=4\mathrm{R}$, where $R$ is gas constant) goes from phase space point …

Q7.Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts ${\mathrm{L}}_1,{\mathrm{L}}_2$ by AB plane and ${\mathrm{L}}_3,{\mathrm{L}}_4$ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses ${\mathrm{L}}_1$ and …

Q8.A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $\overrightarrow{\mathrm{E}}$ and magnetic field, $\overrightarrow{\mathrm{B}}$ vectors associated with the wave in Cartesian frame are :

Q9.Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B . The separation between the images of O , formed by each refracting surface is :

Q10.Two bodies A and B of equal mass are suspended from two massless springs of spring constant ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity …

Q11.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities …

Q12.A sand dropper drops sand of mass $\mathrm{m}(\mathrm{t})$ on a conveyer belt at a rate proportional to the square root of speed $(\mathrm{v})$ of the belt, i.e. $\frac{\mathrm{dm}}{\mathrm{dt}}\propto \sqrt{\mathrm{v}}$. If P is the power delivered to run the belt at constant s …

Q13.A convex lens mode of glass (refractive index $=$ 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index $=1.33$ ), its focal length changes to

Q14.A capacitor, ${\mathrm{C}}_1=6\mu \mathrm{F}$ is charged to a potential difference of ${\mathrm{V}}_0=5\mathrm{V}$ using a 5 V battery. The battery is removed and another capacitor, ${\mathrm{C}}_2=12\mu \mathrm{F}$ is inserted in place of the battery. When the switch ' S ' …

Q15.Three equal masses $m$ are kept at vertices ( $A,B,C$ ) of an equilateral triangle of side a in free space. At $\mathrm{t}=0$, they are given an initial velocity ${\vec{V}}_A=V_0\overrightarrow{AC},{\vec{V}}_B=V_0\overrightarrow{BA}$ and …

Q16.Match List-I with List-II.

Choose the correct answer from the options given below :

Q17.The truth table for the circuit given below is :

Q18.A cup of coffee cools from $90^{\circ }\mathrm{C}$ to $80^{\circ }\mathrm{C}$ in t minutes when the room temperature is $20^{\circ }\mathrm{C}$. The time taken by the similar cup of coffee to cool from $80^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ at the same room temperatur …

Q19.The number of spectral lines emitted by atomic hydrogen that is in the $4^{\text{th}}$ energy level, is

Q20.The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9\times 10^{-4}$ Tesla. If the solenoid carries a current of 0.29 A , then the length of the solenoid is $\_\_\_\_$ $\pi \mathrm{cm}$.

Q21.A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is $7\times 10^8\mathrm{V}/\mathrm{s}$ then the integer value of the distance bet …

Q22.A physical quantity Q is related to four observables $a,b,c,d$ as follows: $Q=\frac{a{b}^4}{cd}$ where, $\mathrm{a}=(60\pm 3)\mathrm{Pa};\mathrm{b}=(20\pm 0.1)\mathrm{m};\mathrm{c}=(40\pm 0.2){\mathrm{Nsm}}^{-2}$ and $\mathrm{d}=(50\pm 0.1)\mathrm{m}$, then the per …

Q23.Two planets, A and B are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2R_A$. The planet $B$ is $4\sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum …

Q24.Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time $\mathrm{t}=0$, for the first time. The maximum possible number of crossing(s) (inc …

Q25.Match List-I with List-II:
List-I: (A) Magnetic induction (B) Magnetic intensity (C) Magnetic flux (D) Magnetic moment
List-II: (I) Ampere meter² (II) Weber (III) Gauss (IV) Ampere/meter
Choose the correct answer from the options given below:

Q1.The calculated spin-only magnetic moments of ${\mathrm{K}}_3\left[\mathrm{Fe}(\mathrm{OH}{)}_6\right]$ and ${\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{OH}{)}_6\right]$ respectively are :

Q2.For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n ?
[E: Energy of the stationary state,
Z : atomic number, $\mathrm{n}=$ principal quantum number]

Q3.Given below are two statements :

Statement (I) : In partition chromatography, stationary phase is thin film of liquid present in the inert support.
Statement (II) : In paper chromatography, the material of paper acts as a stationary phase.
In the light of the above statements, c …

Q4.Identify the essential amino acids from below :
(A) Valine
(B) Proline
(C) Lysine
(D) Threonine
(E) Tyrosine

Choose the correct answer from the options given below:

Q5.Which among the following halides will generate the most stable carbocation in Nucleophillic substitution reaction?

Q6.Consider the equilibrium
$\mathrm{CO}(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})\rightleftharpoons {\mathrm{CH}}_4(\mathrm{g})+{\mathrm{H}}_2\mathrm{O}(\mathrm{g})$
If the pressure applied over the system increases by two fold at constant temperature then
(A) Concentration of …

Q7.Given below are two statements :

Statement (I) : NaCl is added to the ice at $0^{\circ }\mathrm{C}$, present in the ice cream box to prevent the melting of ice cream.

