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JEE Main 2026 24 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202624 Jan, Evening shift

Physics 16Chemistry 23Mathematics 24

Physics

Q28A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity willElectromagnetic Waves
Q29The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the…Oscillations and Waves
Q30Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is _ _ _ cm.Optics
Q31In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the…Units and Measurements
Q34The binding energy for the following nuclear reactions are expressed in MeV. ₂He³+₀n¹→ ₂He⁴ +20 MeV; ₂He⁴+₀n¹→ ₂He⁵ -0.9 MeV. If X₃, X₄, X₅ denote the…Atoms and Nuclei
Q35When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice…Dual Nature of Matter and Radiation
Q37Five persons P₁, P₂, P₃, P₄ and P₅ recorded object distance (u) and image distance (v) using same convex lens having power +5D as (25,96), (30,62), (35,37)…Optics
Q38In the Young's double slit experiment the intensity produced by each one of the individual slits is I o. The distance between two slits is 2 mm. The distance…Optics
Q39A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is…Laws of Motion
Q40A cubical block of density ρ b =600 kg/m³ floats in a liquid of density ρ e =900 kg/m³. If the height of block is H=8.0 cm then height of the submerged part…Properties of Solids and Liquids
Q42A regular hexagon is formed by six wires each of resistance r Ω and the corners are joined to the centre by wires of same resistance. If the current enters at…Current Electricity
Q45A moving coil galvanometer of resistance 100 Ω shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this…Magnetic Effects of Current and Magnetism
Q46A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000-x) μ J of work is done in blowing it further to make its diameter 14 cm…Properties of Solids and Liquids
Q48A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I₁. A small co-centric cylinder of length L/2 and radius R/3…Rotational Motion
Q49A point charge q=1 μ C is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q=24 μ C, distributed uniformly…Electrostatics
Q50In a meter bridge experiment to determine the value of unknown resistance, first the resistances 2 Ω and 3 Ω are connected in the left and right gaps of the…Current Electricity

Chemistry

Q51Find out the statements which are not true. A. Resonating structures with more number of covalent bonds and lesser charge separation are more stable. B. In…Some Basic Principles of Organic Chemistry
Q52A student has planned to prepare acetanilide from aniline using acetic anhydride. The student has started from 9.3 g of aniline. However, the student has…Organic Compounds Containing Nitrogen
Q53The number of possible tripeptides formed involving alanine (ala), glycine (gly) and valine (val), where no amino acid has been used more than once is:Biomolecules
Q54Two liquids A and B form an ideal solution at temperature T K. At T K, the vapour pressures of pure A and B are 55 and 15 kN m ⁻² respectively. What is the…Solutions
Q55Pair of species among the following having same bond order as well as paramagnetic character will be-Chemical Bonding and Molecular Structure
Q56At 298 K, the mole percentage of N₂(g) in air is 80%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of N₂(g) in water at…Solutions
Q57Choose the INCORRECT statementp-Block Elements
Q59In the Group analysis of cations, Ba²⁺ Ca²⁺ are precipitated respectively asPrinciples Related to Practical Chemistry
Q60The heat of atomisation of methane and ethane are 'x' kJ mol ⁻¹ and 'y' kJ mol ⁻¹ respectively. The longest wavelength (λ) of light capable of breaking the…Atomic Structure
Q61The wavelength of light absorbed for the following complexes are in the order [Co(NH₃)₆]³⁺ (I); [Co(H₂O)₆]³⁺ (II); [Co(CN)₆]³⁻ (III); [Co(NH₃)₅(H₂O)]³⁺ (IV)…Coordination Compounds
Q62Consider the following gaseous equilibrium in a closed container of volume 'V' at T(K). P₂(g)+Q₂(g) 2PQ(g). 2 moles each of P₂(g), Q₂(g) and PQ(g) are present…Equilibrium
Q63The correct order of C, N, O and F in terms of second ionisation potential isClassification of Elements and Periodicity in Properties
Q64"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6 oxidation state in "X". The color of the potassium salt of X…d- and f-Block Elements
Q65One mole of Cl₂(g) was passed into 2 L of cold 2M KOH solution. After the reaction, the concentrations of Cl^-, ClO^(- a)nd OH^(- a)re respectively (assume…p-Block Elements
Q67The unsaturated ether on acidic hydrolysis produces carbonyl compounds as shown below:- CH₃-CH=CH-O-CH=CH₂ H₃O⁺ CH₃-CH₂-CH=O and O=CH-CH₃. Based on this…Organic Compounds Containing Oxygen
Q68Given below are two statements: Statement I: The dipole moment of R-CN is greater than R-NC and R-NC can undergo hydrolysis under acidic medium to produce R…Organic Compounds Containing Nitrogen
Q69The wavelength of spectral line obtained in the spectrum of Li²⁺ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, isAtomic Structure
Q70Given below are two statements: Statement I: Cross aldol condensation between two different aldehydes will always produce four different products. Statement…Organic Compounds Containing Oxygen
Q71Grignard reagent RMgBr (P) reacts with water and forms a gas (Q). One gram of Q occupies 1.4 dm ³ at STP. (P) on reaction with dry ice in dry ether followed…Organic Compounds Containing Halogens
Q72Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be 1/30 of the molar conductivity of another weak acid HZ with concentration of 0.02…Redox Reactions and Electrochemistry
Q73The half−life of ⁶⁵Zn is 245 days. After x days, 75% of original activity remained. The value of x in days is _ _ _. (Nearest integer) (Given: log 3 = 0.4771…Chemical Kinetics
Q74A chromium complex with a formula CrCl₃·6H₂O has a spin only magnetic moment value of 3.87 BM and its solution conductivity corresponds to 1: 2 electrolyte…Coordination Compounds
Q750.25 g of an organic compound "A" containing carbon, hydrogen and oxygen was analysed using the combustion method. There was an increase in mass of CaCl₂ tube…Purification and Characterisation of Organic Compounds

