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JEE Main 2026 April 08, Shift 2 Question Paper with Solutions

All 72 questions from the JEE Main 2026 (April 08, Shift 2) shift — Physics (24), Chemistry (24) and Mathematics (24) — 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.

Physics24 questions

Q26Single correctUnits and Measurements
A new unit () of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of units if light takes 6 min. 40s to cover this distance?
(A)
(B)
(C)
(D)
Q27Single correctUnits and Measurements
Consider the equation Where H = magnetic field; E = electric field, = permittivity, x = distance, t = time. The values of p, q, r and s respectively are:
(A)
(B)
(C)
(D)
Q28Single correctLaws of Motion
A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take g = 10 m/)
(A)
(B)
(C)
(D)
Q29Single correctKinematics
A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ...... m. (Take g = 10 m/)
(A)
(B)
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(D)
Q30Single correctOptics
A thin biconvex lens is prepared from the glass () both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ......... cm.
(A)
(B)
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(D)
Q31Single correctKinematics
Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ________ m. (Take g = 10 m/)
(A)
(B)
(C)
(D)
Q32Single correctRotational Motion
A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t = 0 the cylinder has a translational velocity m/s, perpendicular to its axis and a rotational velocity about the centre. The time taken by the cylinder to start rolling is ____ seconds. (coefficient of kinetic friction and g = 9.8 m/)
(A)
(B)
(C)
(D)
Q33Single correctProperties of Solids and Liquids
A liquid of density 600 kg/ flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 c and that at B is 20 m. Both the points A and B are in same horizontal plane, the speed of the liquid at A is 10 cm/s. The difference in pressures at A and B points is ______ Pa.
(A)
(B)
(C)
(D)
Q34Single correctProperties of Solids and Liquids
A spherical liquid drop of radius R acquires the terminal velocity when falls through a gas of viscosity . Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity falling through the same gas. The ratio of terminal velocities is ____ .
(A)
(B)
(C)
(D)
Q36Single correctThermodynamics
Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume is ____ J.
(A)
(B)
(C)
(D)
Q37Single correctOscillations and Waves
The frequency of oscillation of a mass m suspended by a spring is . If the length of the spring is cut to half, the same mass oscillates with frequency . The value of is ______ .
(A)
(B)
(C)
(D)
Q38Single correctDual Nature of Matter and Radiation
A monochromatic source of light operating at kW emits photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ____. (Take J.s and m/s).
(A)
(B)
(C)
(D)
Q39Single correctMagnetic Effects of Current and Magnetism
A current carrying circular loop of radius cm with unit normal is placed in a magnetic field, . If T and current A, the torque experienced by the loop is ____ Wb.A. ().
(A)
(B)
(C)
(D)
Q40Single correctElectromagnetic Induction and Alternating Currents
A cm long solenoid has turns per cm and area of c. The current through the solenoid coil varies from A to A in s. The e.m.f. induced in the coil is V. The value of is ____ .
(A)
(B)
(C)
(D)
Q41Single correctElectrostatics
Two point charges and are placed at points and respectively. Force on charge is ____ N. (Take SI Units).
(A)
(B)
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Q42Single correctOptics
Light ray incident along a vector emerges out along vector as shown in the figure below. The value of C is ____ . (Medium 1 above the interface has , medium 2 below has .)
A horizontal interface separates medium 1 (mu1 = 1, above) from medium 2 (mu2 = 1.5, below). An incident ray from point A strikes point O on the interface making angle alpha with the vertical normal, and the refracted ray continues from O to point B in the lower medium making angle beta with the normal; beta < alpha indicating bending toward the normal.
(A)
(B)
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Q43Single correctDual Nature of Matter and Radiation
and be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength and , respectively. If then the work function of material is given by :
(A)
(B)
(C)
(D)
Q44Single correctAtoms and Nuclei
Two radioactive substances A and B of mass numbers and respectively, shows spontaneous -decay with same Q value of MeV. The ratio of energies of -rays produced by A and B is ____ .
(A)
(B)
(C)
(D)
Q45Single correctElectronic Devices
The output for the given inputs and to the circuit is :
A logic circuit: inputs A and B feed two AND gates whose outputs combine into a final OR gate giving output Y. Alongside are the input waveforms: A is high (1) during the interval t = 1 to 2 s and low otherwise; B is high (1) during t = 0 to 1 s and low otherwise. Time axis marked at 0, 1, 2, 3 s.
(A)
(B)
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Q46NumericalElectrostatics
A parallel plate capacitor is having separation between plates . It has a capacitance of when the space between the plates is filled with an insulating material of resistivity and resistance . Relative permittivity of the insulating material is . The value of is ________. (Take permittivity of free space )
Q47NumericalOptics
Some distant star is to be observed by some telescope of diameter of objective lens a, at an angular resolution of radian. If the wavelength of light from the star reaching the telescope is , the minimum diameter of the objective lens of the telescope is ______ cm. (nearest integer)
Q48NumericalMagnetic Effects of Current and Magnetism
A particle carrying a charge of is moving with velocity of in a region having magnetic field . It moves a distance of meter along when it completes 5 revolutions. The value of is ______.
Q49NumericalCurrent Electricity
The stored charge in the capacitor in steady state of the following circuit is ______ .
Circuit with a 12 V source connected to a ladder network of resistors. The top branch has 5 ohm, 4 ohm and 10 ohm resistors in series; the bottom branch has 2 ohm and 2 ohm resistors; vertical branches contain 12 ohm, 10 ohm and 4 ohm resistors, and a 100 microfarad capacitor is connected on the right side across the last vertical branch.
Q50NumericalKinematics
Two masses of and are accelerated from an initial speed of and , respectively. The distances traversed by the masses in the second are and , respectively. The ratio of their momenta after is . The value of x is ______.

