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JEE Main 2024 April 06, Shift 2 Question Paper with Solutions

All 90 questions from the JEE Main 2024 (April 06, Shift 2) shift — Physics (30), Chemistry (30) and Mathematics (30) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics30 questions

Q1Single correctUnits and Measurements
Given below are two statements : Statement (I) : Dimensions of specific heat is . Statement (II) : Dimensions of gas constant is . In the light of the above statements, choose the most appropriate answer from the options given below.
(A)
(B)
(C)
(D)
Q2Single correctKinematics
A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in . Time required to reach the ground, if it is dropped from the top of the tower, is :
(A)
(B)
(C)
(D)
Q3Single correctLaws of Motion
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 m/) :
(A)
(B)
(C)
(D)
Q4Single correctLaws of Motion
A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely :
(A)
(B)
(C)
(D)
Q5Single correctWork, Energy and Power
When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :
(A)
(B)
(C)
(D)
Q6Single correctGravitation
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 depth under surface of earth ?
(A)
(B)
(C)
(D)
Q7Single correctMechanical Properties of Fluids
Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : R = Radius of bubble S = Surface tension of bubble)
(A)
(B)
(C)
(D)
Q8Single correctThermodynamics
A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by C. The work done by the gas is: Given, R = 8.3 J mo.
(A)
(B)
(C)
(D)
Q9Single correctKinetic Theory of Gases
Energy of 10 non rigid diatomic molecules at temperature is :
(A)
(B)
(C)
(D)
Q10Single correctElectrostatics
Two identical conducting spheres and with charge on each, repel each other with a force 16 N. A third identical uncharged conducting sphere is successively brought in contact with the two spheres. The new force of repulsion between P and S is :
(A)
(B)
(C)
(D)
Q11Single correctCurrent Electricity
The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is : ( Given C)
(A)
(B)
(C)
(D)
Q12Single correctMagnetism and Matter
Match List-I with List-II :
Choose the correct answer from the options given below :
Match table: List-I (Y vs X) A-D physical quantities; List-II (Shape of Graph) four Y-vs-X graphs labelled I (line through origin), II (rise then fall), III (constant horizontal line), IV (1/x decay).
(A)
(B)
(C)
(D)
Q13Single correctElectromagnetic Induction
In a coil, the current changes from A to A in 0.2 s and induces an emf of 0.1 V. The self inductance of the coil is :
(A)
(B)
(C)
(D)
Q14Single correctElectromagnetic Waves
In the given electromagnetic wave , intensity of the associated light beam is (in W/ : (Given )
(A)
(B)
(C)
(D)
Q15Single correctExperimental Skills
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 MSR = 8.45 cm, VC = 26. For mark on paper seen through slab MSR = 7.12 cm, VC = 41. For powder particle on the top surface of the glass slab MSR = 4.05 cm, VC = 1. (MSR = Main Scale Reading, VC = Vernier Coincidence). Refractive index of the glass slab is :
(A)
(B)
(C)
(D)
Q16Single correctRay Optics and Optical Instruments
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 :
(A)
(B)
(C)
(D)
Q17Single correctDual Nature of Radiation and Matter
When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13eV, electron emission takes place. The stopping potential is: (Given hc eVnm )
(A)
(B)
(C)
(D)
Q18Single correctAtoms
The longest wavelength associated with Paschen series is : (Given SI unit)
(A)
(B)
(C)
(D)
Q19Single correctSemiconductor Electronics
The acceptor level of a p-type semiconductor is 6eV. The maximum wavelength of light which can create a hole would be : Given hc eVnm.
(A)
(B)
(C)
(D)
Q20Single correctUnits and Measurements
In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 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 instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?
(A)
(B)
(C)
(D)
Q21NumericalMotion in a Straight Line
A particle moves in a straight line so that its displacement x at any time t is given by . Its acceleration at any time t is where n = ___________
Q22NumericalSystem of Particles and Rotational Motion
Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______ kg.
Q23NumericalMechanical Properties of Solids
A wire of cross sectional area A, modulus of elasticity 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 radian on the points of support. The value of A is _______ (consider ). (given : g m/ )
A horizontal wire of total span labelled 2L stretched between two vertical rigid wall supports (hatched fixed supports at left and right). A 2 kg block (hatched square labelled 2kg) hangs from the midpoint, pulling the wire down into a shallow V. The small sag depth at the middle is labelled x, and the small angle between the sagging wire and the horizontal at each support is labelled theta.
Q24NumericalWaves
Two open organ pipes of lengths 60 cm and 90 cm resonate at and harmonics respectively. The difference of frequencies for the given modes is _______ Hz. (Velocity of sound in air m/s )
Q25NumericalElectrostatic Potential and Capacitance
A capacitor of F capacitance whose plates are separated by 10 mm through air and each plate has area 4 c is now filled equally with two dielectric media of , respectively as shown in figure. If new force between the plates is 8 N. The supply voltage is _______ V.
A parallel-plate capacitor shown side-on with two horizontal plates separated by gap d. The gap between the plates is filled by two dielectric slabs stacked one above the other (each occupying half the gap): the upper region labelled K1 = 2 and the lower region labelled K2 = 3. Vertical double-headed arrow on the left marks the separation d.
Q26NumericalCurrent Electricity
In the given figure an ammeter A consists of a 240 coil connected in parallel to a 10 shunt. The reading of the ammeter is _______ mA.
A series circuit driven by a 24 V battery (cell symbol labelled 24 V at the bottom). In series is a resistor labelled 140.4 ohm (zig-zag resistor at top). Then a parallel combination forming the ammeter A: a 240 ohm coil branch in parallel with a 10 ohm shunt branch, with the ammeter symbol (circle with A) on the right side of the loop.
Q27NumericalMoving Charges and Magnetism
A coil having 100 turns, area of , 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 is _______ J.
Q28NumericalAlternating Current
For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 25nF. If resistance of 200 and 100mH inductor is being used in the given circuit. The frequency of ac source is _______ Hz. (given )
Q29NumericalWave Optics
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 _______.
Q30NumericalAtoms
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 eVnm, e C ).

