JEE Main 2025 · 24 Jan 2025 · Shift 2

Q1.Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits …

Q2.Arrange the following in the ascending order of wavelength ( $\lambda$ ) :
(A) Microwaves $\left({\lambda }_1\right)$
(B) Ultraviolet rays ( ${\lambda }_2$ )
(C) Infrared rays ( ${\lambda }_3$ )
(D) X-rays $\left({\lambda }_4\right)$

Choose the most appropriate answer from the optio …

Q3.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R).
Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (A) : The magnetic field in that regi …

Q4.A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

Q5.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R) : Free expansion of an …

Q6.In the first configuration (1) as shown in the figure, four identical charges ( ${\mathrm{q}}_0$ ) are kept at the corners $\mathrm{A},\mathrm{B},\mathrm{C}$ and D of square of side length ' a '. In the second configuration (2), the same charges are shifted to mid points …

Q7.The position vector of a moving body at any instant of time is given as $\overrightarrow{\mathrm{r}}=\left(5{\mathrm{t}}^2\hat{\mathrm{i}}-5\mathrm{t}\hat{\mathrm{j}}\right)\mathrm{m}$. The magnitude and direction of velocity at $\mathrm{t}=2\mathrm{s}$ is,

Q8.A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

Q9.N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segme …

Q10.In photoelectric effect, the stopping potential ( ${\mathrm{V}}_0$ ) v/s frequency (v) curve is plotted.
( h is the Planck's constant and ${\varphi }_0$ is work function of metal)
(A) ${\mathrm{V}}_0\mathrm{v}/\mathrm{s}v$ is linear
(B) The slope of …

Q11.The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit)

Q12.A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is $2\mathrm{cm}\times 2\mathrm{cm}$ and the area of the landscape photographed is $400{\mathrm{km}}^2$. The focal length of the lens in the drone camera is :

Q13.The output of the circuit is low (zero) for :
(A) $\mathrm{X}=0,\mathrm{Y}=0$
(B) $X=0,Y=1$
(C) $X=1,Y=0$
(D) $\mathrm{X}=1,\mathrm{Y}=1$

Choose the correct answer from the options given below :

Q14.The temperature of a body in air falls from $40^{\circ }\mathrm{C}$ to $24^{\circ }\mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ }\mathrm{C}$. The temperature of the body in the next 4 minutes will be :

Q15.The energy E and momentum p of a moving body of mass $m$ are related by some equation. Given that c represents the speed of light, identify the correct equation.

Q16.A small uncharged conducting sphere is placed in contact with an identical sphere but having $4\times 10^{-8}$ C charge and then removed to a distance such that the force of repulsion between them is $9\times 10^{-3}\mathrm{N}$. The distance between them is (Take …

Q17.In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are orthogonal to each other. The polarizer ${\mathrm{P}}_3$ covers both the slits with its transmission axis at $45^{\circ }$ to t …

Q18.A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is ______.
[Take mass of electron …

Q19.A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes $\left(\frac{3}{\pi }\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ______ ML.

Q20.The ratio of the power of a light source ${\mathrm{S}}_1$ to that the light source ${\mathrm{S}}_2$ is $2.{\mathrm{S}}_1$ is emitting $2\times 10^{15}$ photons per second at 600 nm . If the wavelength of the source ${\mathrm{S}}_2$ is 300 nm , then the number of photons per se …

Q21.The increase in pressure required to decrease the volume of a water sample by $0.2\%$ is $\mathrm{P}\times 10^5{\mathrm{Nm}}^{-2}$. Bulk modulus of water is $2.15\times 10^9{\mathrm{Nm}}^{-2}$. The value of P is ______ .

Q22.Acceleration due to gravity on the surface of earth is ' g '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ______ g.

