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JEE Main 2024 29 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202429 Jan, Morning shift

Physics 27Chemistry 23Mathematics 30

Physics

Q57When a hydrogen atom going from n=2 to n=1 emits a photon, its recoil speed is x/5 ~m / s. Where x= _ _ _ _. (Use, mass of hydrogen atom =1.6 × 10⁻²⁷ ~kg)Atoms and Nuclei
Q59A 16 Ω wire is bend to form a square loop. A 9 ~V battery with internal resistance 1 Ω is connected across one of its sides. If a 4 μ F capacitor is connected…Electrostatics
Q66A square loop of side 10 ~cm and resistance 0.7 Ω is placed vertically in east-west plane. A uniform magnetic field of 0.20 T is set up across the plane in…Electromagnetic Induction and Alternating Currents
Q67An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +σ. The electron…Electrostatics
Q73The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of 20 ~cm from its center is 1.5 × 10⁻⁵ ~T ~m. The magnetic…Magnetic Effects of Current and Magnetism
Q74A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 ~m high and 0.1 ~m wide. The minimum velocity u with which that ball just…Kinematics
Q76In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ~ms⁻¹ and 65 ~ms⁻¹ respectively…Properties of Solids and Liquids
Q78A cylinder is rolling down on an inclined plane of inclination 60^(°). It's acceleration during rolling down will be x/(√(3)) m / s², where x= _ _ _ _ (use…Rotational Motion
Q79When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x/8, where x= _ _ _ _ _.Oscillations and Waves
Q5953A capacitor of capacitance 100 μ F is charged to a potential of 12 ~V and connected to a 6.4 ~mH inductor to produce oscillations. The maximum current in the…Electromagnetic Induction and Alternating Currents
Q6059The explosive in a Hydrogen bomb is a mixture of ₁ H², ₁ H³ and ₃ Li⁶ in some condensed form. The chain reaction is given by ₃ Li⁶+ ₀ n¹ → ₂ He⁴+ ₁ H³ ₁ H²+ ₁…Atoms and Nuclei
Q6295If the radius of curvature of the path of two particles of same mass are in the ratio 3: 4, then in order to have constant centripetal force, their velocities…Kinematics
Q6405The electric current through a wire varies with time as I=I₀+β t, where I₀=20 ~A and β=3 ~A / s. The amount of electric charge crossed through a section of…Current Electricity
Q6481The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of 24 Ω is applied. The resistance of galvanometer coil will be:Current Electricity
Q6482A galvanometer having coil resistance 10 Ω shows a full scale deflection for a current of 3 ~mA. For it to measure a current of 8 ~A, the value of the shunt…Current Electricity
Q6590The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of…Dual Nature of Matter and Radiation
Q6716Match List I with List II List - I List - II (A) B · d l=μ o i c +μ o ε o (d φ E)/(d t) (I) Gauss' law for electricity (B) E · d l=(d φ B)/(d t) (II) Gauss'…Electromagnetic Induction and Alternating Currents
Q6985Two charges of 5 Q and -2 Q are situated at the points (3 a, 0) and (-5 a, 0) respectively. The electric flux through a sphere of radius ' 4 a ' having center…Electrostatics
Q7054A biconvex lens of refractive index 1.5 has a focal length of 20 ~cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:Optics
Q7088A convex mirror of radius of curvature 30 ~cm forms an image that is half the size of the object. The object distance is:Optics
Q7171At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as R.)Gravitation
Q7432Two vessels A and B are of the same size and are at same temperature. A contains 1 ~g of hydrogen and B contains 1 ~g of oxygen. P A and P B are the pressures…Thermodynamics
Q7851A body starts moving from rest with constant acceleration covers displacement S₁ in first (p-1) seconds and S₂ in first p seconds. The displacement S₁+S₂ will…Kinematics
Q8032Given below are two statements: Statement I: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be…Properties of Solids and Liquids
Q8320The resistance R=V/I where V=(200 ± 5) V and I=(20 ± 0.2) A, the percentage error in the measurement of R is:Units and Measurements
Q8594The potential energy function (in J) of a particle in a region of space is given as U=(2 x²+3 y³+2 z). Here x, y and z are in meter. The magnitude of x…Work, Energy and Power
Q8625A block of mass 100 ~kg slides over a distance of 10 ~m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work…Work, Energy and Power