Chemistry30 questions

Q31Single correctSolutions
Molality ( m ) of 3M aqueous solution of NaCl is : (Given : Density of solution g m, Molar mass in gmo : Na , Cl )
(A)
(B)
(C)
(D)
Q32Single correctChemical and Ionic Equilibrium
The ratio for the reaction : is :
(A)
(B)
(C)
(D)
Q33Single correctRedox Reactions
Match List - I with List - II.
List-IList-II
A. I. Decomposition
B. II. Displacement
C. III. Disproportionation
D. IV. Combination
Choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q34Single correctp-Block Elements
The number of ions from the following that are expected to behave as oxidising agent is :
(A)
(B)
(C)
(D)
Q35Single correctp-Block Elements
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 other elements can expand their covalence due to presence of d orbitals. (D) Heavier elements do not form p bonds. (E) Carbon can exhibit negative oxidation states. Choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q36Single correctPurification and Characterisation of Organic Compounds
The correct statement among the following, for a "chromatography" purification method is :
(A)
(B)
(C)
(D)
Q37Single correctSome Basic Principles of Organic Chemistry
The incorrect statement regarding the geometrical isomers of 2-butene is :
(A)
(B)
(C)
(D)
Q38Single correctElectrochemistry
How can an electrochemical cell be converted into an electrolytic cell?
(A)
(B)
(C)
(D)
Q39Single correctd- and f-Block Elements
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 :
(A)
(B)
(C)
(D)
Q40Single correctCoordination Compounds
The correct IUPAC name of is :
(A)
(B)
(C)
(D)
Q41Single correctChemical Bonding and Molecular Structure
Given below are two statements : Statement I : and both exhibit s d hybridisation. Statement II : Both and exhibit s hybridisation. In the light of the above statements, choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q42Single correctCoordination Compounds
Match List I with List II
List - I (Reaction)List - II (Type of redox reaction)
A. I.
B. II.
C. III.
D. IV.
(A)
(B)
(C)
(D)
Q43Single correctSome Basic Principles of Organic Chemistry
The correct arrangement for decreasing order of electrophilic substitution for above compounds is :
Four benzene rings labelled (I), (II), (III), (IV). (I) is toluene: a benzene ring (drawn with three internal double-bond lines, Kekule) bearing a CH3 substituent at the top-right position. (II) is plain benzene drawn with a circle inside the hexagon, no substituent. (III) is anisole: a benzene ring (circle inside) bearing an OCH3 group at the top. (IV) is (trifluoromethyl)benzene: a benzene ring (Kekule) bearing a CF3 group at the top-right. Labels (I)-(IV) appear centered beneath each ring.
(A)
(B)
(C)
(D)
Q44Single correctAldehydes, Ketones and Carboxylic Acids
Consider the given reaction, identify the major product P.
(A)
(B)
(C)
(D)
Q45Single correctHaloalkanes and Haloarenes
Consider the above chemical reaction. Product " A " is :
A cyclohexane ring (hexagon) attached at one vertex to a CH carbon; that CH bears a chlorine (Cl drawn above on the carbon next to the ring junction) and continues to a CH3 (top) and a -CH2-CH3 ethyl chain to the right, i.e. a secondary alkyl chloride built on a cyclohexyl group, reacting with + NaOH over H2O (with H2O above the reaction arrow) to give 'Major Product A'.
(A)
(B)
(C)
(D)
Q46Single correctOrganic Chemistry - Some Basic Principles and Techniques
The major products formed :
A and B respectively are:
Reaction scheme. Starting material: anisole drawn as a benzene ring with OCH3 substituent at top. Arrow labelled 'HNO3, H2SO4' over it leading to 'A'. Then a second arrow labelled 'Br2 (excess)' on top and 'Fe' below leading to 'B'.
(A)
(B)
(C)
(D)
Q47Single correctOrganic Chemistry - Amines
Identify the product (A) in the following reaction.
Reaction scheme. Aniline drawn as benzene ring with NH2 substituent. Reagent steps listed: (i) NaNO2 + HCl, (ii) Cu2Cl2, (iii) NaOH, 623 K, 300 atm, (iv) H+. Product labelled (A).
