JEE Main 2024 · 06 Apr 2024 · Shift 2

Q1.The number of electrons per second in the filament of a 110 W bulb operating at 220 V is : (Given $\mathrm{e}=1.6\times 10^{-19}\mathrm{C}$ )

Q2.The acceptor level of a p-type semiconductor is 6 eV . The maximum wavelength of light which can create a hole would be : Given hc $=1242\mathrm{eV}\mathrm{nm}$.

Q3.For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm . The refractive index of the material is :

Q4.Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force 16 N . A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is :

Q5.A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_2$. Time required to reach the ground, if it is dropped f …

Q6.A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking $30^{\circ }$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: …

Q7.In the given electromagnetic wave ${\mathrm{E}}_{\mathrm{y}}=600\sin (\omega \mathrm{t}-\mathrm{kx}){\mathrm{Vm}}^{-1}$, intensity of the associate light beam is (in $\mathrm{W}/{\mathrm{m}}^2$: $($ Given …

Q8.Energy of 10 non rigid diatomic molecules at temperature T is :

Q9.When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

Q10.The longest wavelength associated with Paschen series is : (Given ${\mathrm{R}}_{\mathrm{H}}=1.097\times 10^7\mathrm{SI}$ unit)

Q11.Given below are two statements :\\
Statement (I) : Dimensions of specific heat is $\left[{\mathrm{L}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}\right]$.\\
Statement (II) : Dimensions of gas constant is $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}{\mathrm{K}}^{-1}\right]$.\\
In the light of …

Q12.Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : R = Radius of bubble, $S=$ Surface tension of bubble)

Q13.Match List-I with List-II :

Q14.In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text{th }}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the i …

Q15.When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13 eV , electron emission takes place. The stopping potential is :\\
(Given hc $=1240\mathrm{eV}\mathrm{nm}$ )

Q16.In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $=49$ MSD; 20 divisions on main scale in each cm For mark on paper\\
$\mathrm{MSR}=8.45\mathrm{cm},\mathrm{VC}=26$\\
For mark on paper see …

Q17.Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth?

Q18.A total of 48J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ }\mathrm{C}$. The work done by the gas is :\\
Given, $\mathrm{R}=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$.

Q19.In a coil, the current changes from -2 A to +2 A in 0.2 s and induces an emf of 0.1 V . The self inductance of the coil is :

Q20.A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg . The branch pulls the chain by a force equal to (if $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ ):

Q21.For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF . If resistance of $200\Omega$ and 100 mH inductor is being used in the given circuit. The frequency of ac source is $\_\_\_\_$ $\times 10^3\mathrm{Hz}$. (gi …

Q22.Three point masses of 2 kg, 4 kg and 6 kg are placed at the corners of an equilateral triangle of side 2 m. The moment of inertia of the system about an axis passing through the centroid and perpendicular to the plane of the triangle is ______ ${\mathrm{kgm}}^2$.

Q23.Two open organ pipes of lengths 60 cm and 90 cm resonate at $6^{\text{th }}$ and $5^{\text{th }}$ harmonics respectively. The difference of frequency for the given modes is ______ Hz.

(Velocity of sound in air $=333\mathrm{m}/\mathrm{s}$ )

Q24.A particle moves in a straight line so that its displacement x at any time t is given by ${\mathrm{x}}^2=1+{\mathrm{t}}^2$. Its acceleration at any time t is ${\mathrm{x}}^{-\mathrm{n}}$ where $\mathrm{n}=$ ______.

Q25.A capacitor of $10\mu \mathrm{F}$ capacitance whose plates are separated by 10 mm through air and each plate has area $4{\mathrm{cm}}^2$ is now filled equally with two dielectric media of ${\mathrm{K}}_1=2,{\mathrm{K}}_2=3$ respectively as shown in figure. If new force betw …

Q26.A wire of cross sectional area A, modulus of elasticity $2\times 10^{11}{\mathrm{Nm}}^{-2}$ and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle $\theta =\frac{1}{100}$ …

Q27.Two coherent monochromatic light beams of intensities I and 4I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is xI. The value of $x$ is ______.

Q28.A coil having 100 turns, area of $5\times 10^{-3}{\mathrm{m}}^2$, carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ }$ is ______ …

Q29.In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ______ nm. (Given hc …

Q30.In the given figure an ammeter A consists of a $240\Omega$ coil connected in parallel to a $10\Omega$ shunt. The reading of the ammeter is ______ mA.

