JEE Main 2024 · 01 Feb 2024 · Shift 2

Q1.In an ammeter, $5\%$ of the main current passes through the galvanometer. If resistance of the galvanometer is G , the resistance of ammeter will be :

Q2.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 semicon …

Q3.From the statements given below :
(A) The angular momentum of an electron in ${\mathrm{n}}^{\text{th }}$ orbit is an integral multiple of h .
(B) Nuclear forces do not obey inverse square law.
(C) Nuclear forces are spin dependent.
(D) Nuclear forces are central and charge indep …

Q4.A diatomic gas $(\gamma =1.4)$ does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is :

Q5.A disc of radius R and mass M is rolling horizontally without slipping with speed $\nu$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

Q6.Conductivity of a photodiode starts changing only if the wavelength of incident light is less than 660 nm . The band gap of photodiode is found to be $\left(\frac{\mathrm{X}}{8}\right)\mathrm{eV}$. The value of X is :
(Given, …

Q7.A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

Q8.If frequency of electromagnetic wave is 60 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 m ) is :

Q9.A cricket player catches a ball of mass 120 g moving with $25\mathrm{m}/\mathrm{s}$ speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):

Q10.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 $\mathrm{h}=6.63\times 10^{-34}\mathrm{Js}$ )

Q11.A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm . The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit, will be:

Q12.${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are two hollow concentric cubes enclosing charges 2 Q and 3 Q respectively as shown in figure. The ratio of electric flux passing through ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is :

Q13.If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2\mathrm{km}/\mathrm{s}$, the root mean square velocity of oxygen at the same condition in $\mathrm{km}/\mathrm{s}$ is :

Q14.Train A is moving along two parallel rail tracks towards north with speed $72\mathrm{km}/\mathrm{h}$ and train B is moving towards south with speed $108\mathrm{km}/\mathrm{h}$. Velocity of train B with respect to A and velocity of ground with respect to B are (in …

Q15.A galvanometer ( G ) of $2\Omega$ resistance is connected in the given circuit. The ratio of charge stored in ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is :

Q16.In a metre-bridge when a resistance in the left gap is $2\Omega$ and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with $2\Omega$, the balance length changes by :

Q17.Match List - I with List - II.

List - I (Number)
List - II (Significant figure)

Choose the correct answer from the options given below :

Q18.A transformer has an efficiency of $80\%$ and works at 10 V and 4 kW. If the secondary voltage is 240 V, then the current in the secondary coil is :

Q19.A light planet is revolving around a massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the force of attraction between planet and star is proportional to ${\mathrm{R}}^{-3/2}$ then choose the correct option :

Q20.A body of mass 4 kg experiences two forces ${\overrightarrow{\mathrm{F}}}_1=5\hat{\mathrm{i}}+8\hat{\mathrm{j}}+7\hat{\mathrm{k}}$ and ${\overrightarrow{\mathrm{F}}}_2=3\hat{\mathrm{i}}-4\hat{\mathrm{j}}-3\hat{\mathrm{k}}$. The acceleration acting on the body is :

Q21.A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass 9 m is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_2}$ is ____.

Q22.A particle initially at rest starts moving from reference point $\mathrm{x}=0$ along x-axis, with velocity $v$ that varies as $v=4\sqrt{\mathrm{x}}\mathrm{m}/\mathrm{s}$. The acceleration of the particle is ____ ${\mathrm{ms}}^{-2}$.

Q23.A moving coil galvanometer has 100 turns and each turn has an area of $2.0{\mathrm{cm}}^2$. The magnetic field produced by the magnet is 0.01 T and the deflection in the coil is 0.05 radian when a current of 10 mA is passed through it. The torsional constant of the suspension …

Q24.One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will …

Q25.A particular hydrogen - like ion emits the radiation of frequency $3\times 10^{15}\mathrm{Hz}$ when it makes transition from $\mathrm{n}=2$ to $\mathrm{n}=1$. The frequency of radiation emitted in transition from $\mathrm{n}=3$ to $\mathrm{n}=1$ is …

Q26.In an electrical circuit drawn below the amount of charge stored in the capacitor is ______ $\mu \mathrm{C}$.