Mathematics

Q1Let y=y(x) be a differentiable function in the interval (0,∞) such that y(1)=2, and lim t→ x ((t²y(x)-x²y(t))/(x-t))=3 for each x>0. Then 2y(2) is equal toDifferential Equations
Q2Let a=2 i-5 j+5 k and b= i- j+3 k. If c is a vector such that 2(a× c)+3(b× c)= 0 and (a- b)· c=-97, then | c× k|² is equal toVector Algebra
Q3The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the…Permutations and Combinations
Q4Let [t] denote the greatest integer less than or equal to t. If the function f(x)= b² sin ((π)/2[(π)/2(cos x+ sin x) cos x]), x<0 (sin x-1/2 sin 2x)/(x³), x>0…Limit, Continuity and Differentiability
Q5Let a₁,a₂,a₃,a₄ be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a₁+a₂+a₃+a₄=48 and a₁a₂a₃a₄+l⁴=361, then…Sequence and Series
Q6Consider the following three statements for the function f:(0,∞) defined by f(x)=| log e x|-|x-1|: (I) f is differentiable at all x>0. (II) f is increasing in…Limit, Continuity and Differentiability
Q7Let the angles made with the positive x -axis by two straight lines drawn from the point P(2,3) and meeting the line x+y=6 at a distance √(2/3) from the point…Coordinate Geometry
Q8The largest value of n, for which 40ⁿ divides 60!, isPermutations and Combinations
Q9Let the image of parabola x²=4y, in the line x-y=1 be (y+a)²=b(x-c), a,b,c. Then a+b+c is equal toCoordinate Geometry
Q10The smallest positive integral value of a, for which all the roots of x⁴-ax²+9=0 are real and distinct, is equal toComplex Numbers and Quadratic Equations
Q11Let X=:1≤ x≤19 and for some a,b, Y= +b:x X. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of…Statistics and Probability
Q13Let the length of the latus rectum of an ellipse (x²)/(a²)+(y²)/(b²)=1, (a>b), be 30. If its eccentricity is the maximum value of the function…Coordinate Geometry
Q14(1/3+4/7)+(1/(3²)+1/3×4/7+(4²)/(7²))+(1/(3³)+1/(3²)×4/7+1/3×(4²)/(7²)+(4³)/(7³))+ upto infinite terms, is equal toSequence and Series
Q15Let P=[p ij ] and Q=[q ij ] be two square matrices of order 3 such that q ij =2^((i+j-1))p ij and det (Q)=2¹⁰. Then the value of det (adj(adj P)) is:Matrices and Determinants
Q16The sum of all values of α, for which the shortest distance between the lines (x+1)/(α)=(y-2)/(-1)=(z-4)/(-α) and x/(α)=(y-1)/2=(z-1)/(2α) is 2, isThree Dimensional Geometry
Q17Let f(x)=∫(7x¹⁰+9x⁸)/((1+x²+2x⁹)²)dx, x>0, lim x→0 f(x)=0 and f(1)=1/4. If A= 0 0 1 1/4 f'(1) 1 α² 4 1 and B=adj(adj A) be such that |B|=81, then α² is equal toMatrices and Determinants
Q18Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y²=x and y=|α x-5|-|1-α x|+α x². Then (f(0)+f(1)) is equal toIntegral Calculus
Q19If the domain of the function f(x)= sin ⁻¹(1/(x²-2x-2)) is (-∞,α] [β,γ] [δ,∞), then α+β+γ+δ is equal toSets, Relations and Functions
Q20Let f be a function such that 3f(x)+2f(m/19x)=5x, x≠0, where m=Σ i=1 ⁹(i)². Then f(5)-f(2) is equal toSets, Relations and Functions
Q21Let (h,k) lie on the circle C: x²+y²=4 and the point (2h+1, 3k+2) lie on an ellipse with eccentricity e. Then the value of 5/(e²) is equal to _ _ _.Coordinate Geometry
Q22If f(x) satisfies the relation f(x)=eˣ+∫₀¹(y+xeˣ)f(y) dy, then e+f(0) is equal to _ _ _.Integral Calculus
Q23The number of elements in the set [0,180°]: tan (x+100°)= tan (x+50°) tan x tan (x-50°) is _ _ _.Trigonometry
Q24Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set P(S)× P(S) such that A B=…Statistics and Probability
Q25Let z=(1+i)(1+2i)(1+3i) (1+ni), where i=√(-1). If |z|²=44200, then n is equal to _ _ _.Complex Numbers and Quadratic Equations