Q23.A solid/long straight wire of circular cross-section with radius 'a' carries a steady current I uniformly distributed across the cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by: [graph options in source]

Q24.Which of the following figure represents the relation between Celsius (C) and Fahrenheit (F) temperatures? [graph options in source]

Q25.A particle oscillates along the x-axis according to x(t) = x₀ sin²(πt/2), where x₀ = 1 m. The kinetic energy (K) of the particle as a function of x is correctly represented by the graph: [graph options in source]

Q1.Based on the data given below: …

Q2.Given below are two statements :

Statement(I) :

Statement(II) :

In the light of the above statements, choose the correct answer from the options given below :

Q3.For reaction

(Major)

The correct order of set of reagents for the above conversion is :

Q4.For hydrogen atom, the orbital/s with lowest energy is/are :
(A) 4 s
(B) $3{\mathrm{p}}_{\mathrm{x}}$
(C) $3d_{x^2-y^2}$
(D) $3d_{z^2}$
(E) $4p_z$

Choose the correct answer from the options given below :

Q5.In the given structure, number of sp and ${\mathrm{sp}}^2$ hybridized carbon atoms present respectively are :

Q6.Which of the following mixing of 1 M base and 1 M acid leads to the largest increase in temperature?

Q7.Given below are two statements :

Statement(I) : Experimentally determined oxygen-oxygen bond lengths in the ${\mathrm{O}}_3$ are found to be same and the bond length is greater than that of a $\mathrm{O}=\mathrm{O}$ (double bond) but less than that of a single …

Q8.Find the compound ' $A$ ' from the following reaction sequences.

Q9.Match List-I with List-II.

\begin{tabular}{ll}
\begin{tabular}{l}
List-I \\
(Transition metal ion)
\end{tabular} & \begin{tabular}{l}
List-II \\
(Spin only magnetic moment)
\end{tabular} \\
(A) ${\mathrm{Ti}}^{3+}$ & (I) 3.87 \\
(B) ${\mathrm{V}}^{2+}$ & (II) 0.00 \\
(C) …

Q10.The elemental composition of a compound is $54.2\%,\mathrm{C},9.2\%\mathrm{H}$ and $36.6\%\mathrm{O}$. If the molar mass of the compound is $132\mathrm{g}{\mathrm{mol}}^{-1}$, the molecular formula of the compound is :
[Given : The relative atomic mass of …

Q11.When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be :

Q12.The conditions and consequence that favours the ${\mathrm{t}}_{2\mathrm{g}}{}^3,{\mathrm{e}}_{\mathrm{g}}{}^1$ configuration in a metal complex are :

Q13.Identify correct statement/s :
(A) $-{\mathrm{OCH}}_3$ and $-{\mathrm{NHCOCH}}_3$ are activating group
(B) -CN and -OH are meta directing group
(C) -CN and $-{\mathrm{SO}}_3\mathrm{H}$ are meta directing group
(D) Activating groups act as ortho - and para directing groups …

Q14.Given below are two statements :

Statement (I) : The first ionization energy of Pb is greater than that of Sn

Statement(II) : The first ionization energy of Ge is greater than that of Si .

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

Q15.$\mathrm{S}(\mathrm{g})+\frac{3}{2}{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{SO}}_3(\mathrm{g})+2\mathrm{x}\mathrm{kcal}$
${\mathrm{SO}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{SO}}_3(\mathrm{g})+\mathrm{y}\mathrm{kcal}$
The he …

Q16.Match List-I with List-II

List-I
(A) $\mathrm{RCN}\underset{\text{ (ii) }{\mathrm{H}}_3{\mathrm{O}}^{+}}{\overset{\text{(i) }{\mathrm{SnCl}}_2,\mathrm{HCl}}{\to }}\mathrm{RCHO}$
(B) (see structure)
(C) (see structure)
(D) (see structure)

List-II
(I) Etard reaction
(II) Gatterman -Ko …

Q17.The structure of the major product formed in the following reaction is :
(see structure)

Q18.Match List-I with List-II.