Chemistry24 questions

Q51Single correctSome Basic Concepts in Chemistry
Match List - I with List - II.
List - I Mass of substanceList - II Number of atoms
A. 1.8 mg waterI.
B. 9.8 mg sulphuric acidII.
C. 1.8 mg carbonIII.
D. 5.85 mg salt (NaCl)IV.
(A)
(B)
(C)
(D)
Q52Single correctSolutions
Given below are two statements:
Given: Molar mass of C, H, O, Cl are 12, 1, 16 and 35.5 , respectively.
Statement I: In 30%(w/w) solution of methanol in (at T K), the mole fraction of is equal to 0.33.
Statement II: Mixture of methanol and shows positive deviation from Raoult's law.
In the light of the above statements, choose the correct answer from the options given below:
(A)
(B)
(C)
(D)
Q53Single correctChemical Bonding and Molecular Structure
Bromine trifluoride autoionizes to form and . The shapes of the cation and anion are respectively ______, and ______.
(A)
(B)
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Q54Single correctSolutions
Which of the following statements are not correct?
A. For water, magnitude of is more than the magnitude of .
B. The elevation in boiling point of water when a non-volatile solute is added to it is larger in magnitude than its depression in freezing point.
C. Osmotic pressure measurement is preferred over any other colligative property to determine molar mass of proteins and polymers.
D. The dimerised form of benzoic acid in benzene is
Dimerised form of benzoic acid in benzene shown as two benzoic acid molecules linked by hydrogen bonds: C6H5-C(=O)-OH ... O=C-(OH)-C6H5
(A)
(B)
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(D)
Q55Single correctEquilibrium
Consider the following reactions in which all the reactants and products are present in gaseous state:
;
;
The value of for the equilibrium is:
(A)
(B)
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(D)
Q56Single correctRedox Reactions and Electrochemistry
Given at 298 K:
Volt
Volt
The in Volt at 298 K is given by:
(A)
(B)
(C)
(D)
Q57Single correctChemical Kinetics
Given below are two statements:
and
Statement I: When , the room temperature rate constant is doubled by a increase in temperature (298 K to 308 K).
Statement II: For a first order reaction , the plot of /s versus /mol is a straight line passing through the origin with positive slope. Here is the initial concentration of A and is the half life of reaction.
In the light of the above statements, choose the correct answer from the options given below:
Graph with y-axis t(1/2)/s and x-axis [A]0/mol L^-1, showing a straight line of positive slope passing through the origin (as drawn in Statement II).
(A)
(B)
(C)
(D)
Q58Single correctClassification of Elements and Periodicity in Properties
Match List - I with List - II.
List - I Electronic configuration of neutral atom (where n = 2)List - II 1st Ionization Energy ()
A. I. 2080
B. II. 899
C. III. 800
D. IV. 1402
(A)
(B)
(C)
(D)
Q59Single correctp-Block Elements
Find the correct statements related to group 15 hydrides.
A. Reducing nature increases from to .
B. Tendency to donate lone pair of electrons decreases from to .
C. The stability of hydrides decreases from to .
D. HEH bond angle decreases from to (E = Elements of group 15).
Choose the correct answer from the options given below:
(A)
(B)
(C)
(D)
Q60Single correctd- and f-Block Elements
Given below are two statements:
Statement I: The number of pairs among , , and in which both ions are coloured is 3.
Statement II: The number of pairs among , and ions in which both are diamagnetic is 3.
In the light of the above statements, choose the correct from the options given below:
(A)
(B)
(C)
(D)
Q61Single correctd- and f-Block Elements
