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JEE Main 2026 28 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202628 Jan, Morning shift

Physics 17Chemistry 20Mathematics 23

Physics

Q26Given below are two statements: Statement I: A plane wave after passing through prism remains as plane wave but passing through small pin hole may become…Optics
Q31For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 Ω is same when both the cells are connected…Current Electricity
Q32The electric field of an electromagnetic wave travelling through a medium is given by E(x,t)=25 sin (2.0×10¹⁵t-10⁷x) n then the refractive index of the medium…Electromagnetic Waves
Q33In the potentiometer, when the cell in the secondary circuit is shunted with 4 Ω resistance, the balance is obtained at the length 120 cm of wire. Now when…Current Electricity
Q34Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The…Kinematics
Q35The magnetic field at the centre of a current carrying circular loop of radius R is 16 μ T. The magnetic field at a distance x= 3R on its axis from the centre…Magnetic Effects of Current and Magnetism
Q37A block of mass 5 kg is moving on an inclined plane which makes an angle of 30° with the horizontal. Friction coefficient between the block and inclined plane…Laws of Motion
Q38When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4^(th) mark on vernier scale…Units and Measurements
Q39The electric current in the circuit is given as i=i₀(t/T). The r.m.s current for the period t=0 to t=T is _ _ _.Electromagnetic Induction and Alternating Currents
Q41Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0×10⁻⁵ m² and 4.5×10⁻⁵ m², respectively…Properties of Solids and Liquids
Q42The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index = 1.7) are same. If the curvature of…Optics
Q44Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from…Electrostatics
Q4510 kg of ice at -10° C is added to 100 kg of water to lower its temperature from 25° C. Consider no heat exchange to surroundings. The decrement to the…Thermodynamics
Q46A convex lens of refractive index 1.5 and focal length f=18 cm is immersed in water. The difference in focal lengths of the given lens when it is in water and…Optics
Q47A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n cm. The…Rotational Motion
Q48The ratio of de Broglie wavelength of a deutron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n:1. The value of n is _ _ _…Dual Nature of Matter and Radiation
Q49The displacement of a particle, executing simple harmonic motion with time period T, is expressed as x(t)=A sin ω t, where A is the amplitude. The maximum…Oscillations and Waves

Chemistry

Q51Given below are two statements: Statement I: The number of species among BF₄^-, SiF₄, XeF₄ and SF₄, that have unequal E–F bond lengths is two. Here, E is the…Chemical Bonding and Molecular Structure
Q5220.0 dm³ of an ideal gas 'X' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa. Which of the following…Chemical Thermodynamics
Q53An organic compound undergoes first order decomposition. The time taken for decomposition to (1/8)^(th) and (1/10)^(th) of its initial concentration are t 1/8…Chemical Kinetics
Q55Given below are two statements: Statement I: The number of pairs, from the following, in which both the ions are coloured in aqueous solution is 3. [ Sc³⁺…d- and f-Block Elements
Q57The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. (R = Rydberg constant)Atomic Structure
Q58Ph - CH = CH₂ [HBr](PhCOO)₂ Product. Consider the above reaction A. The reaction proceeds through a more stable radical intermediate. B. The role of peroxide…Hydrocarbons
Q61Regarding the hydrides of group 15 elements EH₃ (E = N, P, As, Sb), select the correct statement from the following: A. The stability of hydrides decreases…p-Block Elements
Q62Consider the following reaction sequence: Compound (x) [76.6% C, 6.38% H, vapour density 47] [(ii) H₃O⁺](i) CO₂, NaOH, 120° C, high pressure Compound (y)…Organic Compounds Containing Oxygen
Q63At T(K), 2 moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg. At this stage, one mole of A and…Solutions
Q64CORRECT order of stability for the following is CH₂=CH^-, CH₃-CH₂^-, CH C^-Some Basic Principles of Organic Chemistry
Q65Consider a weak base 'B' of pK b =5.699. 'x' mL of 0.02 M HCl and 'y' mL of 0.02 M weak base 'B' are mixed to make 100 mL of a buffer of pH 9 at 25°C. The…Equilibrium
Q66Given below are two statements: Statement I: Griss–Ilosvay test is used for the detection of nitrite ion, which involves the use of sulphanilic acid and α…Principles Related to Practical Chemistry
Q67Given below are two statements for the following reaction sequence. Compound 'X' (molecular formula C₃H₆Cl₂) excess of NaNH₂ Compound 'Y'; Y dil. H₂SO₄, Hg²⁺…Hydrocarbons
Q68The correct statement among the following is:Coordination Compounds
Q70In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.Classification of Elements and Periodicity in Properties
Q710.53 g of an organic compound (x) when heated with excess of nitric acid (concentrated) and then with silver nitrate gave 0.75 g of silver bromide…Purification and Characterisation of Organic Compounds
Q72Consider the following redox reaction taking place in acidic medium BH₄^-(aq)+ClO₃^-(aq) H₂BO₃^-(aq)+Cl^-(aq) If the Nernst equation for the above balanced…Redox Reactions and Electrochemistry
Q73X is the number of geometrical isomers exhibited by [Pt(NH₃)(H₂O)BrCl]. Y is the number of optically inactive isomer(s) exhibited by [CrCl₂(ox)₂]³⁻. Z is the…Coordination Compounds
Q74Consider the dissociation equilibrium of the following weak acid HA H⁺(aq)+A^-(aq) If the pKa of the acid is 4, then the pH of 10 mM HA solution is _ _ _…Equilibrium
Q75500 mL of 1.2 M KI solution is mixed with 500 mL of 0.2 M KMnO₄ solution in basic medium. The liberated iodine was titrated with standard 0.1 M Na₂S₂O₃…Redox Reactions and Electrochemistry

