JEE Main 2025 · 28 Jan 2025 · Shift 1

Q1.Two capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_1$ and $U_2$, respectively. Which of the given statements is true ?

Q2.In the experiment for measurement of viscosity '$\eta$' of given liquid with a ball having radius R, consider following statements.
A. Graph between terminal velocity V and R will be a parabola
B. The terminal velocities of different diameter balls are constant for a given liquid …

Q3.Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas incr …

Q4.Three infinitely long wires with linear charge density $\lambda$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface ?

Q5.A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point $E$ (at the lev …

Q6.Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge "q" is released at a distance "a" from the wire with a speed ${\mathrm{v}}_o$ along the direction of current in the wire. The particle gets attracted to the wire due to magnet …

Q7.A Carnot engine (E) is working between two temperatures 473 K and 273 K. In a new system two engines - engine ${\mathrm{E}}_1$ works between 473 K to 373 K and engine ${\mathrm{E}}_2$ works between 373 K to 273 K. If ${\eta }_{12}$, ${\eta }_1$ and ${\eta }_2$ are the efficiencies of …

Q8.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the co …

Q9.For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Q10.A bead of mass '$m$' slides without friction on the wall of a vertical circular hoop of radius 'R' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is 'R'. If …

Q11.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In a central force field, the work done is independent of the path chosen
Reason R: Every force encountered in mechanics does not have an associated potential energy. …

Q12.Choose the correct nuclear process from the below options
[p: proton, n: neutron, ${\mathrm{e}}^{-}$: electron, ${\mathrm{e}}^{+}$: positron, v: neutrino, $\bar{\nu }$: antineutrino]

Q13.Which of the following circuits has the same output as that of the given circuit?

Q14.Find the equivalent resistance between two ends of the following circuit.

Q15.A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

Q16.Due to presence of an em-wave whose electric component is given by $\mathrm{E}=100\sin (\omega \mathrm{t}-\mathrm{kx}){\mathrm{NC}}^{-1}$, a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous o …

Q17.A particle of mass ' $m$ ' and charge ' $q$ ' is fastened to one end 'A' of a massless string having equilibrium length $\ell$, whose other end is fixed at point ' $O$ '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric f …

Q18.A proton of mass '${\mathrm{m}}_{\mathrm{p}}$' has same energy as that of a photon of wavelength '$\lambda$'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is. (Here $E$ denotes the common energy of the proton …

Q19.The centre of mass of a thin rectangular plate (fig x ) with sides of length a and b , whose mass per unit area $(\sigma )$ varies as $\sigma =\frac{{\sigma }_0\mathrm{X}}{\mathrm{ab}}$ (where ${\sigma }_0$ is a constant), would be $\_\_\_\_$

Q20.A thin prism ${\mathrm{P}}_1$ with angle $4^{\circ }$ made of glass having refractive index 1.54, is combined with another thin prism ${\mathrm{P}}_2$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism ${\mathrm{P}}_2$ in degrees …

Q21.A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum frac …

Q22.The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is $n$ times higher than the …

Q23.In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[{\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}}\right]$. If $b=3$, the value of $c$ is $\_\_\_\_$

Q24.Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of intertia $I_1$ and $I_2$, respectively. For $R_2=2R_1$, the ratio of $I_1$ and $I_2$ would be $1/\mathrm{x}$, where $\mathrm{x}=$ $\_\_\_\_$

Q25.A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with $10^{\text{th}}$ bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same …

Q1.The incorrect decreasing order of atomic radii is :

Q2.Given below are two statements :

Statement I: In the oxalic acid vs ${\mathrm{KMnO}}_4$ (in the presence of dil ${\mathrm{H}}_2{\mathrm{SO}}_4$) titration the solution needs to be heated initially to $60^{\circ }\mathrm{C}$, but no heating is required in Ferrous ammonium sulpha …

Q3.Given below are two statements :

Statement I :
(see structure A)
will undergo alkaline hydrolysis at a faster rate than
(see structure B)

Statement II :
(see structure C)
intramolecular substitution takes place first by involving lone pair of electrons on nitrogen.
In the light …

Q4.A weak acid HA has degree of dissociation x. Which option gives the correct expression of $\mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}$ ) ?