Given below are two statements for catalytic properties of transition metals.
Statement I: First row transition metals which act as catalyst utilise their 3d electrons only for formation of bonds between reactant molecules and atoms on the surface of catalyst.
Statement II: There is increase in the concentration of reactants on the surface of catalyst which strengthens the bonds in reacting molecules.
In the light of the above statements, choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q62Single correctPurification and Characterisation of Organic Compounds
Given below are two statements :
Statement I: Vapours of the liquid with higher boiling point condense before vapours of the liquid with lower boiling points in fractional distillation.
Statement II: The vapours rising up in the fractionating column become richer in high boiling component of the mixture.
In the light of the above statements, choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q63Single correctSome Basic Principles of Organic Chemistry
The major product of which of the following reaction is not obtained by rearrangement reaction?
(A)
(B)
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(D)
Q65Single correctHydrocarbons
n-Butane on monochlorination under photochemical condition gives an optically active compound "P". "P" on further chlorination gives dichloro compounds.
The number of dichloro compounds obtained (ignore stereoisomers) is :
(A)
(B)
(C)
(D)
Q66Single correctOrganic Compounds Containing Halogens
Given below are two statements :
Statement I: Due to increase in van der Waals forces, the order of boiling points is .
(A)
(B)
(C)
(D)
Q67Single correctOrganic Compounds Containing Nitrogen
Consider the following reaction.
A piperidine ring with a carbonyl (lactam/amide C=O on ring carbon adjacent to N), the nitrogen bearing a CH(CH3)-CHO side chain (2-methyl aldehyde). Reagents: (i) NaBH4/MeOH, (ii) NaOH(aq.), heat, (iii) H3O+ giving product P.
(A)
(B)
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Q68Single correctOrganic Compounds Containing Nitrogen
Which statements are True?
A. In Hoffmann bromamide degradation, 4 moles of NaOH and 2 moles of are consumed per mole of an amide
B. Hoffmann bromamide reaction is not given by alkyl amides
C. Primary amines can be synthesized by Hoffmann bromamide degradation.
D. Secondary amide on reaction with and NaOH will give secondary amine.
E. The by-products of Hoffmann degradation are and .
Choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q69Single correctBiomolecules
The incorrect statement from the following with respect to carbohydrates is :
(A)
(B)
(C)
(D)
Q70Single correctBiomolecules
Which of the following amino acid will give violet coloured complex with neutral ferric chloride solution?
(A)
(B)
(C)
(D)
Q71NumericalCoordination Compounds
Number of paramagnetic complexes among the following is ______.
Q72NumericalOrganic Compounds Containing Oxygen
'x' is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. 'y' is the major product obtained from the benzene by reacting it with ethanoyl chloride in the presence of anhydrous . Product (major) obtained by heating x and y in the presence of alkali is z. Total number of electrons in z is ______
Q73NumericalAtomic Structure
Consider two radiations of wavelengths
1.
2.
The ratio of the energies of these two radiations is ______ (Nearest integer).
Q74NumericalChemical Thermodynamics
Consider the reaction:

The magnitude of enthalpy change for the reaction in is ______. (Nearest integer)
Given: , ,
Q75NumericalEquilibrium
Solid carbon, CaO and are mixed and allowed to attain equilibrium at T K.


