JEE Main 2025 · 04 Apr 2025 · Shift 2

Q1.A radioactive material $P$ first decays into $Q$ and then Q decays to non-radioactive material R . Which of the following figure represents time dependent mass of $\mathrm{P},\mathrm{Q}$ and R ?

Q2.There are 'n' number of identical electric bulbs, each is designed to draw a power p independently from the mains supply. They are now joined in series across the main supply. The total power drawn by the combination is :

Q3.Consider a rectangular sheet of solid material of length $\ell =9\mathrm{cm}$ and width $\mathrm{d}=4\mathrm{cm}$. The coefficient of linear expansion is $\alpha =3.1\times 10^{-5}{\mathrm{K}}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet …

Q4.Given below are two statements :
Statement (I) : The dimensions of Planck's constant and angular momentum are same.
Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.

In …

Q5.A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^5\mathrm{N}$ at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $\theta$ of the rod axis from its original po …

Q6.From the combination of resistors with resistance values ${\mathrm{R}}_1={\mathrm{R}}_2={\mathrm{R}}_3=5\Omega$ and ${\mathrm{R}}_4=10\Omega$, which of the following combination is the best circuit to get an equivalent resistance of $6\Omega$ ?

Q7.A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to $\mathrm{arc}\mathrm{AB}$ to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to …

Q8.There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K . If the vessels are connected to each other by a thin tube allowing …

Q9.An object is kept at rest at a distance of 3 R above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational consta …

Q10.Three parallel plate capacitors ${\mathrm{C}}_1,{\mathrm{C}}_2$ and ${\mathrm{C}}_3$ each of capacitance $5\mu \mathrm{F}$ are connected as shown in figure. The effective capacitance between points A and B , when the space between the parallel plates of …

Q11.The displacement x versus time graph is shown below.
(A) The average velocity during 0 to 3 s is $10\mathrm{m}/\mathrm{s}$
(B) The average velocity during 3 to 5 s is $0\mathrm{m}/\mathrm{s}$
(C) The instantaneous velocity at $\mathrm{t}=2\mathrm{s}$ is …

Q12.A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8\mathrm{m}/\mathrm{s}$. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

Q1.The correct order of basicity for the following molecules is :

Q2.The incorrect relationship in the following pairs in relation to ionisation enthalpies is :

Q3.Which among the following compounds give yellow solid when reacted with $\mathrm{NaOI}/\mathrm{NaOH}$ ?
(A)
(B) ${\mathrm{CH}}_3-{\mathrm{CH}}_2-{\mathrm{CH}}_2-\mathrm{OH}$
(C)
(D)
(E)

Choose the correct answer from the options given below :

Q4.A dipeptide, "x" on complete hydrolysis gives "y" and "z". "y" on treatment with aq. ${\mathrm{HNO}}_2$ produces lactic acid. On the other hand "z" on heating gives the following cyclic molecule.

Based on the information given, the dipeptide X is:

Q5.In which pairs, the first ion is more stable than the second?
(A)
&
(B)
&
(C)
&
(D)
&

Q6.Given below are two statements :

Statement (I) : Alcohols are formed when alkyl chlorides are treated with aqueous potassium hydroxide by elimination reaction.

Statement (II): In alcoholic potassium hydroxide, alkyl chlorides form alkenes by abstracting the hydrogen from the …

Q7.Given below are two statements :

Statement (I) : Molal depression constant ${\mathrm{K}}_{\mathrm{f}}$ is given by $\frac{{\mathrm{M}}_1{\mathrm{RT}}_{\mathrm{f}}}{\Delta {\mathrm{S}}_{\text{fus }}}$, where symbols have their usual meaning.
Statement (II) : ${\mathrm{K}}_{\mathrm{f}}$ …

Q8.The IUPAC name of the following compound is -

Q9.A toxic compound "A" when reacted with NaCN in aqueous acidic medium yields an edible cooking component and food preservative 'B'. "B" is converted to "C" by diborane and can be used as an additive to petrol to reduce emission. "C" upon reaction with oleum at …

Q10.The correct order of ${\left[{\mathrm{FeF}}_6\right]}^{3-},{\left[{\mathrm{CoF}}_6\right]}^{3-},\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right]$ and ${\left[\mathrm{Ni}(\mathrm{CN}{)}_4\right]}^{2-}$ complex species based on the number of unpaired electrons present is :

Q11.Consider the given data :
(a)

(b) …

Q12.Consider the ground state of chromium atom $(Z=24)$. How many electrons are with Azimuthal quantum number $l=1$ and $l=2$ respectively?

