JEE Main 2024 · 09 Apr 2024 · Shift 2

Q1.A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2:1$. After disintegration they will move :-

Q2.The following figure represents two biconvex lenses ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ having focal length 10 cm and 15 cm respectively. The distance between ${\mathrm{L}}_1$ & ${\mathrm{L}}_2$ is :

Q3.The temperature of a gas is $-78^{\circ }\mathrm{C}$ and the average translational kinetic energy of its molecules is K . The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is :

Q4.A hydrogen atom in ground state is given an energy of 10.2 eV . How many spectral lines will be emitted due to transition of electrons?

Q5.The magnetic field in a plane electromagnetic wave is ${\mathrm{B}}_{\mathrm{y}}=\left(3.5\times 10^{-7}\right)\sin \left(1.5\times 10^3\mathrm{x}+0.5\times 10^{11}\mathrm{t}\right)\mathrm{T}$. The corresponding electric field will be

Q6.A square loop of side 15 cm being moved towards right at a constant speed of $2\mathrm{cm}/\mathrm{s}$ as shown in figure. The front edge enters the 50 cm wide magnetic field at $t=0$. The value of induced emf in the loop at $\mathrm{t}=10\mathrm{s}$ will be :

Q7.Two cars are travelling towards each other at speed of $20\mathrm{m}{\mathrm{s}}^{-1}$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of $2\mathrm{m}{\mathrm{s}}^{-2}$. The distance between them when they come to rest is …

Q8.The $I-V$ characteristics of an electronic device shown in the figure. The device is :

Q9.The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is :

Q10.The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $\mathrm{h}/\sqrt{2mE}$. The dimensional formula for Planck's constant is :

Q11.A satellite of $10^3\mathrm{kg}$ mass is revolving in circular orbit of radius 2 R . If $\frac{10^4\mathrm{R}}{6}J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius :
(use …

Q12.The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be

Q13.Five charges $+q,+5q,-2q,+3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface S is :

Q14.A proton and a deutron ( $\mathrm{q}=+\mathrm{e},m=2.0\mathrm{u}$ ) having same kinetic energies enter a region of uniform magnetic field $\overrightarrow{\mathrm{B}}$, moving perpendicular to $\overrightarrow{\mathrm{B}}$. The ratio of the radius $r_d$ of deutron pat …

Q15.UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV . The maximum kinetic energy of ejected photoelectrons will be :

Q16.The energy released in the fusion of 2 kg of hydrogen deep in the sun is ${\mathrm{E}}_{\mathrm{H}}$ and the energy released in the fission of 2 kg of ${}^{235}\mathrm{U}$ is ${\mathrm{E}}_{\mathrm{U}}$. The ratio $\frac{{\mathrm{E}}_{\mathrm{H}}}{{\mathrm{E}}_{\mathrm{U}}}$ is …

Q17.A real gas within a closed chamber at $27^{\circ }\mathrm{C}$ undergoes the cyclic process as shown in figure. The gas obeys $P{V}^3=\mathrm{RT}$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R=8\mathrm{J}/\mathrm{molK}$ ):

Q18.A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' F ' is applied at the mid point of the rope so that the rope makes an angle of $45^{\circ }$ with respect to the vertical axis as shown in figure. The magnitude of F is :

Q19.A spherical ball of radius $1\times 10^{-4}\mathrm{m}$ and density $10^5\mathrm{kg}/{\mathrm{m}}^3$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value …

Q20.In the truth table of the above circuit the value of X and Y are :

Q21.A straight magnetic strip has a magnetic moment of $44{\mathrm{Am}}^2$. If the strip is bent in a semicircular shape, its magnetic moment will be ____ ${\mathrm{Am}}^2$.
(Given $\pi =\frac{22}{7}$ )

Q22.A particle of mass 0.50 kg executes simple harmonic motion under force $\mathrm{F}=-50\left({\mathrm{Nm}}^{-1}\right)\mathrm{x}$. The time period of oscillation is $\frac{x}{35}s$. The value of $x$ is ................
(Given $\pi =\frac{22}{7}$ )

Q23.A capacitor of reactance $4\sqrt{3}\Omega$ and a resistor of resistance $4\Omega$ are connected in series with an ac source of peak value $8\sqrt{2}\mathrm{V}$. The power dissipation in the circuit is ____ W.