Mathematics

Q1Let f be a polynomial function such that f(x²+1)=x⁴+5x²+2, for all x. Then ∫₀³ f(x) dx is equal toIntegral Calculus
Q2For three unit vectors a, b, c satisfying | a- b|²+| b- c|²+| c- a|²=9 and |2 a+k b+k c|=3, the positive value of k isVector Algebra
Q3If the distances of the point (1,2,a) from the line (x-1)/1=y/2=(z-1)/1 along the lines L₁:(x-1)/3=(y-2)/4=(z-a)/b and L₂:(x-1)/1=(y-2)/4=(z-a)/c are equal…Three Dimensional Geometry
Q4The area of the region R=\(x,y): xy≤ 8, 1≤ y≤ x², x≥ 0 isIntegral Calculus
Q5The value of Σ k=1 ^(∞)(-1)^(k+1)((k(k+1))/(k!)) isSequence and Series
Q6If g(x)=3x²+2x-3, f(0)=-3 and 4g(f(x))=3x²-32x+72, then f(g(2)) is equal to:Sets, Relations and Functions
Q7The common difference of the A.P.: a₁,a₂,,a m is 13 more than the common difference of the A.P.: b₁,b₂,,b n. If b₃₁=-277, b₄₃=-385 and a₇₈=327, then a₁ is…Sequence and Series
Q8Let y=y(x) be the solution of the differential equation xdy/dx- sin 2y=x³(2-x³) cos ² y, x≠0. If y(2)=0, then tan (y(1)) is equal toDifferential Equations
Q9Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+2 2y=4. If the co-ordinates of the vertex A are (α,β), then…Coordinate Geometry
Q10If (tan (A-B))/(tan A)+(sin ²C)/(sin ²A)=1, A,B,C (0,(π)/2), thenTrigonometry
Q11The value of lim x→0 (log e (sec (ex)· sec (e²x)· · sec (e¹⁰x)))/(e²-e^(2 cos x)) is equal toLimit, Continuity and Differentiability
Q12Let z be a complex number such that |z-6|=5 and |z+2-6i|=5. Then the value of z³+3z²-15z+141 is equal toComplex Numbers and Quadratic Equations
Q13If α,β, where α<β, are the roots of the equation λ x²-(λ+3)x+3=0 such that 1α- 1β=1/3, then the sum of all possible values of λ isComplex Numbers and Quadratic Equations
Q14Let S=\1,2,3,4,5,6,7,8,9. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated…Permutations and Combinations
Q15A bag contains 10 balls out of which k are red and (10-k) are black, where 0≤ k≤10. If three balls are drawn at random without replacement and all of them are…Statistics and Probability
Q16Let A, B and C be three 2×2 matrices with real entries such that B=(I+A)⁻¹ and A+C=I. If BC= 1 -5 -1 2 and CB x₁ x₂ = 12 -6, then x₁+x₂ isMatrices and Determinants
Q18The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation…Statistics and Probability
Q19Let S= ³+ax²+bx+c: a,b,c and a,b,c≤20 be a set of polynomials. Then the number of polynomials in S, which are divisible by x²+2, isComplex Numbers and Quadratic Equations
Q20If ∫((1-5 cos ²x)/(sin ⁵x cos ²x))dx=f(x)+C, where C is the constant of integration, then f(π6)-f(π4) is equal toIntegral Calculus
Q21For some θ (0, π2), let the eccentricity and the length of the latus rectum of the hyperbola x²-y² sec ²θ=8 be e₁ and l₁, respectively, and let the…Coordinate Geometry
Q23The value of Σ r=1 ²⁰(|√(π(∫₀^(r) x| sin π x| dx))|) is _ _ _Integral Calculus
Q24If k= tan (π4+1/2 cos ⁻¹(2/3))+ tan (1/2 sin ⁻¹(2/3)), then the number of solutions of the equation sin ⁻¹(kx-1)= sin ⁻¹x- cos ⁻¹x is _ _ _Trigonometry
Q25In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R-(a,b), then a²+b² is…Sequence and Series