List-I
(A) Adenine
(B) Cytosine
(C) Thymine
(D) Uracil

List-II
(I) (see structure)
(II) (see structure)
(III) (see structure)
(IV) (see structure)

Choose the correct answer from the options given below :

Q19.The successive 5 ionisation energies of an element are 800 , 2427, 3658, 25024 and $32824\mathrm{kJ}/\mathrm{mol}$, respectively. By using the above values predict the group in which the above element is present :

Q20.The observed and normal masses of compound ${\mathrm{MX}}_2$ are 65.6 and 164 respectively. The percent degree of ionisation of ${\mathrm{MX}}_2$ is ____ %.
(Nearest integer)

Q21.The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is ____ .

Q22.Consider a complex reaction taking place in three steps with rate constants ${\mathrm{k}}_1,{\mathrm{k}}_2$ and ${\mathrm{k}}_3$ respectively. The overall rate constant k is given by the expression $\mathrm{k}=\sqrt{\frac{{\mathrm{k}}_1{\mathrm{k}}_3}{{\mathrm{k}}_2}}$. I …

Q23.The hydrocarbon $(\mathrm{X})$ with molar mass $80\mathrm{g}{\mathrm{mol}}^{-1}$ and $90\%$ carbon has ____ degree of unsaturation.

Q24.In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide ( AgBr ). The percentage of Bromine in the organic compound is ______ $\times 10^{-1}$ % (Nearest integer).
(Given : Molar mass of Ag is 108 and Br is …

Q25.For the reaction H₂(g) + I₂(g) ⇌ 2HI(g), the attainment of equilibrium is predicted correctly by: [molar concentration vs time graph options in source]

Q1.The equation of the chord, of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid-point is $(3,1)$ is :

Q2.The function $f:(-\infty ,\infty )\to (-\infty ,1)$, defined by $f(x)=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is :

Q3.If $\alpha >\beta >\gamma >0$, then the expression
${\cot }^{-1}\left\{\beta +\frac{\left(1+{\beta }^2\right)}{(\alpha -\beta )}\right\}+{\cot }^{-1}\left\{\gamma +\frac{\left(1+{\gamma }^2\right)}{(\beta -\gamma )}\right\}$ …

Q4.Let $\mathrm{f}:(0,\infty )\to \mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition ${\mathrm{x}}^2{\mathrm{f}}^{\prime }(\mathrm{x})=2\mathrm{xf}(\mathrm{x})+3$, with $f(1)=4$. Then $2f(2)$ is equal to:

Q5.Let
$\mathrm{A}=\left\{\mathrm{x}\in (0,\pi )-\left\{\frac{\pi }{2}\right\}:{\log }_{(2/\pi )}|\sin \mathrm{x}|+{\log }_{(2/\pi )}|\cos \mathrm{x}|=2\right\}$
and
$B=\{x\ge 0:\sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $\mathrm{n}(\mathrm{A}\cup \mathrm{B})$ is equal to:

Q6.Let the position vectors of three vertices of a triangle be $4\vec{p}+\vec{q}-3\vec{r},-5\vec{p}+\vec{q}+2\vec{r}$ and $2\vec{p}-\vec{q}+2\vec{r}$. If the position vectors of the orthocenter and the circumcenter of the triangle are …

Q7.Let $[\mathrm{x}]$ denote the greatest integer function, and let $m$ and $n$ respectively be the numbers of the points, where the function $\mathrm{f}(\mathrm{x})=[\mathrm{x}]+|\mathrm{x}-2|$, $-2<\mathrm{x}<3$, is not continuous and not differentiable.