Q13.Given below are two statements:

Statement (I): The first ionisation enthalpy of group 14 elements is higher than the corresponding elements of group 13.
Statement (II): Melting points and boiling points of group 13 elements are in general much higher than those the corresponding …

Q14.Consider the following plots of log of rate constant k ($\log k$) vs $\frac{1}{T}$ for three different reactions. The correct order of activation energies of these reactions is

Q15.'X' is the number of electrons in ${\mathrm{t}}_{2g}$ orbitals of the most stable complex ion among $[\mathrm{Fe}({\mathrm{NH}}_3{)}_6{]}^{3+}$, $[\mathrm{Fe}({\mathrm{Cl}}_6){]}^{3-}$, $[\mathrm{Fe}({\mathrm{C}}_2{\mathrm{O}}_4{)}_3{]}^{3-}$ and $[\mathrm{Fe}({\mathrm{H}}_2\mathrm{O}{)}_6{]}^{3+}$. The n …

Q16.The elements of Group 13 with highest and lowest first ionisation enthalpies are respectively:

Q17.Consider the following molecule (X). The major product formed when X reacts with HBr (Markovnikov addition) is:

Q18.Given below are two statements:

Statement (I): for $\mathrm{ClF}{}_3$, all three possible structures may be drawn as follows.

Statement (II): Structure III is most stable, as the orbitals having the lone pairs are axial, where the $\ell p-bp$ repulsion is minimum.

In the light of the …

Q19.Half life of zero order reaction $\mathrm{A}\to$ product is 1 hour, when initial concentration of reaction is $2.0{\mathrm{mol}\mathrm{L}}^{-1}$. The time required to decrease concentration of A from 0.50 to $0.25{\mathrm{mol}\mathrm{L}}^{-1}$ is:

Q20.Sea water, which can be considered as a 6 molar (6 M) solution of NaCl, has a density of $2{\mathrm{g}\mathrm{mL}}^{-1}$. The concentration of dissolved oxygen (${\mathrm{O}}_2$) in sea water is 5.8 ppm. Then the concentration of dissolved oxygen (${\mathrm{O}}_2$) in sea water, is …

Q21.The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is ______ kg.
(Nearest integer)
Given: Molar mass (in ${\mathrm{g}\mathrm{mol}}^{-1}$) of Ca-40, O-16, C-12

Q22.A metal complex with a formula ${\mathrm{MCl}}_4\cdot 3{\mathrm{NH}}_3$ is involved in ${\mathrm{sp}}^3{\mathrm{d}}^2$ hybridisation. It upon reaction with excess of ${\mathrm{AgNO}}_3$ solution gives 'x' moles of AgCl. Consider 'x' is equal to the number of lone pairs of electron present …

Q23.The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185{\mathrm{S}\mathrm{cm}}^2{\mathrm{mol}}^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and $70{\mathrm{S}\mathrm{cm}}^2{\mathrm{mol}}^{-1}$, respectively. If molar conductance of 0. …

Q24.$x$ mg of $\mathrm{Mg}(\mathrm{OH}{)}_2$ (molar mass $=58$) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ______ mg. (Nearest integer)
(Given: $\mathrm{Mg}(\mathrm{OH}{)}_2$ is assumed to dissociate completely in …

Q1.Let $\mathrm{a}>0$. If the function $\mathrm{f}(\mathrm{x})=6{\mathrm{x}}^3-45\mathrm{a}{\mathrm{x}}^2+108{\mathrm{a}}^2\mathrm{x}+1$ attains its local maximum and minimum values at the points ${\mathrm{x}}_1$ and ${\mathrm{x}}_2$ respectively such that …

Q2.Let f be a differentiable function on $\mathbf{R}$ such that $\mathrm{f}(2)=1$, $f^{\prime }(2)=4$. Let ${\lim }_{x\to 0}(f(2+x){)}^{3/x}=e^{\alpha }$. Then the number of times the curve $y=4x^3-4x^2-4(\alpha -7)x-\alpha$ meets x-axis is :-

Q3.The sum of the infinite series ${\cot }^{-1}\left(\frac{7}{4}\right)+{\cot }^{-1}\left(\frac{19}{4}\right)+{\cot }^{-1}\left(\frac{39}{4}\right)+{\cot }^{-1}\left(\frac{67}{4}\right)+\dots$ is :-

Q4.Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$ and R be a relation on A defined by xRy if and only if $2\mathrm{x}-\mathrm{y}\in \{0,1\}$. Let $\ell$ be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and sym …

Q5.Let the product of ${\omega }_1=(8+\mathrm{i})\sin \theta +(7+4\mathrm{i})\cos \theta$ and ${\omega }_2=(1+8\mathrm{i})\sin \theta +(4+7\mathrm{i})\cos \theta$ be $\alpha +\mathrm{i}\beta$, $\mathrm{i}=\sqrt{-1}$. Let p and q be the maximum and the minimum values of …

Q6.Let the values of p, for which the shortest distance between the lines $\frac{\mathrm{x}+1}{3}=\frac{\mathrm{y}}{4}=\frac{\mathrm{z}}{5}$ and $\vec{r}=(p\hat{i}+2\hat{j}+\hat{k})+\lambda (2\hat{i}+3\hat{j}+4\hat{k})$ is $\frac{1}{\sqrt{6}}$, be $a,b$, …

Q7.The axis of a parabola is the line $\mathrm{y}=\mathrm{x}$ and its vertex and focus are in the first quadrant at distances $\sqrt{2}$ and $2\sqrt{2}$ units from the origin, respectively. If the point $(1,\mathrm{k})$ lies on the parabola, then a possible value of k is : …

Q8.Let the domains of the functions
$\mathrm{f}(\mathrm{x})={\log }_4{\log }_3{\log }_7\left(8-{\log }_2\left({\mathrm{x}}^2+4\mathrm{x}+5\right)\right)$ and
$\mathrm{g}(\mathrm{x})={\sin }^{-1}\left(\frac{7\mathrm{x}+10}{\mathrm{x}-2}\right)$ be $(\alpha ,\beta )$ and …

Q9.A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $\mathrm{P}:{\mathrm{y}}^2=\mathrm{x}-2$ at the point B in the first quadrant. The area, of the region bounded by the line AB, parabola P and the x-axis, is :-

Q10.Let the sum of the focal distances of the point $\mathrm{P}(4,3)$ on the hyperbola $\mathrm{H}:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ be $8\sqrt{\frac{5}{3}}$. If for H, the length of the latus rectum is $\ell$ and the product of …

Q11.Let the matrix $A=\left[\begin{array}{lll}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right]$ satisfy $A^n=A^{n-2}+A^2-I$ for $\mathrm{n}\ge 3$. Then the sum of all the elements of ${\mathrm{A}}^{50}$ is :-

Q12.If the sum of the first 20 terms of the series

is $\frac{\mathrm{m}}{\mathrm{n}}$, where m and n are coprime, then $\mathrm{m}+\mathrm{n}$ is equal to …

Q13.If

where …

Q14.Let for two distinct values of $p$ the lines $y=x+p$ touch the ellipse $\mathrm{E}:\frac{{\mathrm{x}}^2}{4^2}+\frac{{\mathrm{y}}^2}{3^2}=1$ at the points A and B. Let the line $\mathrm{y}=\mathrm{x}$ intersect E at the points C and $D$. Then the area of the quadrilateral …

Q15.Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectiv …

Q16.If a curve $y=y(x)$ passes through the point $\left(1,\frac{\pi }{2}\right)$ and satisfies the differential equation $\left(7x^4\cot y-e^x\mathrm{cosec}y\right)\frac{dx}{dy}=x^5,x\ge 1$, then at $x=2$, the value of cosy is:

Q17.The centre of a circle C is at the centre of the ellipse $\mathrm{E}:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1,\mathrm{a}>\mathrm{b}$. Let C pass through the foci $F_1$ and $F_2$ of $E$ such that the circle $C$ and the ellipse E intersec …

Q18.Let $f(x)+2f\left(\frac{1}{x}\right)=x^2+5$ and $2g(x)-3g\left(\frac{1}{2}\right)=x,x>0$. If $\alpha ={\int }_1^{2}f(x)dx$, and $\beta ={\int }_1^2\mathrm{g}(\mathrm{x})\mathrm{dx}$, then the value of $9\alpha +\beta$ is:

Q19.Let A be the point of intersection of the lines
${\mathrm{L}}_1:\frac{\mathrm{x}-7}{1}=\frac{\mathrm{y}-5}{0}=\frac{\mathrm{z}-3}{-1}$ and
${\mathrm{L}}_2:\frac{\mathrm{x}-1}{3}=\frac{\mathrm{y}+3}{4}=\frac{\mathrm{z}+7}{5}$. Let B and C be the point on the lines …

Q20.Let the mean and the standard deviation of the observation $2,3,3,4,5,7,\mathrm{a},\mathrm{b}$ be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is:

Q21.If $\alpha$ is a root of the equation $x^2+x+1=0$ and ${\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\left({\alpha }^{\mathrm{k}}+\frac{1}{{\alpha }^{\mathrm{k}}}\right)}^2=20$, then n is equal to

Q22.If …

Q23.A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\frac{11}{50}$, the n is equal to

Q24.Let m and $\mathrm{n},(\mathrm{m}<\mathrm{n})$ be two 2-digit numbers. Then the total numbers of pairs $(m,n)$, such that $\gcd (m,n)=6$, is

Q25.Let the three sides of a triangle ABC be given by the vectors $2\hat{i}-\hat{j}+\hat{k}$, $\hat{i}-3\hat{j}-5\hat{k}$ and $3\hat{i}-4\hat{j}-4\hat{k}$. Let G be the centroid of the triangle ABC. Then …