JEE Main 2025 · 22 Jan 2025 · Shift 1

Q1.Given below are two statements:

Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.

Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier scale division.

In the lig …

Q2.A line charge of length $\frac{{}^{\prime }{\mathrm{a}}^{\prime }}{2}$ is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line is $\lambda \mathrm{C}$ per unit length, then the total electric flux through all the faces of the cube wi …

Q3.Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $R_p=1\Omega$ as shown in the figure. An external resistance of ${\mathrm{R}}_{\mathrm{e}}=2\Omega$ is connected via the sliding contact.

Q4.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.

Reason (R): The speed of lig …

Q5.Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of bigger body is 400 K. If the energy radiate from the smaller body is E, the energy radiated from the bigger body is ( …

Q6.An amount of ice of mass $10^{-3}\mathrm{kg}$ and temperature $-10^{\circ }\mathrm{C}$ is transformed to vapour of temperature $110^{\circ }$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice …

Q7.An electron in the ground state of the hydrogen atom has the orbital radius of $5.3\times 10^{-11}\mathrm{m}$ while that for the electron in third excited state is $8.48\times 10^{-10}\mathrm{m}$. The ratio of the de Broglie wavelengths of electron in the ground state to th …

Q8.In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $[{\mathrm{R}}_1]$ and $[{\mathrm{R}}_2]$, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is

Q9.An electron is made to enters symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the field region with a horizontal component of velocity $10^6\mathrm{m}/\mathrm{s}$. If the magnitude of the …

Q10.A closed organ and an open organ tube filled by two different gases having same bulk modulus but different densities ${\rho }_1$ and ${\rho }_2$ respectively. The frequency of $9^{\text{th }}$ harmonic of closed tube is identical with $4^{\text{th }}$ harmonic of open tube. If th …

Q11.A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius $\mathrm{R}/2$ is removed from the original disc as shown in the figure. Find the moment of inertia of the rem …

Q12.A small point of mass $m$ is placed at a distance $2R$ from the centre 'O' of a big uniform solid sphere of mass M and radius R. The gravitational force on 'm' due to M is ${\mathrm{F}}_1$. A spherical part of radius $\mathrm{R}/3$ is removed from the big sphere as shown in th …

Q13.The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of wavelength 550 nm on these two metal surface, then photo-electric effect is possible for the case of

Q14.If B is magnetic field and ${\mu }_0$ is permeability of free space, then the dimensions of ($\mathrm{B}/{\mu }_0$) is

Q15.A bob of mass m is suspended at a point O by a light string of length $l$ and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_0$ at the point 'A', the string becomes slack when the bob reaches at the point 'D'. The ra …

Q16.Given below are two statements:

Statement-I: The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.

Statement-II: The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal …

Q17.Which of the following circuits represents a forward biased diode?

Choose the correct answer from the options given below:

Q18.A parallel-plate capacitor of capacitance $40\mu \mathrm{F}$ is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant $\mathrm{K}=2$. Due to the introduction of dielectric material, the extra …

Q19.Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself.

Q20.Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is ______.

Q21.The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature $\mathrm{R}=2\mathrm{m}$. Another car approaches him from behind with a uniform speed of …

Q22.Three conductors of same length having thermal conductivity ${\mathrm{k}}_1$, ${\mathrm{k}}_2$ and ${\mathrm{k}}_3$ are connected as shown in figure.
| $1.{\mathrm{k}}_1$ | | …

Q23.The position vectors of two 1 kg particles, (A) and (B), are given by
${\overrightarrow{\mathrm{r}}}_{\mathrm{A}}=\left({\alpha }_1{\mathrm{t}}^2\hat{\mathrm{i}}+{\alpha }_2\hat{\mathrm{t}}\hat{\mathrm{j}}+{\alpha }_{3}t\hat{\mathrm{k}}\right)\mathrm{m}$
and …

Q24.A particle is projected at an angle of $30^{\circ }$ from horizontal at a speed of $60\mathrm{m}/\mathrm{s}$. The height traversed by the particle in the first second is ${\mathrm{h}}_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$. …

Q25.A closed organ tube and an open organ tube are filled by two different gases having the same bulk modulus but different densities ρ₁ and ρ₂ respectively. The frequency of the 9th harmonic of the closed tube is identical with the 4th harmonic of the open tube. If the length of the …

Q1.A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A. The amount of the aluminium deposited at the cathode is ______.
[Given : molar mass of aluminium and chlorine are $27\mathrm{g}{\mathrm{mol}}^{-1}$ and $35.5\mathrm{g}{\mathrm{mol}}^{-1}$ …

Q2.Which of the following statement is not true for radioactive decay?

Q3.How many different stereoisomers are possible for the given molecule?

Q4.Which of the following electronegativity order is incorrect?

Q5.Lanthanoid ions with $4{\mathrm{f}}^7$ configuration are :
(A) ${\mathrm{Eu}}^{2+}$
(B) ${\mathrm{Gd}}^{3+}$
(C) ${\mathrm{Eu}}^{3+}$
(D) ${\mathrm{Tb}}^{3+}$
(E) ${\mathrm{Sm}}^{2+}$

Choose the correct answer from the options given below :

Q6.Which of the following acids is a vitamin ?