Q24.An electric field $\overrightarrow{\mathrm{E}}=(2x\hat{\mathrm{i}}){\mathrm{NC}}^{-1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is ................ ${\mathrm{Nm}}^2/\mathrm{C}$.

Q25.A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, if takes t s . When it rolls down the plane then it takes ${\left(\frac{\alpha }{2}\right)}^{1/2}\mathrm{ts}$, where $\alpha$ is ____

Q26.To determine the resistance ( R ) of a wire, a circuit is designed below, The V-I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of R is ______ $\Omega$.

Q27.The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is

Q28.Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen When one of the slits is covered with a very thin glass plate (refractive index $=1.5$ ), the central maximum is shifted to a position previously …

Q29.A force $\left(3x^2+2x-5\right)N$ displaces a body from $\mathrm{x}=2\mathrm{m}$ to $\mathrm{x}=4\mathrm{m}$. Work done by this force is ...........J.

Q30.At room temperature $\left(27^{\circ }\mathrm{C}\right)$, the resistance of a heating element is $50\Omega$. The temperature coefficient of the material is $2.4\times 10^{-4}{}^{\circ }{\mathrm{C}}^{-1}$. The temperature of the element, when its resistance is $62\Omega$ …

Q1.The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency ' A ' $\times 10^{12}$ hertz and that has a radiant intensity in that direction of $\frac{1}{{}^{\prime }{\mathrm{B}}^{\prime }}$ watt per steradian. ' A ' a …

Q2.The correct stability order of the following resonance structures of ${\mathrm{CH}}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CHO}$ is

Q3.Total number of stereo isomers possible for the given structure:

Q4.The correct increasing order for bond angles among ${\mathrm{BF}}_3,{\mathrm{PF}}_3$ and $\mathrm{C}\ell {\mathrm{F}}_3$ is :

Q5.The coordination environment of ${\mathrm{Ca}}^{2+}$ ion in its complex with EDTA ${}^{4-}$ is :

Q6.The incorrect statement about Glucose is :

Q7.In the above reaction product ' P ' is

Q8.Which of the following compound can give positive iodoform test when treated with aqueous KOH solution followed by potassium hypoiodite.

Q9.For a sparingly soluble salt ${\mathrm{AB}}_2$, the equilibrium concentrations of ${\mathrm{A}}^{2+}$ ions and ${\mathrm{B}}^{-}$ions are $1.2\times 10^{-4}\mathrm{M}$ and $0.24\times 10^{-3}\mathrm{M}$, respectively. The solubility product of ${\mathrm{AB}}_2$ is :

Q10.Major product of the following reaction is

Q11.Given below are two statements :

Statement I: The higher oxidation states are more stable down the group among transition elements unlike p-block elements.

Statement II : Copper can not liberate hydrogen from weak acids.

In the light of the above statements, choose the correct …

Q12.The incorrect statement regarding ethyne is

Q13.Which of the following compounds will give silver mirror with ammoniacal silver nitrate?
(A) Formic acid
(B) Formaldehyde
(C) Benzaldehyde
(D) Acetone

Choose the correct answer from the options given below :

Q14.Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols carry their usual meaning :

Q15.The electronic configuration of Einsteinium is :
(Given atomic number of Einsteinium $=99$ )

Q16.Number of oxygen atoms present in chemical formula of fuming sulphuric acid is ____.