Statement (II) : On addition of NaCl to ice at $0^{\circ }\mathrm{C}$, there is a depression in freezing po …

Q8.Given below are two statements :

Statement (I) : On nitration of m -xylene with ${\mathrm{HNO}}_3,{\mathrm{H}}_2{\mathrm{SO}}_4$ followed by oxidation, 4-nitrobenzene-1, 3-dicarboxylic acid is obtained as the major product.
Statement (II) : ${\mathrm{CH}}_3$ group is …

Q9.0.1 M solution of KI reacts with excess of ${\mathrm{H}}_2{\mathrm{SO}}_4$ and ${\mathrm{KIO}}_3$ solution. According to equation
$5{\mathrm{I}}^{-}+{\mathrm{IO}}_3^{-}+6{\mathrm{H}}^{+}\to 3{\mathrm{I}}_2+3{\mathrm{H}}_2\mathrm{O}$
Identify the correct statement …

Q10.${\mathrm{O}}_2$ gas will be evolved as a product of electrolysis of :
(A) an aqueous solution of ${\mathrm{AgNO}}_3$ using silver electrodes.
(B) an aqueous solution of ${\mathrm{AgNO}}_3$ using platinum electrodes.
(C) a dilute solution of …

Q11.Identify the homoleptic complexes with odd number of d electrons in the central metal.
(A) ${\left[{\mathrm{FeO}}_4\right]}^{2-}$
(B) ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$
(C) ${\left[\mathrm{Fe}(\mathrm{CN}{)}_5\mathrm{NO}\right]}^{2-}$
(D) …

Q12.Total number of sigma ($\sigma$) ______ and pi($\pi$) ______ bonds respectively present in hex-1-en-4-yne are :

Q13.If $\mathrm{C}$ (diamond) $\to \mathrm{C}$ (graphite) $+\mathrm{X}\mathrm{kJ}{\mathrm{mol}}^{-1}$ …

Q14.Given below are two statements :

Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.
Statement (II) : If the uncertainty in the measurement of position and uncertainty in measurement of mome …

Q15.Which one of the following reaction sequences will give an azo dye ?

Q16.Drug X becomes ineffective after $50\%$ decomposition. The original concentration of drug in a bottle was $16\mathrm{mg}/\mathrm{mL}$ which becomes 4 $\mathrm{mg}/\mathrm{mL}$ in 12 months. The expiry time of the drug in months is ______ .
Assume that the decompositio …

Q17.The type of oxide formed by the element among $\mathrm{Li},\mathrm{Na},\mathrm{Be},\mathrm{Mg},\mathrm{B}$ and Al that has the least atomic radius is :

Q18.First ionisation enthalpy values of first four group 15 elements are given below. Choose the correct value for the element that is a main component of apatite family :

Q19.Which one of the following, with HBr will give a phenol?

Q20.Consider the following low-spin complexes
${\mathrm{K}}_3\left[\mathrm{Co}{\left({\mathrm{NO}}_2\right)}_6\right],{\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right],{\mathrm{K}}_3\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$, …

Q21.Isomeric hydrocarbons → negative Baeyer's test (Molecular formula ${\mathrm{C}}_9{\mathrm{H}}_{12}$ )
The total number of isomers from above with four different non-aliphatic substitution sites is -

Q22.In the Claisen-Schmidt reaction to prepare, dibenzalacetone from 5.3 g benzaldehyde, a total of 3.51 g of product was obtained. The percentage yield in this reaction was ______ %.

Q23.In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of sulphur in the compound is ______
$\times 10^{-1}\%$.
(Molar mass : $\mathrm{O}=16,\mathrm{S}=32,\mathrm{Ba}=137$ in $\mathrm{g}{\mathrm{mol}}^{-1}$ )

Q24.Total number of non bonded electrons present in ${\mathrm{NO}}_2^{-}$ ion based on Lewis theory is ____.

Q1.If the set of all $\mathrm{a}\in \mathbf{R}$, for which the equation $2{\mathrm{x}}^2+(\mathrm{a}-5)\mathrm{x}+15=3\mathrm{a}$ has no real root, is the interval $(\alpha ,\beta )$, and $X=\{x\in Z:\alpha <x<\beta \}$, then ${\sum }_{x\in X}{x}^2$ is equal to

Q2.If $\sin \mathrm{x}+{\sin }^2\mathrm{x}=1,\mathrm{x}\in \left(0,\frac{\pi }{2}\right)$, then …

Q3.Let the area enclosed between the curves $|\mathrm{y}|=1-{\mathrm{x}}^2$ and ${\mathrm{x}}^2+{\mathrm{y}}^2=1$ be $\alpha$. If $9\alpha =\beta \pi +\gamma ;\beta ,\gamma$ are integers, then the value of $|\beta -\gamma |$ equals

Q4.If the domain of the function ${\log }_5\left(18\mathrm{x}-{\mathrm{x}}^2-77\right)$ is $(\alpha ,\beta )$ and the domain of the function ${\log }_{(x-1)}\left(\frac{2x^2+3x-2}{x^2-3x-4}\right)$ is $(\gamma ,\delta )$, then ${\alpha }^2+{\beta }^2+{\gamma }^2$ is equal to :