Q1.Molality ( m ) of 3 M aqueous solution of NaCl is: (Given : Density of solution $=1.25\mathrm{g}{\mathrm{mL}}^{-1}$, Molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ : Na-23, Cl-35.5)

Q2.The incorrect statements regarding enzymes are:
(A) Enzymes are biocatalysts.
(B) Enzymes are non-specific and can catalyse different kinds of reactions.
(C) Most Enzymes are globular proteins.
(D) Enzyme - oxidase catalyses the hydrolysis of maltose into glucose.
Choose the corr …

Q3.Consider the above chemical reaction. Product " A " is:

Q4.During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in ${\mathrm{NH}}_4\mathrm{OH}$ solution when sodium carbonate extract was first acidified with dil. ${\mathrm{HNO}}_3$ and then ${\mathrm{AgNO}}_3$ s …

Q5.How can an electrochemical cell be converted into an electrolytic cell ?

Q6.Arrange the following elements in the increasing order of number of unpaired electrons in it.
(A) Sc
(B) Cr
(C) V
(D) Ti
(E) Mn

Choose the correct answer from the options given below:

Q7.Match List-I with List-II.

Q8.The major products formed:

A and B respectively are:

Q9.The incorrect statement regarding the geometrical isomers of 2-butene is:

Q10.Given below are two statements:

Statement I: ${\mathrm{PF}}_5$ and ${\mathrm{BrF}}_5$ both exhibit ${\mathrm{sp}}^3\mathrm{d}$ hybridisation.
Statement II: Both ${\mathrm{SF}}_6$ and ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ exhibit …

Q11.The number of ions from the following that are expected to behave as oxidising agent is:
${\mathrm{Sn}}^{4+},{\mathrm{Sn}}^{2+},{\mathrm{Pb}}^{2+},{\mathrm{Tl}}^{3+},{\mathrm{Pb}}^{4+},{\mathrm{Tl}}^{+}$

Q12.Identify the product (A) in the following reaction.

Q13.The correct statements among the following, for a "chromatography" purification method is:

Q14.Evaluate the following statements related to group 14 elements for their correctness.
(A) Covalent radius decreases down the group from C to Pb in a regular manner.
(B) Electronegativity decreases from C to Pb down the group gradually.
(C) Maximum covalence of C is 4 whereas othe …

Q15.Match List-I with the List-II

List-I (Reaction)

(A) ${\mathrm{N}}_{2(\mathrm{g})}+{\mathrm{O}}_{2(\mathrm{g})}\to 2{\mathrm{NO}}_{(\mathrm{g})}$

(B) …

Q16.Consider the given reaction, identify the major product P.

Q17.The correct IUPAC name of $\left[{\mathrm{PtBr}}_2{\left({\mathrm{PMe}}_3\right)}_2\right]$ is:

Q18.Match List-I with List-II

List-I (Tetrahedral Complex)

(A) ${\mathrm{TiCl}}_4$

(B) ${\left[{\mathrm{FeO}}_4\right]}^{2-}$

(C) ${\left[{\mathrm{FeCl}}_4\right]}^{-}$

(D) ${\left[{\mathrm{CoCl}}_4\right]}^{2-}$

List-II (Electronic configuration)

(I) …

Q19.The ratio $\frac{{\mathrm{K}}_{\mathrm{P}}}{{\mathrm{K}}_{\mathrm{C}}}$ for the reaction:
${\mathrm{CO}}_{(\mathrm{g})}+\frac{1}{2}{\mathrm{O}}_{2(\mathrm{g})}\rightleftharpoons {\mathrm{CO}}_{2(\mathrm{g})}$ is:

Q20.An amine ( X ) is prepared by ammonolysis of benzyl chloride. On adding p-toluenesulphonyl chloride to it the solution remains clear. Molar mass of the amine ( X ) formed is ______ $\mathrm{g}{\mathrm{mol}}^{-1}$.
(Given molar mass in ${\mathrm{gmol}}^{-1}$ C: 12, H: 1, O: 16, N: 14 …

Q21.Consider the following reactions
$\mathrm{NiS}+{\mathrm{HNO}}_3+\mathrm{HCl}\to \mathrm{A}+\mathrm{NO}+\mathrm{S}+{\mathrm{H}}_2\mathrm{O}$

The number of protons that do not involve in hydrogen bonding in the product B is ______.