(A)
(B)
(C)
(D)
Q48Single correctInorganic Chemistry - Qualitative Analysis
During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in NOH solution when sodium carbonate extract was first acidified with dil. HN and then AgN solution was added. This indicates presence of :
(A)
(B)
(C)
(D)
Q49Single correctInorganic Chemistry - s-Block Elements
Match List I with List II
(A)
(B)
(C)
(D)
Q50Single correctBiological Chemistry - Biomolecules
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 correct answer from the option given below :
Two benzene ring structures joined by 'and'. Left structure: ring with OCH3 at top, NO2 and Br substituents on the ring. Right structure: ring with OCH3 at top, NO2 substituent, and Br at the bottom position.
(A)
(B)
(C)
(D)
Q51NumericalInorganic Chemistry - Hydrogen and its Compounds
Consider the following reactions. The number of protons that do not involve in hydrogen bonding in the product B is ______.
Two reactions. (1) NiS + HNO3 + HCl -> A + NO + S + H2O. (2) A + NH4OH + dimethylglyoxime (two H3C-C=N-OH groups joined by a vertical bond between the central carbons) -> B + NH4Cl + H2O.
Q52NumericalPhysical Chemistry - Atomic Structure
For hydrogen atom, energy of an electron in first excited state is eV. K.E. of the same electron of hydrogen atom is xeV. Value of x is ______ eV. (Nearest integer)
Q53NumericalPhysical Chemistry - Solutions
An amine (X) is prepared by ammonolysis of benzyl chloride. On adding p-toluenesulphonyl chloride to the solution remains clear. Molar mass of the amine (X) formed is ______ gmo. (Given molar mass is integer)
Q54NumericalPhysical Chemistry - Chemical Thermodynamics
For the reaction at 298 K, . kJ mo and kJ mo . The reaction will become spontaneous above ______ K.
Q55NumericalPhysical Chemistry - Chemical Kinetics
Consider two different first order reactions given below (Reaction 1) (Reaction 2) The ratio of and represent the time taken to complete and of Reaction 1 and Reaction 2, respectively, then the value of the ratio is ______ (nearest integer). [Given : and ]
Q56NumericalInorganic Chemistry - d- and f-Block Elements
Total number of and , the spin-only magnetic moment value of the species with least oxidising ability is ______ BM (Nearest integer). (Given atomic number V = 23, Mn = 25, Cr = 24)
Q57NumericalOrganic Chemistry - Some Basic Principles and Techniques
Number of carbocations from the following that are not stabilized by hyperconjugation is ______.
A set of drawn carbocations (positively charged carbon centres), including: a cyclopentadienyl-type cation, structures labelled (tert-Butyl)(tert-Butyl) with a CH3 bearing positive charge, a CH2-OCH3 cation, a small cyclic cation, and a nitrogen-containing N=CH2 cation. Each carries a '+' charge marking the carbocation centre.
Q58NumericalPhysical Chemistry - Solutions
When ' z ' mL methanol (molar mass g; density g/c) is added to 100 mL water (density g/c), the following diagram is obtained.
______ (nearest integer). [Given : Molal freezing point depression constant of water at 273.15 K is 1.86 K kg mo]
Vapour pressure (y-axis) vs Temperature/K (x-axis) diagram. Two intersecting curves labelled 'Frozen system' and 'Methanolic solution' (and 'Water'). Temperature axis marks 270.65 and 273.15 K at the relevant intersection points.
Q59NumericalInorganic Chemistry - Chemical Bonding and Molecular Structure
Total number of species from the following with central atom utilising hybrid orbitals for bonding is ______. , , , , , , , , , ,
Q60NumericalOrganic Chemistry - Some Basic Principles and Techniques
The ratio of number of oxygen atoms to bromine atoms in the product Q is ______ .
Reaction scheme. Anisole drawn as benzene ring with OCH3 at top. Arrow labelled 'HNO3, H2SO4' leading to P (major product). Then arrow labelled '2Br2, Fe' leading to Q (major product).