Chemistry

Q1From the compounds given below, number of compounds which give positive Fehling's test is _ _ _ _ _. Benzaldehyde, Acetaldehyde, Acetone, Acetophenone…Organic Compounds Containing Oxygen
Q4Number of compounds among the following which contain sulphur as heteroatom is _ _ _ _ _ _. Furan, Thiophene, Pyridine, Pyrrole, Cysteine, TyrosineBiomolecules
Q5Number of compounds with one lone pair of electrons on central atom amongst following is _ _ _ _ _. O₃, H₂ O, SF₄, ClF₃, NH₃, BrF₅, XeF₄Chemical Bonding and Molecular Structure
Q6The number of species from the following which are paramagnetic and with bond order equal to one is _ _ _ _ _. H₂, He₂⁺, O₂⁺, N₂²⁻, O₂²⁻, F₂, Ne₂⁺, B₂Chemical Bonding and Molecular Structure
Q8For the reaction N₂ O 4(~g) 2 NO 2(~g), K p =0.492 ~atm at 300 ~K. K c for the reaction at same temperature is _ _ _ _ _ × 10⁻². (Given: R=0.082 ~L ~atm…Equilibrium
Q9For a reaction taking place in three steps at same temperature, overall rate constant K=(K₁ ~K₂)/(~K₃). If Ea₁, Ea₂ and Ea₃ are 40, 50 and 60 ~kJ / mol…Chemical Kinetics
Q13The mass of zinc produced by the electrolysis of zine sulphate solution with a steady current of 0.015 ~A for 15 minutes is _ _ _ _ _ × 10⁻⁴ ~g. (Atomic mass…Redox Reactions and Electrochemistry
Q22The osmotic pressure of a dilute solution is 7 × 10⁵ ~Pa at 273 ~K. Osmotic pressure of the same solution at 283 ~K is _ _ _ _ _ × 10⁴ Nm⁻².Solutions
Q23A solution of H₂ SO₄ is 31.4% H₂ SO₄ by mass and has a density of 1.25 ~g / mL. The molarity of the H₂ SO₄ solution is _ _ _ _ M (nearest integer) [Given…Some Basic Concepts in Chemistry
Q89The interaction between π bond and lone pair of electrons present on an adjacent atom is responsible forSome Basic Principles of Organic Chemistry
Q219Type of amino acids obtained by hydrolysis of proteins is:Biomolecules
Q388The difference in energy between the actual structure and the lowest energy resonance structure for the given compound isChemical Bonding and Molecular Structure
Q574Match List I with List II List - I (Substances) List - II (Element Present) (A) Ziegler catalyst (I) Rhodium (B) Blood Pigment (II) Cobalt (C) Wilkinson…Coordination Compounds
Q793KMnO₄ decomposes on heating at 513 ~K to form O₂ along withd- and f-Block Elements
Q1159Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Aryl halides cannot be prepared by…Organic Compounds Containing Halogens
Q1535Identify the incorrect pair from the following:p-Block Elements
Q1592Given below are two statements: Statement I: The electronegativity of group 14 elements from Si to Pb, gradually decreases. Statement II: Group 14 contains…Classification of Elements and Periodicity in Properties
Q1621Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The first ionisation enthalpy decreases…Classification of Elements and Periodicity in Properties
Q1781Appearance of blood red colour, on treatment of the sodium fusion extract of an organic compound with FeSO₄ in presence of concentrated H₂ SO₄ indicates the…Principles Related to Practical Chemistry
Q1789Chlorine undergoes disproportionation in alkaline medium as shown below: aCl 2(~g) +b OH (aq) ⁻ → c ClO (aq) ⁻+d Cl (aq) ⁻+e H₂ O (l) The values of a, b, c…Redox Reactions and Electrochemistry
Q1800In alkaline medium, MnO₄⁻ oxidises I⁻ toRedox Reactions and Electrochemistry
Q2214The correct set of four quantum numbers for the valence electron of rubidium atom (Z=37) is:Atomic Structure
Q2308Which of the following is not correct?Chemical Thermodynamics