Q7.A liquid when kept inside a thermally insulated closed vessel at $25^{\circ }\mathrm{C}$ was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?

Q8.Radius of the first excited state of Helium ion is given as :
${\mathrm{a}}_0\to$ radius of first stationary state of hydrogen atom.

Q9.Given below are two statements :

Statement I: ${\mathrm{CH}}_3-\mathrm{O}-{\mathrm{CH}}_2-\mathrm{Cl}$ will undergo ${\mathrm{S}}_{\mathrm{N}}1$ reaction though it is a primary halide.

Statement II:

will not undergo ${\mathrm{S}}_{\mathrm{N}}2$ reaction very easily though it is …

Q10.Given below are two statements :

Statement I: One mole of propyne reacts with excess of sodium to liberate half a mole of ${\mathrm{H}}_2$ gas.

Statement II : Four g of propyne reacts with ${\mathrm{NaNH}}_2$ to liberate ${\mathrm{NH}}_3$ gas which occupies 224 mL at STP.

In t …

Q11.A vessel at 1000 K contains ${\mathrm{CO}}_2$ with a pressure of 0.5 atm. Some of ${\mathrm{CO}}_2$ is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm, then ${\mathrm{K}}_{\mathrm{p}}$ is :

Q12.The IUPAC name of the following compound is :

Q13.Which of the following electrolyte can be sued to obtain ${\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_8$ by the process of electrolysis?

Q14.The compounds which give positive Fehling's test are :
(A)
(B)
(C) ${\mathrm{HOCH}}_2-\mathrm{CO}-(\mathrm{CHOH}{)}_3-{\mathrm{CH}}_2-\mathrm{OH}$
(D)
(E)

Choose the CORRECT answer from the options given below :

Q15.In which of the following complexes the CFSE, ${\Delta }_0$ will be equal to zero?

Q16.Arrange the following solutions in order of their increasing boiling points.
(i) $10^{-4}\mathrm{M}\mathrm{NaCl}$
(ii) $10^{-4}\mathrm{M}$ Urea
(iii) $10^{-3}\mathrm{M}\mathrm{NaCl}$
(iv) $10^{-2}\mathrm{M}\mathrm{NaCl}$

Q17.The products formed in the following reaction sequence are :

Q18.From the magnetic behaviour of ${\left[{\mathrm{NiCl}}_4\right]}^{2-}$ (paramagnetic) and $\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right]$ (diamagnetic), choose the correct geometry and oxidation state.

Q19.The incorrect statements regarding geometrical isomerism are :
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene sho …

Q20.Some ${\mathrm{CO}}_2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of ${\mathrm{CO}}_2$ gas was later passed through an aqueous solution of $\mathrm{Ca}(\mathrm{OH}{)}_2$. The excess unreacted $\mathrm{Ca}(\mathrm{OH}{)}_2$ …

Q21.In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl . The percentage composition of chlorine in the compound is ____ %.
[Given : molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of $\mathrm{Ag}:108$, $\mathrm{Cl}=35.5]$

Q22.The number of molecules/ions that show linear geometry among the following is ____。 …

Q23.$\mathrm{A}\to \mathrm{B}$

The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is …

Q24.Consider the following sequence of reactions :
(i) $\mathrm{Sn}+\mathrm{HCl}$
(see structure)
(ii) ${\mathrm{NaNO}}_2,\mathrm{HCl}$
$\underset{\text{ (iii) }{\mathrm{Cu}}_2{\mathrm{Cl}}_2}{\overset{0^{\circ }\mathrm{C}}{\to }}\underset{\text{ Product }}{\mathrm{A}}$
(iv) Na, Ether

Mola …

Q1.The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

Q2.Let $f:\mathbf{R}\to \mathbf{R}$ be a twice differentiable function such that $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbf{R}$. If $f^{\prime }(0)=4a$ and $f$ satisfies $f^{\prime \prime }(x)-3a{f}^{\prime }(x)-f(x)=0$, $a>0$, then the area of the region …

Q3.Let the triangle PQR be the image of the triangle with vertices $(1,3),(3,1)$ and $(2,4)$ in the line $x+2y=2$. If the centroid of $△PQR$ is the point $(\alpha ,\beta )$, then $15(\alpha -\beta )$ is equal to :

Q4.Let $z_1,z_2$ and $z_3$ be three complex numbers on the circle $|z|=1$ with $\arg (z_1)=\frac{-\pi }{4},\arg (z_2)=0$ and $\arg (z_3)=\frac{\pi }{4}$. If …

Q5.Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of $16\left({\left({\sec }^{-1}x\right)}^2+{\left({\mathrm{cosec}}^{-1}x\right)}^2\right)$ is :

Q6.A coin is tossed three times. Let X denote the number of times a tail follows a head. If $\mu$ and ${\sigma }^2$ denote the mean and variance of X, then the value of $64\left(\mu +{\sigma }^2\right)$ is :

Q7.Let $a_1,a_2,a_3\dots$ be a G.P. of increasing positive terms. If $a_1{a}_5=28$ and $a_2+a_4=29$, then $a_6$ is equal to

Q8.Let $L_1:\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $L_2:\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_1$ and $L_2$ ?