Q17.A transition metal 'M' among Sc, Ti, V, Cr, Mn and Fe has the highest second ionisation enthalpy. The spin only magnetic moment value of ${\mathrm{M}}^{+}$ion is
____ BM (Near integer)
(Given atomic number …

Q18.The vapour pressure of pure benzene and methyl benzene at $27^{\circ }\mathrm{C}$ is given as 80 Torr and 24 Torr, respectively. The mole fraction of methyl benzene in vapour phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same tempe …

Q19.Consider the following test for a group-IV cation.
${\mathrm{M}}^{2+}+{\mathrm{H}}_2\mathrm{S}\to \mathrm{A}$ (Black precipitate) + byproduct
$\mathrm{A}+$ aqua regia $\to \mathrm{B}+\mathrm{NOCl}+\mathrm{S}+{\mathrm{H}}_2\mathrm{O}$ …

Q20.Consider the following first order gas phase reaction at constant temperature
$\mathrm{A}(\mathrm{g})\to 2\mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$
If the total pressure of the gases is found to be 200 torr after 23 sec . and 300 torr upon the complete decompos …

Q21.In the given TLC, the distance of spot $\mathrm{A}\&\mathrm{B}$ are $5\mathrm{cm}\&7\mathrm{cm}$, from the bottom of TLC plate, respectively.
$R_f$ value of $B$ is $x\times 10^{-1}$ times more than $A$. The value of $x$ is ____.

Q22.Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter $10^{-15}\mathrm{m}$ is $\_\_\_\_$ $\times 10^9{\mathrm{ms}}^{-1}$ (nearest integer)
[Given : mass of electron …

Q23.Number of compounds from the following which cannot undergo Friedel-Crafts reactions is : $\_\_\_\_$
toluene, nitrobenzene, xylene, cumene, aniline, chlorobenzene, m-nitroaniline, m-dinitrobenzene

Q24.Total number of electron present in $({\pi }^{\ast })$ molecular orbitals of $\mathrm{O}{}_2$, $\mathrm{O}{}_2{}^{+}$ and $\mathrm{O}{}_2{}^{-}$ is $\_\_\_\_$.

Q25.When $\Delta H_{\text{vap}}=30kJ/mol$ and $\Delta S_{\text{vap}}=75{\mathrm{J}\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$, then the temperature of vapour, at one atmosphere is $\_\_\_\_$ K.

Q26.Match List I with List II:
List-I (Cell): A. Leclanché cell B. Ni-Cd cell C. Fuel cell D. Mercury cell
List-II (Use/Property/Reaction): I. Converts energy of combustion into electrical energy II. Does not involve any ion in solution and is used in hearing aids III. Recharg …

Q27.Match List I with List II:
List-I: A. K₂[Ni(CN)₄] B. [Ni(CO)₄] C. [Co(NH₃)₆]Cl₃ D. Na₃[CoF₆]
List-II: I. sp³ II. sp³d² III. dsp² IV. d²sp³
Choose the correct answer from the options given below:

Q28.Match List I with List II:
List-I (Element): A. N B. S C. Br D. Kr
List-II (Electronic Configuration): I. [Ar] 3d¹⁰ 4s² 4p⁵ II. [Ne] 3s² 3p⁴ III. [He] 2s² 2p³ IV. [Ar] 3d¹⁰ 4s² 4p⁶
Choose the correct answer from the options given below:

Q29.Match List I with List II (Group-13 elements B, Al, Ga, In, Tl):
List-I: A. Melting point [K] B. Ionic Radius [M³⁺/pm] C. First ionization enthalpy [kJ mol⁻¹] D. Atomic Radius [pm]
List-II: I. Tl > In > Ga > Al > B II. B > Tl > Al ≈ Ga > In III. Tl > In > Al > Ga > B IV. …

Q1.${\mathrm{Lim}}_{x\to 0}\frac{e-(1+2x{)}^{\frac{1}{2x}}}{x}$ is equal to :

Q2.Consider the line L passing through the points $(1,2,3)$ and $(2,3,5)$. The distance of the point $\left(\frac{11}{3},\frac{11}{3},\frac{19}{3}\right)$ from the line L along the line $\frac{3x-11}{2}=\frac{3y-11}{1}=\frac{3z-19}{2}$ is equal to :