Q27.A coil of 200 turns and area $0.20{\mathrm{m}}^2$ is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2\pi }{\beta }$ volt. The value of …

Q28.In Young's double slit experiment, monochromatic light of wavelength $5000\mathring{A}$ is used. The slits are 1.0 mm apart and screen is placed at 1.0 m away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time i …

Q29.A uniform rod AB of mass 2 kg and Length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi }{\mathrm{x}}\mathrm{s}$, where $\mathrm{x}=$

Q30.Suppose a uniformly charged wall provides a uniform electric field of $2\times 10^4\mathrm{N}/\mathrm{C}$ normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge …

Q1.The transition metal having highest $3^{\text{rd }}$ ionisation enthalpy is :

Q2.Given below are two statements :

Statement (I) : A $\pi$ bonding MO has lower electron density above and below the inter-nuclear asix.

Statement (II) : The ${\pi }^{\ast }$ antibonding MO has a node between the nuclei.

In the light of the above statements, choose the most appropr …

Q3.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In aqueous solutions ${\mathrm{Cr}}^{2+}$ is reducing while ${\mathrm{Mn}}^{3+}$ is oxidising in nature.

Reason (R) : Extra stability to half filled electr …

Q4.Match List - I with List - II.

List-I (Reactants)
(A) Phenol, $\mathrm{Zn}/\Delta$
(B) Phenol, ${\mathrm{CHCl}}_3,\mathrm{NaOH},\mathrm{HCl}$
(C) Phenol, ${\mathrm{CO}}_2,\mathrm{NaOH},\mathrm{HCl}$
(D) Phenol, Conc. ${\mathrm{HNO}}_3$

List-II (Products)
(I) Salic …

Q5.Given below are two statements :

Statement (I) : Both metal and non-metal 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 appropriat …

Q6.The strongest reducing agent amont the following is:

Q7.Which of the following compounds show colour due to d-d transition?

Q8.The set of meta directing functional groups from the following sets is:

Q9.Select the compound from the following that will show intramolecular hydrogen bonding.

Q10.Lassaigne's test is used for detection of :

Q11.Which among the following has highest boiling point?

Q12.In the given reactions identify A and B .

${\mathrm{CH}}_3-\mathrm{C}\equiv \mathrm{C}-{\mathrm{CH}}_3+{\mathrm{H}}_2\stackrel{\mathrm{Na}/\text{ Liquid }{\mathrm{NH}}_3}{\to }$ "B"

Q13.The number of radial node/s for 3p orbital is:

Q14.The functional group that shows negative resonance effect is:

Q15.[Co(NH₃)₆]³⁺ and [CoF₆]³⁻ are respectively known as:

Q16.Given below are two statements:

Statement (I): SiO₂ and GeO₂ are acidic while SnO and PbO are amphoteric in nature.
Statement (II): Allotropic forms of carbon are due to property of catenation and pπ-dπ bond formation.

In the light of the above statements, choose the most appro …

Q17.Acid D formed in above reaction is:

Q18.Solubility of calcium phosphate (molecular mass, M) in water is W g per 100 mL at 25°C. Its solubility product at 25°C will be approximately.

Q19.Given below are two statements:

Statement (I): Dimethyl glyoxime forms a six-membered covalent chelate when treated with NiCl₂ solution in presence of NH₄OH.
Statement (II): Prussian blue precipitate contains iron both in (+2) and (+3) oxidation states.

In the light of the abov …

Q20.Total number of isomeric compounds (including stereoisomers) formed by monochlorination of 2-methylbutane is ____.

Q21.The following data were obtained during the first order thermal decomposition of a gas A at constant volume:
A(g) → 2B(g) + C(g)

The rate …

Q22.The number of tripeptides formed by three different amino acids using each amino acid once is ____.

Q23.Number of compounds which give reaction with Hinsberg's reagent is ____.

Q24.Mass of ethylene glycol (antifreeze) to be added to 18.6 kg of water to protect the freezing point at $-24^{\circ }\mathrm{C}$ is ____ kg (Molar mass in ${\mathrm{g}}^{-1}$ for ${}^{-1}$ for ethylene glycol $62,{\mathrm{K}}_{\mathrm{f}}$ of water …

Q25.Following Kjeldahl's method, 1g of organic compound released ammonia, that neutralised 10 mL of $2\mathrm{M}{\mathrm{H}}_2{\mathrm{SO}}_4$. The percentage of nitrogen in the compound is ____ %.

Q26.The amount of electricity in Coulomb required for the oxidation of 1 mol of ${\mathrm{H}}_2\mathrm{O}$ to ${\mathrm{O}}_2$ is ____ $\times 10^5\mathrm{C}$.