Q9.The product of all solutions of the equation $e^{5{\left({\log }_{e}x\right)}^2+3}=x^8,x>0$, is :

Q10.If ${\sum }_{r=1}^n{T}_r=\frac{(2n-1)(2n+1)(2n+3)(2n+5)}{64}$, then ${\lim }_{n\to \infty }{\sum }_{r=1}^n\left(\frac{1}{T_r}\right)$ is equal to :

Q11.From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is 'M', is :

Q12.Let $\mathrm{x}=\mathrm{x}(\mathrm{y})$ be the solution of the differential equation $y^{2}dx+\left(x-\frac{1}{y}\right)dy=0$. If $x(1)=1$, then $x\left(\frac{1}{2}\right)$ is :

Q13.Let the parabola $y=x^2+px-3$, meet the coordinate axes at the points $\mathrm{P},\mathrm{Q}$ and R. If the circle C with centre at $(-1,-1)$ passes through the points $P,Q$ and $R$, then the area of $△PQR$ is :

Q14.A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let $r$ be the radius of a circle that has centre at the point $(2,5)$ and intersects the circle C at exactly two points. If the set of all possible values of $r$ is the interval …

Q15.Let for $f(\mathrm{x})=7{\tan }^8\mathrm{x}+7{\tan }^6\mathrm{x}-3{\tan }^4\mathrm{x}-3{\tan }^2\mathrm{x}$, ${\mathrm{I}}_1={\int }_0^{\pi /4}f(\mathrm{x})\mathrm{dx}$ and ${\mathrm{I}}_2={\int }_0^{\pi /4}\mathrm{x}f(\mathrm{x})\mathrm{dx}$. Then …

Q16.Let $f(\mathrm{x})$ be a real differentiable function such that $f(0)=1$ and $f(\mathrm{x}+\mathrm{y})=f(\mathrm{x})f^{\prime }(\mathrm{y})+f^{\prime }(\mathrm{x})f(\mathrm{y})$ for all $\mathrm{x},\mathrm{y}\in \mathbf{R}$. Then …

Q17.Let $\mathrm{A}=\{1,2,3,\dots ,10\}$ and $\mathrm{B}=\left\{\frac{\mathrm{m}}{\mathrm{n}}:\mathrm{m},\mathrm{n}\in \mathrm{A},\mathrm{m}<\mathrm{n}\text{ and }\gcd (\mathrm{m},\mathrm{n})=1\right\}$. Then $\mathrm{n}(\mathrm{B})$ is equal to :

Q18.The area of the region, inside the circle $(x-2\sqrt{3}{)}^2+y^2=12$ and outside the parabola $y^2=2\sqrt{3}x$ is

Q19.Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{\mathrm{m}}{\mathrm{n}}$, where …

Q20.Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :

Q21.Let the function, $f(x)=\{\begin{array}{ll}-3a{x}^2-2,& x<1\\ a^2+bx,& x\ge 1\end{array}$ be differentiable for all $\mathrm{x}\in \mathbf{R}$, where $\mathrm{a}>1,\mathrm{b}\in \mathbf{R}$. If the area of the region enclosed by $y=f(x)$ and the line $\mathrm{y}=-20$ is …

Q22.If ${\sum }_{\mathrm{r}=0}^5\frac{{}^{11}{\mathrm{C}}_{2\mathrm{r}+1}}{2\mathrm{r}+2}=\frac{\mathrm{m}}{\mathrm{n}}$, where $\gcd (\mathrm{m},\mathrm{n})=1$, then $\mathrm{m}-\mathrm{n}$ is equal to ____.

Q23.Let A be a square matrix of order 3 such that $\det (\mathrm{A})=-2$ and $\det (3\mathrm{adj}(-6\mathrm{adj}(3\mathrm{A})))=2^{\mathrm{m}+\mathrm{n}}\cdot 3^{\mathrm{mn}}$, where $\mathrm{m}>\mathrm{n}$. Then $4\mathrm{m}+2\mathrm{n}$ i …

Q24.Let ${\mathrm{L}}_1:\frac{\mathrm{x}-1}{3}=\frac{\mathrm{y}-1}{-1}=\frac{\mathrm{z}+1}{0}$ and ${\mathrm{L}}_2:\frac{\mathrm{x}-2}{2}=\frac{\mathrm{y}}{0}=\frac{\mathrm{z}+4}{\alpha },\alpha \in \mathrm{R}$, be two lines, which intersect at the point B. If P is the foot of perp …

Q25.Let $\overrightarrow{\mathrm{c}}$ be the projection vector of $\overrightarrow{\mathrm{b}}=\lambda \hat{\mathrm{i}}+4\hat{\mathrm{k}},\lambda >0$, on the vector $\vec{a}=\hat{i}+2\hat{j}+2\hat{k}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram formed by the vect …