Q3.Let ${\int }_0^{\mathrm{x}}\sqrt{1-{\left({\mathrm{y}}^{\prime }(\mathrm{t})\right)}^2}\mathrm{dt}={\int }_0^{\mathrm{x}}\mathrm{y}(\mathrm{t})\mathrm{dt},0\le \mathrm{x}\le 3,\mathrm{y}\ge 0$, $y(0)=0$. Then at $x=2,y^{\prime \prime }+y+1$ is equal to :

Q4.Let z be a complex number such that the real part of $\frac{\mathrm{z}-2\mathrm{i}}{\mathrm{z}+2\mathrm{i}}$ is zero. Then, the maximum value of $|\mathrm{z}-(6+8\mathrm{i})|$ is equal to :

Q5.The area (in square units) of the region enclosed by the ellipse $x^2+3y^2=18$ in the first quadrant below the line $\mathrm{y}=\mathrm{x}$ is :

Q6.Let the foci of a hyperbola H coincide with the foci of the ellipse $E:\frac{(x-1{)}^2}{100}+\frac{(y-1{)}^2}{75}=1$ and the eccentricity of the hyperbola H be the reciprocal of the eccentricity of the ellipse E. If the length of the transverse axis of H is $\alpha$ and the leng …

Q7.Two vertices of a triangle ABC are $\mathrm{A}(3,-1)$ and $\mathrm{B}(-2,3)$, and its orthocentre is $\mathrm{P}(1,1)$. If the coordinates of the point C are $(\alpha ,\beta )$ and the centre of the circle circumscribing the triangle PAB is $(\mathrm{h},\mathrm{k})$, then the val …

Q8.If the variance of the frequency distribution is 160, then the value of $\mathrm{c}\in \mathrm{N}$ is

Q9.Let the range of the function
$f(x)=\frac{1}{2+\sin 3x+\cos 3x},x\in \mathrm{IR}$ be $[a,b]$.
If $\alpha$ and $\beta$ are respectively the A.M. and the G.M. of $a$ and $b$, then $\frac{\alpha }{\beta }$ is equal to :

Q10.Between the following two statements:

Statement-I : Let $\vec{a}=\hat{i}+2\hat{j}-3\hat{k}$ and $\overrightarrow{\mathrm{b}}=2\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$. Then the vector $\overrightarrow{\mathrm{r}}$ satisfying …

Q11.${\lim }_{x\to \frac{\pi }{2}}\left(\frac{{\int }_{x^3}^{(\pi /2{)}^3}\left(\sin \left(2t^{1/3}\right)+\cos \left(t^{1/3}\right)\right)dt}{{\left(x-\frac{\pi }{2}\right)}^2}\right)$ is equal to :

Q12.The sum of the coefficient of $x^{2/3}$ and $x^{-2/5}$ in the binomial expansion of ${\left(x^{2/3}+\frac{1}{2}{x}^{-2/5}\right)}^9$ is :

Q13.Let $\mathrm{B}=\left[\begin{array}{ll}1& 3\\ 1& 5\end{array}\right]$ and A be a $2\times 2$ matrix such that ${\mathrm{AB}}^{-1}={\mathrm{A}}^{-1}$. If ${\mathrm{BCB}}^{-1}=\mathrm{A}$ and ${\mathrm{C}}^4+\alpha {\mathrm{C}}^2+\beta \mathrm{I}=\mathrm{O}$, then …

Q14.If ${\log }_{e}y=3{\sin }^{-1}x$, then $(1-x{)}^2{y}^{\prime \prime }-x{y}^{\prime }$ at $x=\frac{1}{2}$ is equal to :

Q15.The integral ${\int }_{1/4}^{3/4}\cos \left(2{\cot }^{-1}\sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right)\mathrm{dx}$ is equal to:

Q16.Let $\mathrm{a},\mathrm{ar},{\mathrm{ar}}^2,\dots \dots$. be an infinite G.P. If ${\sum }_{n=0}^{\infty }{\mathrm{ar}}^n=57$ and ${\sum }_{n=0}^{\infty }{\mathrm{a}}^3{\mathrm{r}}^{3n}=9747$, then $\mathrm{a}+18\mathrm{r}$ is equal to :