Q5.Consider 'n' is the number of lone pair of electrons present in the equatorial position of the most stable structure of ${\mathrm{ClF}}_3$. The ions from the following with 'n' number of unpaired electrons are :
A. ${\mathrm{V}}^{3+}$
B. ${\mathrm{Ti}}^{3+}$
C. ${\mathrm{Cu}}^{2+}$
D. …

Q6.For a given reaction $\mathrm{R}\to \mathrm{P}$, ${\mathrm{t}}_{1/2}$ is related to $[\mathrm{A}{]}_0$ as given in table :

Given : $\log 2$ = 0.3 …

Q7.A molecule ("P") on treatment with acid undergoes rearrangement and gives ("Q") ("Q") on ozonolysis followed by reflux under alkaline condition gives (" R "). The structure of (" R ") is given below :
(see structure)

The structure of (" $\mathbf{P}$ ") is

Q8.Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K . If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following :

Q9.The molecules having square pyramidal geometry are

Q10.The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet colour in non-luminous flame under hot condition in borax bead test is

Q11.Both acetaldehyde and acetone (individually) undergo which of the following reactions?
A. Iodoform Reaction
B. Cannizaro Reaction
C. Aldol condensation
D. Tollen's Test
E. Clemmensen Reduction

Choose the correct answer from the options given below:

Q12.In a multielectron atom, which of the following orbitals described by three quantum numbers with have same energy in absence of electric and magnetic fields?
A. $\mathrm{n}=1,1=0,{\mathrm{m}}_1=0$
B. $\mathrm{n}=2,1=0,{\mathrm{m}}_1=0$
C. $\mathrm{n}=2,1=1,{\mathrm{m}}_1=1$ …

Q13.The products A and B in the following reactions, respectively are
$\mathrm{A}\stackrel{\mathrm{Ag}-{\mathrm{NO}}_2}{⟶}{\mathrm{CH}}_3-{\mathrm{CH}}_2-{\mathrm{CH}}_2-\mathrm{Br}\stackrel{\mathrm{AgCN}}{\to }\mathrm{B}$

Q14.What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute (molar mass $256\mathrm{g}{\mathrm{mol}}^{-1}$) and the decrease in freezing point is 0.40 K ?

Q15.Consider the following elements $\mathrm{In},\mathrm{Tl},\mathrm{Al},\mathrm{Pb},\mathrm{Sn}$ and Ge.

The most stable oxidation states of elements with highest and lowest first ionisation enthalpies, respectively, are

Q16.The correct order of stability of following carbocations is :

Q17.The compounds that produce ${\mathrm{CO}}_2$ with aqueous ${\mathrm{NaHCO}}_3$ solution are :
A.
B.
C.
D.
E.

Choose the correct answer from the options given below :

Q18.Which of the following oxidation reactions are carried out by both ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ and ${\mathrm{KMnO}}_4$ in acidic medium?
A. ${\mathrm{I}}^{-}\to {\mathrm{I}}_2$
B. ${\mathrm{S}}^{2-}\to \mathrm{S}$
C. …

Q19.Given below are two statements :

Statement I: D-glucose pentaacetate reacts with 2, 4-dinitrophenylhydrazine.
Statement II : Starch, on heating with concentrated sulfuric acid at $100^{\circ }\mathrm{C}$ and $2-3$ atmosphere pressure produces glucose.
In the light of the abo …

Q20.Given below is the plot of the molar conductivity vs $\sqrt{\text{concentration}}$ for KCl in aqueous solution.