____ atm

Mathematics24 questions

Q1Single correctSets, Relations and Functions
Consider the relation R on the set defined by if and only if . Then, among the statements :
I. The number of elements in R is 17
II. R is an equivalence relation
(A)
(B)
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(D)
Q2Single correctComplex Numbers and Quadratic Equations
The number of values of , satisfying the equations and , is :
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Q3Single correctMatrices and Determinants
If the system of linear equations:



has infinitely many solutions, then the value of equals:
(A)
(B)
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(D)
Q4Single correctMatrices and Determinants
Let and . If , then equals :
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Q5Single correctTrigonometry
Let upto 40 terms. If is a root of the equation , , then is equal to :
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Q6Single correctStatistics and Probability
A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are and . The probabilities that the candidate reaches late at the examination centre are and if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :
(A)
(B)
(C)
(D)
Q7Single correctStatistics and Probability
A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :
(A)
(B)
(C)
(D)
Q8Single correctBinomial Theorem and its Simple Applications
If , then is equal to :
(A)
(B)
(C)
(D)
Q9Single correctPermutations and Combinations
A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :
(A)
(B)
(C)
(D)
Q10Single correctCo-ordinate Geometry
If a straight line drawn through the point of intersection of the lines and , meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is :
(A)
(B)
(C)
(D)
Q11Single correctCo-ordinate Geometry
Let O be the vertex of the parabola and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is :
(A)
(B)
(C)
(D)
Q12Single correctTrigonometry
Let and , where inverse trigonometric functions take only the principal values. Given below are two statements :
Statement I: .
Statement II: .
In the light of the above statements, choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q13Single correctLimit, Continuity and Differentiability
For the function , consider the following statements:
Statement I : f is differentiable for all .
Statement II: f is increasing in .
In the light of the above statements, choose the correct answer from the options given below :
(A)
(B)
(C)
(D)
Q14Single correctVector Algebra
Let , and a vector be such that . If , then is equal to :
(A)
(B)
(C)
(D)
Q15Single correctThree Dimensional Geometry
Let the foot of perpendicular from the point on the line be the point . Then the distance between the lines and is equal to:
(A)
(B)
(C)
(D)
Q17Single correctDifferential Equations
Let be the solution of the differential equation . Then equals:
(A)
(B)
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(D)
Q18Single correctIntegral Calculus
Let be a function defined as . Let , where . If , then the area of the region bounded by the curves and is:
(A)
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(D)
Q19Single correctLimit, Continuity and Differentiability
Let . If f is continuous at , then the value of is :
(A)
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(D)
Q20Single correctCo-ordinate Geometry
Let represent an ellipse with major axis along y-axis, where f is a strictly decreasing positive function on . If the set of all possible values of a is , then is equal to :
(A)
(B)
(C)
(D)
Q21NumericalComplex Numbers and Quadratic Equations
The sum of squares of all the real solutions of the equation is equal to
Q22NumericalIntegral Calculus
If , then is equal to
Q23NumericalThree Dimensional Geometry
Let a line pass through the origin and be perpendicular to the lines and . If , is the point on at a distance of from the point of intersection of and , then is equal to .................
Q24NumericalCo-ordinate Geometry
Consider the circle . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle , then is equal to......
Q25NumericalSequence and Series
Let f be a polynomial function such that and . Then is equal to ______.

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Frequently Asked Questions

How many questions are in the JEE Main 2026 April 08, Shift 2 paper?

The JEE Main 2026 April 08, Shift 2 paper has 72 questions — Physics (24), Chemistry (24) and Mathematics (24). Every question is on this page with its correct answer and a step-by-step solution.

What is the marking scheme for JEE Main?

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.

Are the answer key and step-by-step solutions provided for the 2026 April 08, Shift 2 paper?

Yes — every question shows the correct answer (answer key) and a detailed step-by-step solution, free to read online.

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