Q17.If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text{th }}$ roll than the number obtained in the $(\mathrm{i}-1{)}^{\text{th }}$ roll, $i=2,3$, is equal to :

Q18.The value of the integral ${\int }_{-1}^2{\log }_e\left(x+\sqrt{x^2+1}\right)dx$ is :

Q19.Let $\alpha ,\beta ;\alpha >\beta$, be the roots of the equation $x^2-\sqrt{2}x-\sqrt{3}=0$. Let $P_n={\alpha }^n-{\beta }^n,n\in N$. Then $(11\sqrt{3}-10\sqrt{2}){\mathrm{P}}_{10}+(11\sqrt{2}+10){\mathrm{P}}_{11}-11{\mathrm{P}}_{12}$ is equal to :

Q20.Let $\vec{a}=2\hat{i}+\alpha \hat{j}+\hat{k},\dot{b}=-\hat{i}+\hat{k},\vec{c}=\beta \hat{j}-\hat{k}$, where $\alpha$ and $\beta$ are integers and $\alpha \beta =-6$. Let the values of the ordered pair ( $\alpha ,\beta$ ) for which the area of the parallelogram of diag …

Q21.Consider the circle $\mathrm{C}:{\mathrm{x}}^2+{\mathrm{y}}^2=4$ and the parabola $P:y^2=8x$. If the set of all values of $\alpha$, for which three chords of the circle C on three distinct lines passing through the point $(\alpha ,0)$ are bisected by the parabola …

Q22.Let the set of all values of $p$, for which
$f(x)=\left(p^2-6p+8\right)\left({\sin }^{2}2x-{\cos }^{2}2x\right)+2(2-p)x+7$ does not have any critical point, be the interval $(\mathrm{a},\mathrm{b})$. Then 16 ab is equal to

Q23.For a differentiable function $\mathrm{f}:IR\to IR$, suppose $f^{\prime }(\mathrm{x})=3f(\mathrm{x})+\alpha$, where $\alpha \in \mathrm{IR},f(0)=1$ and ${\lim }_{x\to -\infty }f(x)=7$. Then $9\mathrm{f}\left(-{\log }_{e}3\right)$ is equal to

Q24.The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is

Q25.Let $\mathrm{A}=\{(\mathrm{x},\mathrm{y}):2\mathrm{x}+3\mathrm{y}=23,\mathrm{x},\mathrm{y}\in \mathrm{N}\}$ and $\mathrm{B}=\{\mathrm{x}:(\mathrm{x},\mathrm{y})\in \mathrm{A}\}$. Then the number of one-one functions from A to B is equal to ____.

Q26.Let $\mathrm{A},\mathrm{B}$ and C be three points on the parabola $y^2=6x$ and let the line segment $AB$ meet the line $L$ through C parallel to the x-axis at the point D. Let M and N respectively be the feet of the perpendiculars from A and B on L.

Then …

Q27.The square of the distance of the image of the point (6, 1, 5) in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$, from the origin is ____.

Q28.If $\left(\frac{1}{\alpha +1}+\frac{1}{\alpha +2}+\dots +\frac{1}{\alpha +1012}\right)$
$-\left(\frac{1}{2\cdot 1}+\frac{1}{4\cdot 3}+\frac{1}{6\cdot 5}+\dots +\frac{1}{2024\cdot 2023}\right)$
$=\frac{1}{2024}$, then $\alpha$ is equal to ____.

Q29.Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2{\sin }^{-1}x+3{\cos }^{-1}x=\frac{2\pi }{5}$, is ____.

Q30.Consider the matrices: $\mathrm{A}=\left[\begin{array}{cc}2& -5\\ 3& \mathrm{m}\end{array}\right],\mathrm{B}=\left[\begin{array}{c}20\\ \mathrm{m}\end{array}\right]$ and $\mathrm{X}=\left[\begin{array}{l}\mathrm{x}\\ \mathrm{y}\end{array}\right]$. Let the set of all m …