JEE Main 2025 · 23 Jan 2025 · Shift 1

Q1.Regarding self-inductance :
A : The self-inductance of the coil depends on its geometry.
B : Self-inductance does not depend on the permeability of the medium.
C : Self-induced e.m.f. opposes any change in the current in a circuit.
D : Self-inductance is electromagnetic analogue …

Q2.A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $\mathrm{y}\pi \times 10^{-2}\mathrm{s}$, where the value of $y$ is
(Acceleration due to gr …

Q3.Given below are two statements:

Statement-I : The hot water flows faster than cold water.

Statement-II : Soap water has higher surface tension as compared to fresh water.

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

Q4.A sub-atomic particle of mass $10^{-30}\mathrm{kg}$ is moving with a velocity $2.21\times 10^6\mathrm{m}/\mathrm{s}$. Under the matter wave consideration, the particle will behave closely like $\_\_\_\_$ . ( $\mathrm{h}=6.63\times 10^{-34}\mathrm{J}.\mathrm{s}$ )

Q5.A spherical surface of radius of curvature $R$, separates air from glass (refractive index $=1.5$ ). The centre of curvature is in the glass medium. A point object ' $O$ ' placed in air on the optic axis of the surface, so that its real image is formed at 'I' inside glass. The li …

Q6.A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus ${\mathrm{n}}_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of ${\mathrm{n}}_2$ to the number of nuclei of …

Q7.Identify the valid statements relevant to the given circuit at the instant when the key is closed.
A. There will be no current through resistor $R$.
B. There will be maximum current in the connecting wires.
C. Potential difference between the capacitor plates A and B is minimum. …

Q8.The position of a particle moving on x -axis is given by $\mathrm{x}(\mathrm{t})=\mathrm{A}\sin \mathrm{t}+\mathrm{B}{\cos }^2\mathrm{t}+{\mathrm{Ct}}^2+\mathrm{D}$, where t is time. The dimension of $\frac{\mathrm{ABC}}{\mathrm{D}}$ is-

Q9.Match the List-I with List-II

Choose the correct answer from the options given below :

Q10.Consider a moving coil galvanometer (MCG) :
A : The torsional constant in moving coil galvanometer has dimensions $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$
B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C : If we increase number …

Q11.A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distanc …

Q12.A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is $\_\_\_\_$ grams.
(Latent heat of fusi …

Q13.What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' $h$ ' in terms of the angle of incidence ' $i$ ' and angle of refraction ' $r$ ', if the glass slab is placed in air medium ?

Q14.A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length 'L' and makes an angle $30^{\circ }$ with the horizontal. The speed of the particle at the bottom of the plane is ${\mathrm{v}}_1$. If the an …

Q15.Refer to the circuit diagram given in the figure, which of the following observation are correct?
A. Total resistance of circuit is $6\Omega$.
B. Current in Ammeter is 1 A
C. Potential across AB is 4 Volts.
D. Potential across CD is 4 Volts.
E. Total resistance of the circuit is …

Q16.The electric flux is $\varphi =\alpha \sigma +\beta \lambda$
where $\lambda$ and $\sigma$ are linear and surface charge density, respectively, $\left(\frac{\alpha }{\beta }\right)$ represents

Q17.Given a thin convex lens (refractive index ${\mu }_2$ ), kept in a liquid (refractive index ${\mu }_1,{\mu }_1<{\mu }_2$ ) having radii of curvature $\left|{\mathrm{R}}_1\right|$ and $\left|{\mathrm{R}}_2\right|$. Its second surface is silver polished. Where should an object be plac …

Q18.The electric field of an electromagnetic wave in free space is
$\overrightarrow{\mathrm{E}}=57\cos \left[7.5\times 10^6\mathrm{t}-5\times 10^{-3}(3\mathrm{x}+4\mathrm{y})\right]$
$(4\hat{\mathrm{i}}-3\hat{\mathrm{j}})\mathrm{N}/\mathrm{C}$.
The associated magnetic fi …

Q19.The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is $\_\_\_\_$ km .