Q22.When ' ${\mathrm{x}}^{\prime }\times 10^{-2}\mathrm{mL}$ methanol (molar mass $=32\mathrm{g}$; density $=0.792\mathrm{g}/{\mathrm{cm}}^3$ ) is added to 100 mL water (density $=1\mathrm{g}/{\mathrm{cm}}^3$ ), the following diagram is obtained.

$\mathrm{x}=$ ............ …

Q23.The ratio of number of oxygen atoms to bromine atoms in the product Q is ______ $\times 10^{-1}$.

Q24.Number of carbocation from the following that are not stabilized by hyperconjugation is ______.

Q25.For the reaction at $298\mathrm{K}$, $2\mathrm{A}+\mathrm{B}\to \mathrm{C}$. $\Delta \mathrm{H}=400\mathrm{kJ}{\mathrm{mol}}^{-1}$ and $\Delta \mathrm{S}=0.2\mathrm{kJ}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$. The reaction will become spontaneous above ______ K.

Q26.Total number of species from the following with central atom utilising $s{p}^2$ hybrid orbitals for bonding is ______. …

Q27.Consider the two different first order reactions given below
$\mathrm{A}+\mathrm{B}\to \mathrm{C}$ (Reaction 1)
$\mathrm{P}\to \mathrm{Q}$ (Reaction 2)
The ratio of the half life of Reaction 1 : Reaction 2 is $5:2$. If ${\mathrm{t}}_1$ and …

Q28.For hydrogen atom, energy of an electron in first excited state is -3.4 eV, K.E. of the same electron of hydrogen atom is x eV. Value of x is ______ $\times 10^{-1}\mathrm{eV}$. (Nearest integer)

Q29.Among ${\mathrm{VO}}_2^{+},{\mathrm{MnO}}_4^{-}$ and ${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}$, the spin-only magnetic moment value of the species with least oxidising ability is ______ BM (Nearest integer).
(Given atomic number $\mathrm{V}=23,\mathrm{Mn}=25,\mathrm{Cr}=24$)

Q1.Let $0\le r\le n$ If ${}^{n+1}{C}_{r+1}:{}^n{C}_r:{}^{n-1}{C}_{r-1}=55:35:21$, then $2n+5r$ is equal to

Q2.A software company sets up m number of computer system to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment The v …

Q3.Suppose the solution of the differential equation $\frac{dy}{dx}=\frac{(2+\alpha )x-\beta y+2}{\beta x-2\alpha y-(\beta \gamma -4\alpha )}$ represents a circle passing through origin. Then radius of the circle is

Q4.Let $A=\{1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only $4x\le 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A\times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m+n$ is …

Q5.If the function $\mathrm{f}(\mathrm{x})={\left(\frac{1}{\mathrm{x}}\right)}^{2\mathrm{x}},x>0$ attains the maximum value at $\mathrm{x}=\frac{1}{\mathrm{e}}$ then

Q6.Let $\vec{a}=2\hat{i}+\hat{j}-\hat{k},\vec{b}=((\vec{a}\times (\hat{i}+\hat{j}))\times \hat{i})\times \hat{i}$. Then the square of the projection of $\vec{a}$ on $\vec{b}$ is

Q7.If $A$ is a square matrix of order 3 such that $\det (A)=3$ and $\det \left(\mathrm{adj}\left(-4\mathrm{adj}.\left(-3\mathrm{adj}\left(3\mathrm{adj}\left((2A{)}^{-1}\right)\right)\right)\right)\right)=2^m{3}^n$. Then $m+2n$ is equ …

Q8.Let $\vec{a}=6\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$. If $\vec{c}$ is a vector such that $|\vec{c}|\ge 6,\vec{a}\cdot \vec{c}=6|\vec{c}|,|\vec{c}-\vec{a}|=2\sqrt{2}$ and the angle between $\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}$ and …

Q9.${\lim }_{n\to \infty }\frac{\left(1^2-1\right)(n-1)+\left(2^2-2\right)(n-2)+\dots \dots \dots +\left((n-1{)}^2-(n-1)\right)\cdot 1}{\left(1^3+2^3+\dots +n^2\right)-\left(1^2+2^2+\dots +n^2\right)}$ is equal to