Mathematics30 questions

Q61Single correctComplex Numbers and Quadratic Equations
If are two distinct complex number such that , then
(A)
(B)
(C)
(D)
Q62Single correctBinomial Theorem and Its Simple Applications
Let . If , then is equal to:
(A)
(B)
(C)
(D)
Q63Single correctPermutations and Combinations
If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at position in this arrangement is :
(A)
(B)
(C)
(D)
Q64Single correctSequences and Series
Let be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle and the same process is repeated infinitely many times. If P is the sum of perimeters and is the sum of areas of all the triangles formed in this process, then :
(A)
(B)
(C)
(D)
Q65Single correctSequences and Series
A software company sets up m number of computer systems 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 value of is equal to:
(A)
(B)
(C)
(D)
Q66Single correctCoordinate Geometry
If be the orthocentre of the triangle whose vertices are and , then the point C lies on the circle:
(A)
(B)
(C)
(D)
Q67Single correctCoordinate Geometry
If the locus of the point, whose distances from the point and are in the ratio , is , then the value of is equal to :
(A)
(B)
(C)
(D)
Q68Single correctLimits, Continuity and Differentiability
is equal to :
(A)
(B)
(C)
(D)
Q69Single correctSets, Relations and Functions
Let . Let R be a relation on A defined by xRy if and only if . Let m be the number of elements in R and n be the minimum number of elements from that are required to be added to R to make it a symmetric relation. Then is equal to :
(A)
(B)
(C)
(D)
Q70Single correctMatrices and Determinants
If A is a square matrix of order 3 such that and , then is equal to :
(A)
(B)
(C)
(D)
Q71Single correctSets, Relations and Functions
Let be a function defined on . Then the range of the function f(x) is equal to ;
(A)
(B)
(C)
(D)
Q72Single correctLimits, Continuity and Differentiability
Suppose for a differentiable function and . If , then is equal to:
(A)
(B)
(C)
(D)
Q73Single correctLimits, Continuity and Differentiability
If the function attains the maximum value at then :
(A)
(B)
(C)
(D)
Q74Single correctIntegral Calculus
If constant, then the maximum value of , is :
(A)
(B)
(C)
(D)
Q75Single correctIntegral Calculus
If the area of the region is then the value of is equal to:
(A)
(B)
(C)
(D)
Q76Single correctDifferential Equations
Suppose the solution of the differential equation represents a circle passing through origin. Then the radius of this circle is :
(A)
(B)
(C)
(D)
Q77Single correctVector Algebra
Let . Then the square of the projection of on is :
(A)
(B)
(C)
(D)
Q78Single correctVector Algebra
Let and . If is a is vector such that and the angle between and is , then is equal to:
(A)
(B)
(C)
(D)
Q79Single correctThree Dimensional Geometry
Let be the image of the point in the line and R be the point . If the area of the triangle PQR is and , then K is equal to :
(A)
(B)
(C)
(D)
Q80Single correctProbability
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:
(A)
(B)
(C)
(D)
Q81NumericalComplex Numbers and Quadratic Equations
Let be roots of . If , then is equal to_______
Q82NumericalSequences and Series
If , and , where , then equal to _______
Q83NumericalConic Sections
The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and , respectively. Let the line touch this hyperbola at . If m is the product of the focal distances of the point , then is equal to _______
Q84NumericalTrigonometry
In a triangle ABC, and . If , where , then is equal to_______
Q85NumericalDeterminants
If the system of equations



has infinitely many solutions, then is equal to_______
Q86NumericalContinuity and Differentiability
Let [t] denote the greatest integer less than or equal to t. Let be a function defined by . Let S be the set of all points in the interval at which f is not continuous. Then is equal to_______
Q87NumericalIntegral Calculus
Let [t] denote the largest integer less than or equal to t. If , where , then is equal to_______
Q88NumericalDifferential Equations
If the solution y(x) of the given differential equation passes through the point , then the value of is equal to_______
Q89NumericalThree Dimensional Geometry
If the shortest distance between the lines and is , then the largest possible value of is equal to _______
Q90NumericalStatistics
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 , where , then is equal to _______

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How many questions are in the JEE Main 2024 April 06, Shift 2 paper?

The JEE Main 2024 April 06, Shift 2 paper has 90 questions — Physics (30), Chemistry (30) and Mathematics (30). Every question is on this page with its correct answer and a step-by-step solution.

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JEE Main awards +4 marks for each correct answer and −1 for a wrong answer, with 0 for questions left unattempted. The paper covers Physics, Chemistry and Mathematics.

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