Q5.Let a straight line L pass through the point $\mathrm{P}(2,-1,3)$ and be perpendicular to the lines $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{1}=\frac{\mathrm{z}-3}{-2}$ and $\frac{\mathrm{x}-3}{1}=\frac{\mathrm{y}-2}{3}=\frac{\mathrm{z}+2}{4}$. If the line L intersects the yz …

Q6.Let $\mathrm{S}=\mathbf{N}\cup \{0\}$. Define a relation $\mathbf{R}$ from S to $\mathbf{R}$ by : …

Q7.Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and B , respectively. A right angled triangle AMN is inscribed in the triangle OAB , where O is the origin and the points M and N lie on the lines OB and AB , respectively. If the area of the triangle AMN is $\frac{4}{9}$ o …

Q8.If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\frac{{\mathrm{x}}^2}{9}+\frac{{\mathrm{y}}^2}{4}=1$, whose mid point is $\left(\frac{5}{2},\frac{1}{2}\right)$, then $\alpha +\beta$ is equal to

Q9.If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at $440^{\text{th }}$ position in this arrangement, is :

Q10.Let $\alpha ,\beta (\alpha \ne \beta )$ be the values of $m$, for which the equations $\mathrm{x}+\mathrm{y}+\mathrm{z}=1;\mathrm{x}+2\mathrm{y}+4\mathrm{z}=\mathrm{m}$ and $x+4y+10z=m^2$ have infinitely many solutions. Then the value of …

Q11.Let $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]$ be a matrix of order $3\times 3$, with ${\mathrm{a}}_{\mathrm{ij}}=(\sqrt{2}{)}^{\mathrm{i}+\mathrm{j}}$. If the sum of all the elements in the third row of ${\mathrm{A}}^2$ is …

Q12.Let P be the foot of the perpendicular from the point $(1,2,2)$ on the line $\mathrm{L}:\frac{\mathrm{x}-1}{1}=\frac{\mathrm{y}+1}{-1}=\frac{\mathrm{z}-2}{2}$. Let the line …

Q13.Let a circle C pass through the points $(4,2)$ and $(0,2)$, and its centre lie on $3x+2y+2=0$. Then the length of the chord, of the circle C , whose midpoint is $(1,2)$, is:

Q14.Let $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]$ be a $2\times 2$ matrix such that ${\mathrm{a}}_{\mathrm{ij}}\in \{0,1\}$ for all i and j . Let the random variable X denote the possible values of the determinant of the matrix A . Then, the variance of X is:

Q15.Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is 29/45, then n is equa …

Q16.The remainder, when $7^{103}$ is divided by 23 , is equal to:

Q17.Let $\mathrm{f}(\mathrm{x})={\int }_0^{\mathrm{x}}\mathrm{t}\left({\mathrm{t}}^2-9\mathrm{t}+20\right)\mathrm{dt},1\le \mathrm{x}\le 5$. If the range of f is $[\alpha ,\beta ]$, then $4(\alpha +\beta )$ equals:

Q18.Let â be a unit vector perpendicular to the vectors $\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-\hat{\mathrm{k}}$, and makes an angle of …

Q19.If for the solution curve $y=f(x)$ of the differential equation $\frac{dy}{dx}+(\tan x)y=\frac{2+\sec x}{(1+2\sec x{)}^2}$,
$x\in \left(\frac{-\pi }{2},\frac{\pi }{2}\right),f\left(\frac{\pi }{3}\right)=\frac{\sqrt{3}}{10}$, then $f\left(\frac{\pi }{4}\right)$ is equal to:

Q20.If $24{\int }_0^{\frac{\pi }{4}}\left(\sin \left|4x-\frac{\pi }{12}\right|+[2\sin x]\right)dx=2\pi +\alpha$, where [•] denotes the greatest integer function, then $\alpha$ is equal to ____.

Q21.If ${\lim }_{t\to 0}{\left({\int }_0^1(3x+5{)}^{t}dx\right)}^{\frac{1}{t}}=\frac{\alpha }{5e}{\left(\frac{8}{5}\right)}^{\frac{2}{3}}$, then $\alpha$ is equal to ____.

Q22.Let $a_1,a_2,\dots ,a_{2024}$ be an Arithmetic Progression such that $a_1+(a_5+a_{10}+a_{15}+\dots +a_{2020})+a_{2024}=2233$. Then $a_1+a_2+a_3+\dots +a_{2024}$ is equal to

Q23.Let integers $a,b\in [-3,3]$ be such that $a+b\ne 0$. Then the number of all possible ordered pairs $(a,b)$, for which $\left|\frac{z-a}{z+b}\right|=1$ and …

Q24.Let $y^2=12x$ be the parabola and $S$ be its focus. Let $PQ$ be a focal chord of the parabola such that $(SP)(SQ)=\frac{147}{4}$. Let $C$ be the circle described taking $PQ$ as a diameter. If the equation of a circle $C$ is $64x^2+64y^2-\alpha x-64\sqrt{3}y=\beta$, then …