Q20.Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of a radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin wi …

Q21.A positive ion A and a negative ion B have charges $6.67\times 10^{-19}\mathrm{C}$ and $9.6\times 10^{-10}\mathrm{C}$, and masses $19.2\times 10^{-27}\mathrm{kg}$ and $9\times 10^{-27}\mathrm{kg}$ respectively. At an instant, the ions are separated by a certain distan …

Q22.Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A}=2\hat{i}+3n\hat{j}+2\hat{k}$ and $\overrightarrow{\mathrm{B}}=2\hat{\mathrm{i}}-2\hat{\mathrm{j}}+4\mathrm{p}\hat{\mathrm{k}}$, respectively. If both the vec …

Q23.An ideal gas initially at $0^{\circ }\mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is $\_\_\_\_$ K.

Q24.A force $\mathrm{f}={\mathrm{x}}^2\mathrm{y}\hat{\mathrm{i}}+{\mathrm{y}}^2\hat{\mathrm{j}}$ acts on a particle in a plane $\mathrm{x}+\mathrm{y}=10$. The work done by this force during a displacement from $(0,0)$ to $(4\mathrm{m},2\mathrm{m})$ is $\_\_\_\_$ Joule (round …

Q25.In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of $8\mathrm{A}/\mathrm{s}$. At an instant when R is $12\Omega$, the value of the current in the circuit will be $\_\_\_\_$ A.

Q1.The element that does not belong to the same period of the remaining elements (modern periodic table) is:

Q2.Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this?
Given: Rydberg constant …

Q3.The incorrect statements among the following is

Q4.${\mathrm{CrCl}}_3.{\mathrm{xNH}}_3$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of $0.558^{\circ }\mathrm{C}$. Assuming $100\%$ ionisation of this complex and coordination number of Cr is 6, the complex will be
(Give …

Q5.${\mathrm{FeO}}_4^{2-}\stackrel{+2.0\mathrm{V}}{\to }{\mathrm{Fe}}^{3+}\stackrel{0.8\mathrm{V}}{\to }{\mathrm{Fe}}^{2+}\stackrel{-0.5\mathrm{V}}{\to }{\mathrm{Fe}}^0$

In the above diagram, the standard electrode potentials are given in volts (over the arrow).
The value of …

Q6.Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Q7.Given below are two statements:

Statement I: Fructose does not contain an aldehydic group but still reduces Tollen's reagent
Statement II: In the presence of base, fructose undergoes rearrangement to give glucose.
In the light of the above statements, choose the correct answer f …

Q8.$2.8\times 10^{-3}\mathrm{mol}$ of ${\mathrm{CO}}_2$ is left after removing $10^{21}$ molecules from its ' x ' mg sample. The mass of ${\mathrm{CO}}_2$ taken initially is
Given: ${\mathrm{N}}_{\mathrm{A}}=6.02\times 10^{23}{\mathrm{mol}}^{-1}$

Q9.Ice at $-5^{\circ }\mathrm{C}$ is heated to become vapor with temperature of $110^{\circ }\mathrm{C}$ at atmospheric pressure. The entropy change associated with this process can be obtained from:

Q10.The d-electronic configuration of an octahedral Co(II) complex having magnetic moment of 3.95 BM is:

Q11.The complex that shows Facial - Meridional isomerism is

Q12.The major product of the following reaction is:

Q13.The correct stability order of the following species/molecules is :

p:

q:

r:

Q14.Propane molecule on chlorination under photochemical condition gives two di-chloro products, " x " and " y ". Amongst " x " and " y ", " x " is an optically active molecule. How many tri-chloro products (consider only structural isomers) will be obtained from "x" when it is furth …

Q15.What amount of bromine will be required to convert 2 g of phenol into 2, 4, 6-tribromophenol? (Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of $\mathrm{C},\mathrm{H},\mathrm{O},\mathrm{Br}$ are 12, $1,16,80$ respectively)

Q16.The correct set of ions (aqueous solution) with same colour from the following is :

Q17.Given below are two statements :

Statement I: In Lassaigne's test, the covalent organic molecules are transformed into ionic compounds.