Then …

Q8.Let the points $\left(\frac{11}{2},\alpha \right)$ lie on or inside the triangle with sides $\mathrm{x}+\mathrm{y}=11,\mathrm{x}+2\mathrm{y}=16$ and $2\mathrm{x}+3\mathrm{y}=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

Q9.In an arithmetic progression, if ${\mathrm{S}}_{40}=1030$ and ${\mathrm{S}}_{12}=57$, then ${\mathrm{S}}_{30}-{\mathrm{S}}_{10}$ is equal to:

Q10.If $7=5+\frac{1}{7}(5+\alpha )+\frac{1}{7^2}(5+2\alpha )+\frac{1}{7^3}(5+3\alpha )+\dots \dots \infty$, then the value of $\alpha$ is:

Q11.If the system of equations
$x+2y-3z=2$
$2\mathrm{x}+\lambda \mathrm{y}+5\mathrm{z}=5$
$14\mathrm{x}+3\mathrm{y}+\mu \mathrm{z}=33$
has infinitely many solutions, then $\lambda +\mu$ is equal to:

Q12.Let $(2,3)$ be the largest open interval in which the function $f(x)=2{\log }_e(x-2)-x^2+ax+1$ is strictly increasing and ( $\mathrm{b},\mathrm{c}$ ) be the largest open interval, in which the function $\mathrm{g}(\mathrm{x})=(\mathrm{x}-1{)}^3(\mathrm{x}+2-\mathrm{a}{)}^2$ …

Q13.Suppose A and B are the coefficients of $30^{\text{th }}$ and $12^{\text{th }}$ terms respectively in the binomial expansion of $(1+x{)}^{2n-1}$. If $2A=5B$, then $n$ is equal to:

Q14.Let $\vec{a}=3\hat{i}-\hat{j}+2\hat{k},\vec{b}=\vec{a}\times (\hat{i}-2\hat{k})$ and $\vec{c}=\vec{b}\times \hat{k}$.

Then the projection of $\vec{c}-2\hat{j}$ on $\vec{a}$ is:

Q15.For some $a,b$, let



${\lim }_{x\to 0}f(x)=\lambda +\mu a+\nu b$. Then $(\lambda +\mu +\nu {)}^2$ is equal to:

Q16.Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B , is equal to:

Q17.The area of the region enclosed by the curves $y=e^x,y=\left|e^x-1\right|$ and $y$-axis is:

Q18.The number of real solution(s) of the equation ${\mathrm{x}}^2+3\mathrm{x}+2=\min \{|\mathrm{x}-3|,|\mathrm{x}+2|\}$ is :

Q19.Let $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $\mathrm{P}(\mathrm{E})$ is :

Q20.If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2},3\right)$ and the directrix $\mathrm{x}+2\mathrm{y}=0$ is $\alpha x^2+\beta y^2-\gamma xy-30x-60y+225=0$, then $\alpha +\beta +\gamma$ is equal to:

Q21.Number of functions $f:\{1,2,\dots ,100\}\to \{0,1\}$, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ____.

Q22.Let P be the image of the point $\mathrm{Q}(7,-2,5)$ in the line $\mathrm{L}:\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{3}=\frac{\mathrm{z}}{4}$ and $\mathrm{R}(5,\mathrm{p},\mathrm{q})$ be a point on $L$. Then the square of the area of $△PQR$ is ____

Q23.Let $y=y(x)$ be the solution of the differential equation $2\cos \mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}=\sin 2\mathrm{x}-4\mathrm{y}\sin \mathrm{x},\mathrm{x}\in \left(0,\frac{\pi }{2}\right)$. If $y\left(\frac{\pi }{3}\right)=0$, then …

Q24.Let $H_1:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $H_2:-\frac{x^2}{A^2}+\frac{y^2}{B^2}=1$ be two hyperbolas having length of latus rectums $15\sqrt{2}$ and $12\sqrt{5}$ respectively. Let their eccentricities be ${\mathrm{e}}_1=\sqrt{\frac{5}{2}}$ and …

Q25.If $\int \frac{2x^2+5x+9}{\sqrt{x^2+x+1}}dx=x\sqrt{x^2+x+1}+\alpha \sqrt{x^2+x+1}+\beta {\log }_{\mathrm{e}}\left|\mathrm{x}+\frac{1}{2}+\sqrt{{\mathrm{x}}^2+\mathrm{x}+1}\right|+\mathrm{C}$, where C is the constant of integration, then $\alpha +2\beta$ is equal to __ …