Q27.For a certain reaction at $300\mathrm{K},\mathrm{K}=10$, then $\Delta {\mathrm{G}}^{\circ }$ for the same reaction is - ____ $\times 10^{-1}\mathrm{kJ}{\mathrm{mol}}^{-1}$.
(Given $\mathrm{R}=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$ )

Q28.Consider the following redox reaction :
${\mathrm{MnO}}_4^{-}+{\mathrm{H}}^{+}+{\mathrm{H}}_2{\mathrm{C}}_2{\mathrm{O}}_4\rightleftharpoons {\mathrm{Mn}}^{2+}+{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_2$

The standard reduction potentials are given as below ( …

Q29.10 mL of gaseous hydrocarbon on combustion gives 40 mL of ${\mathrm{CO}}_2(\mathrm{g})$ and 50 mL of water vapour. Total number of carbon and hydrogen atoms in the hydrocarbon is ____.

Q1.Let $f(\mathrm{x})=\left|2{\mathrm{x}}^2+5\right|\mathrm{x}|-3|,\mathrm{x}\in \mathrm{R}$. If m and n denote the number of points where $f$ is not continuous and not differentiable respectively, then $\mathrm{m}+\mathrm{n}$ is equal to :

Q2.Let $\alpha$ and $\beta$ be the roots of the equation ${\mathrm{px}}^2+\mathrm{qx}-\mathrm{r}=0$, where $\mathrm{p}\ne 0$. If $\mathrm{p},\mathrm{q}$ and r be the consecutive terms of a non-constant G.P and $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{3}{4}$, then the …

Q3.The number of solutions of the equation $4{\sin }^{2}x-4{\cos }^3\mathrm{x}+9-4\cos \mathrm{x}=0;\mathrm{x}\in [-2\pi ,2\pi ]$ is :

Q4.The value of ${\int }_0^1{\left(2x^3-3x^2-x+1\right)}^{\frac{1}{3}}dx$ is equal to:

Q5.Let P be a point on the ellipse $\frac{{\mathrm{x}}^2}{9}+\frac{{\mathrm{y}}^2}{4}=1$. Let the line passing through P and parallel to y -axis meet the circle $x^2+y^2=9$ at point $Q$ such that $P$ and $Q$ are on the same side of the x -axis. Then, the eccentricity o …

Q6.Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of ${\left(\frac{1}{3}{\mathrm{x}}^{\frac{1}{3}}+\frac{1}{2{\mathrm{x}}^{\frac{2}{3}}}\right)}^{18}$. Then ${\left(\frac{\mathrm{n}}{\mathrm{m}}\right)}^{\frac{1}{3}}$ is :

Q7.Let P and 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:

Q8.Consider a $△\mathrm{ABC}$ where $\mathrm{A}(1,3,2),\mathrm{B}(-2,8,0)$ and $\mathrm{C}(3,6,7)$. If the angle bisector of $\angle \mathrm{BAC}$ meets the line BC at D , then the length of the projection of the vector $\overrightarrow{\mathrm{AD}}$ on the vecto …

Q9.Let ${\mathrm{S}}_{\mathrm{n}}$ denote the sum of the first n terms of an arithmetic progression. If ${\mathrm{S}}_{10}=390$ and the ratio of the tenth and the fifth terms is $15:7$, then ${\mathrm{S}}_{15}-{\mathrm{S}}_5$ is equal to:

Q10.If ${\int }_0^{\frac{\pi }{3}}{\cos }^{4}xdx=a\pi +b\sqrt{3}$, where $a$ and $b$ are rational numbers, then $9a+8b$ is equal to :

Q11.If $z$ is a complex number such that $|z|\ge 1$, then the minimum value of $\left|\mathrm{z}+\frac{1}{2}(3+4i)\right|$ is:

Q12.If the domain of the function $f(x)=\frac{\sqrt{x^2-25}}{(4-x^2)}+{\log }_{10}({\mathrm{x}}^2+2\mathrm{x}-15)$ is $(-\infty ,\alpha )\cup [\beta ,\infty )$, then ${\alpha }^2+{\beta }^3$ is equal to :

Q13.Consider the relations ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ defined as ${\mathrm{aR}}_1\mathrm{b}\iff {\mathrm{a}}^2+{\mathrm{b}}^2=1$ for all $\mathrm{a},\mathrm{b},\in \mathrm{R}$ and …