Mathematics

Q28A line with direction ratios 2,1,2 meets the lines x=y+2=z and x+2=2 y=2 z respectively at the points P and Q. If the length of the perpendicular from the…Three Dimensional Geometry
Q29Let f(x)=2ˣ-x², x R. If m and n are respectively the number of points at which the curves y=f(x) and y=f^()(x) intersect the x -axis, then the value of m+n is…Limit, Continuity and Differentiability
Q31The area (in sq. units) of the part of the circle x²+y²=169 which is below the line 5 x-y=13 is (π α)/(2 β)-65/2+(α)/(β) sin ⁻¹(12/13), where α, β are coprime…Integral Calculus
Q32If the points of intersection of two distinct conics x²+y²=4 b and (x²)/16+(y²)/(b²)=1 lie on the curve y²=3 x², then 3 √(3) times the area of the rectangle…Integral Calculus
Q33If (¹¹ C₁)/2+(¹¹ C₂)/3+ +(¹¹ C₉)/10=n/m with gcd(n, m)=1, then n+m is equal to _ _ _ _.Binomial Theorem and Its Simple Applications
Q34Equations of two diameters of a circle are 2 x-3 y=5 and 3 x-4 y=7. The line joining the points (-22/7,-4) and (-1/7, 3) intersects the circle at only one…Coordinate Geometry
Q36Let α, β be the roots of the equation x²-x+2=0 with Im(α)>Im(β). Then α⁶+α⁴+β⁴-5 α² is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q40If the solution curve y=y(x) of the differential equation (1+y²)(1+ log e x) d x+x d y=0, x > 0 passes through the point (1,1) and y(e)=(α- tan (3/2))/(β+ tan…Differential Equations
Q46All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial…Permutations and Combinations
Q52If the mean and variance of the data 65,68,58,44,48,45,60, α, β, 60 where α> β, are 56 and 66.2 respectively, then α²+β² is equal to _ _ _ _ _.Statistics and Probability
Q2382Let O be the origin and the position vectors of A and B be 2 i+2 j+k and 2 i+4 j+4 k respectively. If the internal bisector of AOB meets the line AB at C…Three Dimensional Geometry
Q2529Let P Q R be a triangle with R(-1,4,2). Suppose M(2,1,2) is the mid point of PQ. The distance of the centroid of PQR from the point of intersection of the…Three Dimensional Geometry
Q2733Consider the function f:[1/2, 1] → R defined by f(x)=4 √(2) x³-3 √(2) x-1. Consider the statements (I) The curve y=f(x) intersects the x -axis exactly at one…Limit, Continuity and Differentiability
Q3167If z=1/2-2 i is such that |z+1|=α z+β(1+i), i=√(-1) and α, β R, then α+β is equal toComplex Numbers and Quadratic Equations
Q3320lim x → (π)/2 (1/((x - (π)/2)²)∫ x³ ^(((π)/2)³) cos (t^(1/3))dt) is equal toIntegral Calculus
Q3474If the value of the integral ∫ -(π)/2 ^((π)/2)((x² cos x)/(1+πˣ)+(1+ sin ² x)/(1+e^ sin x²¹²³)) d x=(π)/4(π+a)-2, then the value of a isIntegral Calculus
Q3565A function y=f(x) satisfies f(x) sin 2 x+ sin x-(1+ cos ² x) f^()(x)=0 with condition f(0)=0. Then, f((π)/2) is equal toDifferential Equations
Q3700Suppose f(x)=((2ˣ+2⁻ˣ) tan x √(tan ⁻¹(x²-x+1)))/((7 x²+3 x+1)³). Then the value of f^()(0) is equal toLimit, Continuity and Differentiability
Q3835If f(x)=\ cc2+2 x, -1 ≤ x < 0 1-x/3, 0 ≤ x ≤ 3; g(x)=\ cc-x, -3 ≤ x ≤ 0 x, 0 < x ≤ 1.., then range of (f o g)(x) isSets, Relations and Functions
Q4037For x (-(π)/2, (π)/2), if y(x)=∫ (cosec x+ sin x)/(cosec x sec x+ tan x sin ² x) d x, and lim x →((π)/2)⁻ y(x)=0 then y((π)/4) is equal toIntegral Calculus
Q4472Let A=[ lll 1 0 0 0 α β 0 β α ] and |2 ~A|³=2²¹ where α, β Z, Then a value of α isMatrices and Determinants
Q4666Let A be a square matrix such that AA^(T)=I. Then 1/2 A[(A+A^(T))²+(A-A^(T))²] is equal toMatrices and Determinants
Q4969A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, isStatistics and Probability
Q5031Let (5, a/4) be the circumcenter of a triangle with vertices A(a,-2), B(a, 6) and C(a/4,-2). Let α denote the circumradius, β denote the area and γ denote the…Properties of Triangle
Q5235In an A.P., the sixth term a₆=2. If the product a₁ a₄ a₅ is the greatest, then the common difference of the A.P. is equal toSequence and Series
Q5271If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal toSequence and Series
Q5394Let R be a relation on Z × Z defined by (a, b) R(c, d) if and only if a d-b c is divisible by 5. Then R isSets, Relations and Functions
Q5512In a A B C, suppose y=x is the equation of the bisector of the angle B and the equation of the side A C is 2 x-y=2. If 2 A B=B C and the points A and B are…Coordinate Geometry
Q5629If α,-(π)/2<α<(π)/2 is the solution of 4 cos θ+5 sin θ=1, then the value of tan α isTrigonometry
Q5704Let a, b and c be three non-zero vectors such that b and c are non-collinear. If a+5 b is collinear with c, b+6 c is collinear with a and a+α b+β c=0, then…Vector Algebra