Statement II : The sodium fusion extract of an organic compound having N and S gives prussian blue colour with ${\mathrm{FeSO}}_4$ and …

Q18.Which of the following happens when ${\mathrm{NH}}_4\mathrm{OH}$ is added gradually to the solution containing $1\mathrm{M}{\mathrm{A}}^{2+}$ and $1\mathrm{M}{\mathrm{B}}^{3+}$ ions?

Given : …

Q19.Match the LIST-I with LIST-II

Q20.Which among the following react with Hinsberg's reagent?

(A)

(B)

(C) ${\mathrm{CH}}_3-{\mathrm{NH}}_2$

(D) $\mathrm{N}{\left({\mathrm{CH}}_3\right)}_3$

(E)

Choose the correct answer from the options given below:

Q21.If 1 mM solution of ethylamine produces $\mathrm{pH}=9$, then the ionization constant $\left({\mathrm{K}}_{\mathrm{b}}\right)$ of ethylamine is $10^{-x}$. The value of $x$ is ____ (nearest integer). [The degree of ionization of ethylamine can be neglected with respect t …

Q22.During "S" estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. The percentage of Sulphur in the given compound is
____ %.
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of $\mathrm{Ba}:137,\mathrm{S}:32$, O : 16)

Q23.Consider the following sequence of reactions to produce major product (A)

Molar mass of product (A) is ____ $\mathrm{g}{\mathrm{mol}}^{-1}$.
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of $\mathrm{C}:12,\mathrm{H}:1$, …

Q24.For the thermal decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5(\mathrm{g})$ at constant volume, the following table can be formed, for the reaction mentioned below : …

Q25.The standard enthalpy and standard entropy of decomposition of ${\mathrm{N}}_2{\mathrm{O}}_4$ to ${\mathrm{NO}}_2$ are $55.0\mathrm{kJ}{\mathrm{mol}}^{-1}$ and $175.0\mathrm{J}/\mathrm{K}/\mathrm{mol}$ respectively. The standard free energy change for this reacti …

Q1.The value of …

Q2.Let $\mathrm{I}(\mathrm{x})=\int \frac{\mathrm{dx}}{(\mathrm{x}-11{)}^{\frac{11}{13}}(\mathrm{x}+15{)}^{\frac{15}{13}}}$.

If …

Q3.If the function
$f(x)=\{\begin{array}{cc}\frac{2}{x}\{\sin \left(k_1+1\right)x+\sin \left(k_2-1\right)x\}& ,x<0\\ 4& ,x=0\\ \frac{2}{x}{\log }_e\left(\frac{2+k_{1}x}{2+k_{2}x}\right)& ,x>0\end{array}$
is continuous at $\mathrm{x}=0$, then …

Q4.If the line $3x-2y+12=0$ intersects the parabola $4\mathrm{y}=3{\mathrm{x}}^2$ at the points A and B , then at the vertex of the parabola, the line segment AB subtends an angle equal to

Q5.Let a curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ pass through the points $(0,5)$ and ( ${\log }_{\mathrm{e}}2,\mathrm{k}$ ). If the curve satisfies the differential equation …

Q6.Let $\mathrm{f}(\mathrm{x})={\log }_{\mathrm{e}}\mathrm{x}$ and $\mathrm{g}(\mathrm{x})=\frac{{\mathrm{x}}^4-2{\mathrm{x}}^3+3{\mathrm{x}}^2-2\mathrm{x}+2}{2{\mathrm{x}}^2-2\mathrm{x}+1}$.

Then the domain of fog is

Q7.Let the arc AC of a circle subtend a right angle at the centre O . If the point B on the $\mathrm{arc}\mathrm{AC}$, divides the arc AC such that $\frac{\text{ length of }\mathrm{arc}\mathrm{AB}}{\text{ length of }\mathrm{arc}\mathrm{BC}}=\frac{1}{5}$, and …

Q8.If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

Q9.Let P be the foot of the perpendicular from the point $\mathrm{Q}(10,-3,-1)$ on the line $\frac{\mathrm{x}-3}{7}=\frac{\mathrm{y}-2}{-1}=\frac{\mathrm{z}+1}{-2}$. Then the area of the right angled triangle PQR , where R is the point $(3,-2,1)$, is