Q10.Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $ABC$ and the same process is repeated infinitely many times. If $P$ is the sum of perimeters and $Q$ is the sum of area of all the triangles formed in this pr …

Q11.If all words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315^{\text{th}}$ position in this arrangement is

Q12.Suppose for a function $h,h(0)=0,h(1)=1$ and $h^{\prime }(0)=h^{\prime }(1)=2$. If $g(x)=h\left(e^x\right)e^{h(x)}$, then $g^{\prime }(0)$ is equal to

Q13.Let $\mathrm{P}(\alpha ,\beta ,\gamma )$ be the image of the point $\mathrm{Q}(3,-3,1)$ in the line $\frac{\mathrm{x}-0}{1}=\frac{\mathrm{y}-3}{1}=\frac{\mathrm{z}-1}{-1}$ and R be the point $(2,5,-1)$. If the area of the triangle ${\lambda }^2=74\mathrm{K}$ then K is equal to

Q14.If $z_1,z_2$ are two distinct complex numbers such that $\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1{\bar{z}}_2}\right|=2$, then

Q15.If $\int \frac{1}{a^2{\sin }^{2}x+b^2{\cos }^{2}x}dx=\frac{1}{12}{\tan }^{-1}(3\tan x)+\text{constant}$, then the maximum value of $a\sin x+b\cos x$, is

Q16.Let $f(x)=\frac{1}{7-\sin 5x}$ be a function defined on $\mathbb{R}$. Then the range of the function $f(x)$ is equal to:

Q17.If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is

Q18.If the locus of the point, whose distance from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$, is $a{x}^2+b{y}^2+cxy+dx+ey+170=0$, then the value of $a^2+2b+3c+4d+e$ is

Q19.In a triangle $ABC,BC=7,AC=8,AB=\alpha \in \mathbb{N}$ and $\cos A=\frac{2}{3}$. If $49\cos (3C)+42=\frac{m}{n}$, where $\gcd (m,n)=1$, then $m+n$ is equal to ______.

Q20.If the system of equations

$2x+7y+\lambda z=3$

$3x+2y+5z=4$

$x+\mu y+32z=-1$

has infinitely many solutions, then $(\lambda -\mu )$ is equal to ______.

Q21.From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$ where …

Q22.$S(x)=(1+x)+2(1+x{)}^2+3(1+x{)}^3+3(1+x{)}^4+\dots +60(1+x{)}^{60},x\ne 0$

and $(60{)}^{2}S(60)=a(b{)}^b+b,a,b\in \mathbb{N}$ then $(a+b)$ is equal to ______.

Q23.Let $[t]$ denote the largest integer less than or equal to $t$.

If ${\int }_0^3\left(\left[x^2\right]+\left[\frac{x^2}{2}\right]\right)dx=a+b\sqrt{2}-\sqrt{3}-\sqrt{5}+c\sqrt{6}-\sqrt{7}$ where $a,b,c\in \mathbb{Z}$, then $a+b+c$ is equal to ______.

Q24.Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f:[0,\infty )\to \mathbb{R}$ be a function defined by $f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}]$. Let $S$ be the set of all points in the interval $[0,8]$ at which $f$ is not continuous. Then …

Q25.If the solution $y(x)$ of the given differential equation $\left(e^y+1\right)\cos xdx+e^y\sin xdy=0$ passes through the point $\left(\frac{\pi }{2},0\right)$ then the value of $e^{y\left(\frac{\pi }{6}\right)}$ is equal to ______.

Q26.Let $\alpha ,\beta$ be roots of $x^2+\sqrt{2}x-8=0$. If $U_n={\alpha }^n+{\beta }^n$ then $\frac{U_{10}+\sqrt{2}{U}_9}{2U_8}$ is equal to ______.

Q27.If the shortest distance between the lines $\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-4}{4}$ to $\frac{x-\lambda }{3}=\frac{y-2}{-1}=\frac{z-1}{1}$ and is $\frac{44}{\sqrt{30}}$ then the largest possible value of $|\lambda |$ is equal ____.

Q28.The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and $x=\pm \frac{4}{\sqrt{13}}$ respectively. Let the line $y-\sqrt{3}x+\sqrt{3}=0$ touch this hyperbola at ( $x_0,y_0$ ). If $m$ is the product of the focal distance of the point …