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is $100\Omega$, then the resistance of the same cell with the dilute sol …

Q21.Quantitative analysis of an organic compound (X) shows following % composition.

C : 14.5%
Cl : 64.46%
H : 1.8%
(Empirical formula mass of the compound $(\mathrm{X})$ is
_____ $\times 10^{-1}$
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of …

Q22.The molarity of a $70\%$ (mass/mass) aqueous solution of a monobasic acid ( X ) is _____ M(Nearest integer)
[Given : Density of aqueous solution of ( X ) is $1.25\mathrm{g}{\mathrm{mL}}^{-1}$

Molar mass of the acid is $70\mathrm{g}{\mathrm{mol}}^{-1}$ ]

Q23.Consider the following sequence of reactions:

Chlorobenzene

11.25 mg of chlorobenzene will produce ______ × 10⁻¹ mg of product B.
(Consider the reactions result in complete conversion.)
[Given molar mass of C, H, O, N and Cl as 12, 1, 16, 14 and 35.5 g mol⁻¹ respectively]

Q24.The formation enthalpies, ΔH°_f for H₍g₎ and O₍g₎ are 220.0 and 250.0 kJ mol⁻¹, respectively, at 298.15 K, and ΔH°_f for H₂O₍g₎ is -242.0 kJ mol⁻¹ at the same temperature. The average bond enthalpy of the O-H bond in water at 298.15 K is ______ kJ mol⁻¹ (nearest integer).

Q1.The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0,1, $2,3,4,5,6,7$, such that the sum of their first and last digits should not be more than 8 , is

Q2.Let ABCD be a trapezium whose vertices lie on the parabola ${\mathrm{y}}^2=4\mathrm{x}$. Let the sides AD and BC of the trapezium be parallel to y -axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point $(1,0)$, then the area of ABCD is :

Q3.Two number ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1}+i^{k_2},(i=\sqrt{-1})$ is non-zero, equals

Q4.If $f(x)=\frac{2^x}{2^x+\sqrt{2}},x\in R$, then ${\sum }_{k=1}^{81}f\left(\frac{k}{82}\right)$ is equal to :

Q5.Let $f:R\to R$ be a function defined by
$f(x)=(2+3a)x^2+\left(\frac{a+2}{a-1}\right)x+b,a\ne 1$. If
$f(x+y)=f(x)+f(y)+1-\frac{2}{7}xy$, then the value of $28{\sum }_{i=1}^5|f(i)|$ is:

Q6.Let $\mathrm{A}(\mathrm{x},\mathrm{y},\mathrm{z})$ be a point in xy -plane, which is equidistant from three points $(0,3,2),(2,0,3)$ and $(0,0,1)$.

Let $\mathrm{B}=(1,4,-1)$ and $\mathrm{C}=(2,0,-2)$. Then among the statements
(S1) : $△\mathrm{ABC}$ is an isosceles ri …

Q7.The relation $\mathrm{R}=\{(\mathrm{x},\mathrm{y}):\mathrm{x},\mathrm{y}\in \mathrm{z}$ and $\mathrm{x}+\mathrm{y}$ is even $\}$ is :

Q8.Let the equation of the circle, which touches x -axis at the point ( $\mathrm{a},0$ ), $\mathrm{a}>0$ and cuts off an intercept of length $b$ on $y$-axis be $x^2+y^2-\alpha x+\beta y+\gamma =0$. If the circle lies below x -axis, then the ordered pair …

Q9.Let $<{\mathrm{a}}_{\mathrm{n}}>$ be a sequence such that ${\mathrm{a}}_0=0,{\mathrm{a}}_1=\frac{1}{2}$ and $2{\mathrm{a}}_{\mathrm{n}+2}=5{\mathrm{a}}_{\mathrm{n}+1}-3{\mathrm{a}}_{\mathrm{n}},\mathrm{n}=0,1,2,3,\dots$. Then ${\sum }_{\mathrm{k}=1}^{100}{\mathrm{a}}_{\mathrm{k}}$ is …