Q14.If the mirror image of the point $\mathrm{P}(3,4,9)$ 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 :

Q15.Let $f(\mathrm{x})=\{\begin{array}{c}\mathrm{x}-1,\mathrm{x}\text{ is even, }\\ 2\mathrm{x},\mathrm{x}\text{ is odd, }\end{array}\mathrm{x}\in \mathrm{N}$. If for some $\mathrm{a}\in \mathrm{N},f(f(f(\mathrm{a})))=21$, then …

Q16.Let the system of equations $x+2y+3z=5$, $2x+3y+z=9,4x+3y+\lambda z=\mu$ have infinite number of solutions. Then $\lambda +2\mu$ is equal to :

Q17.Consider 10 observation ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{10}$. such that ${\sum }_{i=1}^{10}(x_i-\alpha )=2$ and ${\sum }_{i=1}^{10}(x_i-\beta {)}^2=40$, where $\alpha ,\beta$ are positive integers. Let the mean and the variance of the observations be …

Q18.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 :

Q19.Let the locus of the mid points of the chords of circle $x^2+(y-1{)}^2=1$ drawn from the origin intersect the line $\mathrm{x}+\mathrm{y}=1$ at P and Q . Then, the length of PQ is :

Q20.If three successive terms of a G.P. with common ratio $\mathrm{r}(\mathrm{r}>1)$ are the lengths of the sides of a triangle and $[\mathrm{r}]$ denotes the greatest integer less than or equal to r , then $3[\mathrm{r}]+[-\mathrm{r}]$ is equal to :

Q21.Let $\mathrm{A}={\mathrm{I}}_2-2{\mathrm{MM}}^{\mathrm{T}}$, where M is real matrix of order $2\times 1$ such that the relation ${\mathrm{M}}^{\mathrm{T}}\mathrm{M}={\mathrm{I}}_1$ holds. If $\lambda$ is a real number such that the relation …

Q22.Let $f:(0,\infty )\to R$ and $F(x)={\int }_0^{x}tf(t)dt$. If $F(x^2)=x^4+x^5$, then ${\sum }_{r=1}^{12}f(r^2)$ is equal to :

Q23.If $y=\frac{(\sqrt{x}+1)(x^2-\sqrt{x})}{x\sqrt{x}+x+\sqrt{x}}+\frac{1}{15}(3{\cos }^{2}x-5){\cos }^{3}x$, then $96y^{\prime }\left(\frac{\pi }{6}\right)$ is equal to :

Q24.Let $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=-\hat{i}-8\hat{j}+2\hat{k}$ and $\overrightarrow{\mathrm{c}}=4\hat{\mathrm{i}}+{\mathrm{c}}_2\hat{\mathrm{j}}+{\mathrm{c}}_3\hat{\mathrm{k}}$ be three vectors such that …

Q25.The lines ${\mathrm{L}}_1,{\mathrm{L}}_2,\dots ,{\mathrm{L}}_{20}$ are distinct. For $\mathrm{n}=1,2,3,\dots ,10$ all the lines ${\mathrm{L}}_{2\mathrm{n}-1}$ are parallel to each other and all the lines ${\mathrm{L}}_{2\mathrm{n}}$ pass through a given point P . The maximum n …

Q26.Three points $\mathrm{O}(0,0),\mathrm{P}\left(\mathrm{a},{\mathrm{a}}^2\right),\mathrm{Q}\left(-\mathrm{b},{\mathrm{b}}^2\right),\mathrm{a}>0,\mathrm{b}>0$, are on the parabola $\mathrm{y}={\mathrm{x}}^2$. Let ${\mathrm{S}}_1$ be the area of the region bounded by the line …

Q27.The sum of squares of all possible values of k , for which area of the region bounded by the parabolas $2y^2=kx$ and $k{y}^2=2(y-x)$ is maximum, is equal to :

Q28.If $\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1+\mathrm{x}-{\mathrm{y}}^2}{\mathrm{y}},\mathrm{x}(1)=1$, then $5\mathrm{x}(2)$ is equal to :

Q29.Let ABC be an isosceles triangle in which A is at $(-1,0),\angle \mathrm{A}=\frac{2\pi }{3},\mathrm{AB}=\mathrm{AC}$ and B is on the positive x -axis. If $\mathrm{BC}=4\sqrt{3}$ and the line BC intersects the line $\mathrm{y}=\mathrm{x}+3$ at $(\alpha ,\beta )$, then …