Q10.Let $\left|\frac{\bar{z}-\mathrm{i}}{2\bar{z}+\mathrm{i}}\right|=\frac{1}{3},z\in \mathbb{C}$, be the equation of a circle with center at C . If the area of the triangle, whose vertices are at the points $(0,0),\mathrm{C}$ and $(\alpha ,0)$ is 11 square units, then …

Q11.Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in R so the R becomes an equivalence relation, is :

Q12.The number of words, which can be formed using all the letters of the word "daughter", so that all the vowels never come together, is

Q13.Let the area of a $△\mathrm{PQR}$ with vertices $\mathrm{P}(5,4),\mathrm{Q}(-2,4)$ and $\mathrm{R}(\mathrm{a},\mathrm{b})$ be 35 square units. If its orthocenter and centroid are $\mathrm{O}\left(2,\frac{14}{5}\right)$ and $\mathrm{C}(\mathrm{c},\mathrm{d})$ respecti …

Q14.If $\frac{\pi }{2}\le x\le \frac{3\pi }{4}$, then ${\cos }^{-1}\left(\frac{12}{13}\cos x+\frac{5}{13}\sin x\right)$ is equal to

Q15.The value of $\left(\sin 70^{\circ }\right)\left(\cot 10^{\circ }\cot 70^{\circ }-1\right)$ is

Q16.Marks obtains by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is …

Q17.Let the position vectors of the vertices $\mathrm{A},\mathrm{B}$ and C of a tetrahedron ABCD be $\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}},\hat{\mathrm{i}}+3\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ and $2\hat{i}+\hat{j}-\hat{k}$ respectively. The altitude from the vert …

Q18.If $\mathrm{A},\mathrm{B}$ and $\left(\mathrm{adj}\left({\mathrm{A}}^{-1}\right)+\mathrm{adj}\left({\mathrm{B}}^{-1}\right)\right)$ are non-singular matrices of same order, then the inverse of …

Q19.If the system of equations
$(\lambda -1)x+(\lambda -4)y+\lambda z=5$
$\lambda \mathrm{x}+(\lambda -1)\mathrm{y}+(\lambda -4)\mathrm{z}=7$
$(\lambda +1)\mathrm{x}+(\lambda +2)\mathrm{y}-(\lambda +2)\mathrm{z}=9$
has infinitely many solutions, then ${\lambda }^2+\lambda$ is equal to

Q20.One die has two faces marked 1 , two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are throw …

Q21.If the area of the larger portion bounded between the curves $x^2+y^2=25$ and $y=|x-1|$ is $\frac{1}{4}(b\pi +c)$, $\mathrm{b},\mathrm{c}\in \mathbb{N}$, then $\mathrm{b}+\mathrm{c}$ is equal to

Q22.The sum of all rational terms in the expansion of ${\left(1+2^{1/3}+3^{1/2}\right)}^6$ is equal to

Q23.Let the circle C touch the line $\mathrm{x}-\mathrm{y}+1=0$, have the centre on the positive x -axis, and cut off a chord of length $\frac{4}{\sqrt{13}}$ along the line $-3x+2y=1$. Let H be the hyperbola $\frac{{\mathrm{x}}^2}{{\alpha }^2}-\frac{{\mathrm{y}}^2}{{\beta }^2}=1$, wh …

Q24.If the set of all values of a , for which the equation $5{\mathrm{x}}^3-15\mathrm{x}-\mathrm{a}=0$ has three distinct real roots, is the interval $(\alpha ,\beta )$, then $\beta -2\alpha$ is equal to

Q25.If the equation $\mathrm{a}(\mathrm{b}-\mathrm{c}){\mathrm{x}}^2+\mathrm{b}(\mathrm{c}-\mathrm{a})\mathrm{x}+\mathrm{c}(\mathrm{a}-\mathrm{b})=0$ has equal roots, where $\mathrm{a}+\mathrm{c}=15$ and $\mathrm{b}=\frac{36}{5}$, then ${\mathrm{a}}^2+{\mathrm{c}}^2$ is equal to __ …