Q10.$\cos \left({\sin }^{-1}\frac{3}{5}+{\sin }^{-1}\frac{5}{13}+{\sin }^{-1}\frac{33}{65}\right)$ is equal to :

Q11.Let ${\mathrm{T}}_{\mathrm{r}}$ be the ${\mathrm{r}}^{\text{th }}$ term of an A.P. If for some m , ${\mathrm{T}}_{\mathrm{m}}=\frac{1}{25},{\mathrm{T}}_{25}=\frac{1}{20}$ and $20{\sum }_{\mathrm{r}=1}^{25}{\mathrm{T}}_{\mathrm{r}}=13$, then …

Q12.If the image of the point $(4,4,3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha ,\beta ,\gamma )$, then $\alpha +\beta +\gamma$ is equal to

Q13.Let M denote the set of all real matrices of order $3\times 3$ and let $S=\{-3,-2,-1,1,2\}$. Let
$S_1=\left\{A=\left[a_{ij}\right]\in M:A=A^T\text{ and }{a}_{ij}\in S,\forall i,j\right\}$ …

Q14.If $\alpha =1+{\sum }_{r=1}^6(-3{)}^{r-1}{}^{12}{C}_{2r-1}$, then the distance of the point $(12,\sqrt{3})$ from the line $\alpha x-\sqrt{3}y+1=0$ is

Q15.Let $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{d}=\vec{a}\times \vec{b}$. If $\overrightarrow{\mathrm{c}}$ is a vector such that …

Q16.Let
$\mathrm{f}(\mathrm{x})=\{\begin{array}{cc}3\mathrm{x},& x<0\\ \min \{1+\mathrm{x}+[\mathrm{x}],\mathrm{x}+2[\mathrm{x}]\},& 0\le \mathrm{x}\le 2\\ 5,& x>2\end{array}$
where [.] denotes greatest integer function. If $\alpha$ and $\beta$ are the number o …

Q17.Let ${\mathrm{E}}_1:\frac{{\mathrm{x}}^2}{9}+\frac{{\mathrm{y}}^2}{4}=1$ be an ellipse. Ellipses ${\mathrm{E}}_{\mathrm{i}}$'s are constructed such that their centres and eccentricities are same as that of ${\mathrm{E}}_1$, and the length of minor axis of ${\mathrm{E}}_{\mathrm{i}}$ …

Q18.If ∫_{-π/2}^{π/2} (96 x² cos²x)/(1+eˣ) dx = απ³ + βπ with α, β ∈ Z, then (α+β)² equals:

Q19.The sum of the squares of all the roots of the equation x² + |2x − 3| − 4 = 0 is:

Q20.Let for some function y = f(x), ∫₀ˣ t·f(t) dt = x²·f(x), x > 0 and f(2) = 3. Then f(6) is equal to:

Q21.Let ${}^n{C}_{r-1}=28$, ${}^n{C}_r=56$ and ${}^n{C}_{r+1}=70$. Let $A(4\cos t,4\sin t)$, $B(2\sin t,-2\cos t)$ and $C(3r-n,r^2-n-1)$ be the vertices of a triangle ABC, where $t$ is a parameter. If $(3x-1{)}^2+(3y{)}^2=\lambda$ is the locus of the centroid of t …

Q22.Let O be the origin, the point A be $z_1$, and the point B be $z_2$ such that $|z_2|=\sqrt{3}|z_1|$ and $\arg (z_2)=\arg (z_1)+\frac{\pi }{6}$. Then the triangle ABO is:

Q23.Three defective oranges are accidentally mixed with seven good ones and it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denotes the number of defective oranges, then the variance of x is:

Q24.The area (in sq. units) of the region {(x, y) : 0 ≤ y ≤ 2|x| + 1, 0 ≤ y ≤ x² + 1, |x| ≤ 3} is: