JEE Main 2024 Question Paper with Solutions

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

A cricket player catches a ball of mass $120 \mathrm{~g}$ moving with $25 \mathrm{~m} / \mathrm{s}$ speed. If the catching process is completed in $0.1 \mathrm{~s}$ then the magnitude of force exerted by the ball on the hand of player will be (in SI unit) :

A diatomic gas $(\gamma=1.4)$ does $200 \mathrm{~J}$ of work when it is expanded isobarically. The heat given to the gas in the process is :

A disc of radius $\mathrm{R}$ and mass $\mathrm{M}$ is rolling horizontally without slipping with speed $v$ . It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

Match List - I with List - II . table { width: 100%; border-collapse: collapse; } table, th, td { border: 1px solid black; } th, td { padding: 10px; text-align: center; } th { background-color: blue; color: white; } List I (Number) List II (Significant figure) (A) 1001 (I) 3 (B) 010.1 (II) 4 (C) 100.100 (III) 5 (D) 0.0010010 (IV) 6 Choose the correct answer from the options given below :

In the given reactions identify $A$ and $B$

The set of meta directing functional groups from the following sets is :

Given below are two statements : Statement (I) : Both metals and non-metals exist in p and d-block elements. Statement (II) : Non-metals have higher ionisation enthalpy and higher electronegativity than the metals. In the light of the above statements, choose the most appropriate answer from the options given below :

Lassaigne's test is used for detection of :

Acid D formed in above reaction is :

The number of solutions of the equation $4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]$ is :

Let $m$ and $n$ be the coefficients of seventh and thirteenth terms respectively in the expansion of $\left(\frac{1}{3} x^{\frac{1}{3}}+\frac{1}{2 x^{\frac{2}{3}}}\right)^{18}$ . Then $\left(\frac{\mathrm{n}}{\mathrm{m}}\right)^{\frac{1}{3}}$ is :

Consider the relations $R_1$ and $R_2$ defined as $a R_1 b \Leftrightarrow a^2+b^2=1$ for all $a, b \in \mathbf{R}$ and $(a, b) R_2(c, d) \Leftrightarrow$ $a+d=b+c$ for all $(a, b),(c, d) \in \mathbf{N} \times \mathbf{N}$ . Then :

Consider 10 observations $x_1, x_2, \ldots, x_{10}$ such that $\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum\limits_{i=1}^{10}\left(x_i-\beta\right)^2=40$ , where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. Then $\frac{\beta}{\alpha}$ is equal to :

If $z$ is a complex number such that $|z| \leqslant 1$ , then the minimum value of $\left|z+\frac{1}{2}(3+4 i)\right|$ is :

Monochromatic light of frequency $6 \times 10^{14} \mathrm{~Hz}$ is produced by a laser. The power emitted is $2 \times 10^{-3} \mathrm{~W}$ . How many photons per second on an average, are emitted by the source ? (Given $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}$ )

A galvanometer $(G)$ of $2 \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is :

If frequency of electromagnetic wave is $60 \mathrm{~MHz}$ and it travels in air along $z$ direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in $\mathrm{m}$ ) is :

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at $25^{\circ} \mathrm{C}$ and resistance of the semiconductor arm is $3 \mathrm{~m} \Omega$ . Arm $\mathrm{BC}$ is cooled at a constant rate of $2^{\circ} \mathrm{C} / \mathrm{s}$ . If the galvanometer $\mathrm{G}$ shows no deflection after $10 \mathrm{~s}$ , then $\alpha$ is :

In an ammeter, $5 \%$ of the main current passes through the galvanometer. If resistance of the galvanometer is $\mathrm{G}$ , the resistance of ammeter will be :

Let $\mathrm{P}$ and $\mathrm{Q}$ be the points on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ which are at a distance of 6 units from the point $\mathrm{R}(1,2,3)$ . If the centroid of the triangle PQR is $(\alpha, \beta, \gamma)$ , then $\alpha^2+\beta^2+\gamma^2$ is :

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$ , while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$ . Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

If the mirror image of the point $P(3,4,9)$ in the line $\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}$ is $(\alpha, \beta, \gamma)$ , then 14 $(\alpha+\beta+\gamma)$ is :

Let $f(x)=\left|2 x^2+5\right| x|-3|, x \in \mathbf{R}$ . If $\mathrm{m}$ and $\mathrm{n}$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $\mathrm{m}+\mathrm{n}$ is equal to :

If $\int\limits_0^{\frac{\pi}{3}} \cos ^4 x \mathrm{~d} x=\mathrm{a} \pi+\mathrm{b} \sqrt{3}$ , where $\mathrm{a}$ and $\mathrm{b}$ are rational numbers, then $9 \mathrm{a}+8 \mathrm{b}$ is equal to :

$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ and $\left[\mathrm{CoF}_6\right]^{3-}$ are respectively known as :

The strongest reducing agent among the following is :

Match List - I with List - II . table { border-collapse: collapse; width: 100%; } th, td { border: 1px solid black; padding: 8px; text-align: left; } th { background-color: #0000FF; color: white; } List I (Reactants) List II (Product) (A) Phenol, Zn/Δ (I) Salicylaldehyde (B) Phenol, CHCl 3 , NaOH, HCl (II) Salicylic acid (C) Phenol, CO 2 , NaOH, HCl (III) Benzene (D) Phenol, Conc. HNO 3 (IV) Picric acid Choose the correct answer from the options given below :

Match List - I with List - II. table { border-collapse: collapse; width: 100%; } th, td { border: 1px solid black; padding: 8px; text-align: left; } th { background-color: blue; color: white; } List I (Compound) List II (Use) (A) Carbon tetrachloride (I) Paint remover (B) Methylene chloride (II) Refrigerators and air conditioners (C) DDT (III) Fire extinguisher (D) Freons (IV) Non Biodegradable insecticide Choose the correct answer from the options given below :

Given below are two statements : Statement (I) : Dimethyl glyoxime forms a six-membered covalent chelate when treated with $\mathrm{NiCl}_2$ solution in presence of $\mathrm{NH}_4 \mathrm{OH}$ . Statement (II) : Prussian blue precipitate contains iron both in $(+2)$ and $(+3)$ oxidation states. In the light of the above statements, choose the most appropriate answer from the options given below :

Find the speed of sound in oxygen gas at STP.

Force on a particle moving in straight line is given by F = 6t² î - 3t ĵ and velocity is v = 3t² î + 6t ĵ. Find power at t = 2.

For the block shown, F1 is the minimum force required to move block upwards and F2 is the minimum force required to prevent it from slipping, find F1 - F2. (μ = 0.1)

If E = (A - x²)/Bt where E is energy, x is displacement and t is time. Find dimensions of AB.

Two solid spheres each of mass 2 kg and radius 75 cm are arranged as shown. Find MOI of the system about the given axis.