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

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JEE Main 202429 Jan, Evening shift

Physics 25Chemistry 24Mathematics 30

Physics

Q57Hydrogen atom is bombarded with electrons accelerated through a potential difference of V, which causes excitation of hydrogen atoms. If the experiment is…Atoms and Nuclei
Q58A particle is moving in a circle of radius 50 ~cm in such a way that at any instant the normal and tangential components of it's acceleration are equal. If…Kinematics
Q61A horizontal straight wire 5 ~m long extending from east to west falling freely at right angle to horizontal component of earths magnetic field 0.60 × 10⁻⁴…Electromagnetic Induction and Alternating Currents
Q69A charge of 4.0 μ C is moving with a velocity of 4.0 × 10⁶ ~ms⁻¹ along the positive y axis under a magnetic field B of strength (2 k) T. The force acting on…Magnetic Effects of Current and Magnetism
Q72Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4: 1 and force F₁ is applied to…Properties of Solids and Liquids
Q74A body of mass 5 ~kg moving with a uniform speed 3 √(2) ~ms⁻¹ in X-Y plane along the line y=x+4. The angular momentum of the particle about the origin will be…Rotational Motion
Q75A simple harmonic oscillator has an amplitude A and time period 6 π second. Assuming the oscillation starts from its mean position, the time required by it to…Oscillations and Waves
Q78In a single slit diffraction pattern, a light of wavelength 6000 A^(o) is used. The distance between the first and third minima in the diffraction pattern is…Optics
Q5925In an a.c. circuit, voltage and current are given by: V=100 sin (100 t) V and I=100 sin (100 t+(π)/3) mA respectively. The average power dissipated in one…Electromagnetic Induction and Alternating Currents
Q5963Given below are two statements: Statement I: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons…Atoms and Nuclei
Q6296A stone of mass 900 ~g is tied to a string and moved in a vertical circle of radius 1 ~m making 10 ~rpm. The tension in the string, when the stone is at the…Kinematics
Q6609Two sources of light emit with a power of 200 ~W. The ratio of number of photons of visible light emitted by each source having wavelengths 300 ~nm and 500…Dual Nature of Matter and Radiation
Q6823A plane electromagnetic wave of frequency 35 ~MHz travels in free space along the X -direction. At a particular point (in space and time) E=9.6 j ~V / m. The…Electromagnetic Waves
Q6986An electric field is given by (6 i+5 j+3 k) N / C. The electric flux through a surface area 30 i ~m² lying in YZ-plane (in SI unit) is:Electrostatics
Q7089If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 ~cm, the focal length of the mirror must be:Optics
Q7284A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance…Gravitation
Q7324N moles of a polyatomic gas (f=6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:Thermodynamics
Q7433The temperature of a gas having 2.0 × 10²⁵ molecules per cubic meter at 1.38 ~atm (Given, k=1.38 × 10⁻²³ JK⁻¹) is:Thermodynamics
Q7765Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform…Magnetic Effects of Current and Magnetism
Q7889A particle is moving in a straight line. The variation of position ' x ' as a function of time ' t ' is given as x=(t³-6 t²+20 t+15) m. The velocity of the…Kinematics
Q7966A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the…Properties of Solids and Liquids
Q8033A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:Properties of Solids and Liquids
Q8213The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 ~m. If it dissipates 10% of its initial energy against air…Oscillations and Waves
Q8321A physical quantity Q is found to depend on quantities a, b, c by the relation Q=(a⁴ b³)/(c²). The percentage error in a, b and c are 3%, 4% and 5%…Units and Measurements
Q8453In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a…Optics

Chemistry

Q3The total number of 'Sigma' and 'Pi' bonds in 2-formylhex-4-enoic acid is _ _ _ _ _.Organic Compounds Containing Oxygen
Q5The total number of molecules with zero dipole moment among CH₄, BF₃, H₂ O, HF, NH₃, CO₂ and SO₂ is _ _ _ _.Chemical Bonding and Molecular Structure
Q6The total number of anti bonding molecular orbitals, formed from 2 s and 2 p atomic orbitals in a diatomic molecule is _ _ _ _.Chemical Bonding and Molecular Structure
Q7The following concentrations were observed at 500 ~K for the formation of NH₃ from N₂ and H₂. At equilibrium; [N₂]=2 × 10⁻² M,[H₂]=3 × 10⁻² M and [NH₃]=1.5 ×…Equilibrium
Q8The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is _ _ _ _ × 10⁻². (Given antilog 0.2006=1.587)Chemical Kinetics
Q13A constant current was passed through a solution of AuCl₄⁻ ion between gold electrodes. After a period of 10.0 minutes, the increase in mass of cathode was…Redox Reactions and Electrochemistry
Q20The oxidation number of iron in the compound formed during brown ring test for NO ₃⁻ⁱron is _ _ _ _.Redox Reactions and Electrochemistry
Q21Molality of 0.8 M H ₂ SO ₄ solution (density 1.06 g cm ⁻³) is _ _ _ _ ×10⁻³ m.Some Basic Concepts in Chemistry
Q22If 50 ~mL of 0.5 M oxalic acid is required to neutralise 25 ~mL of NaOH solution, the amount of NaOH in 50 ~mL of given NaOH solution is _ _ _ g.Some Basic Concepts in Chemistry
Q24Standard enthalpy of vapourisation for CCl₄ is 30.5 ~kJ ~mol⁻¹. Heat required for vapourisation of 284 ~g of CCl₄ at constant temperature is _ _ _ _ kJ…Chemical Thermodynamics
Q37Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed in presence of an acid resultsOrganic Compounds Containing Oxygen
Q38Match List I with List II List - I (Compound) List - II (pK a value) (A) Ethanol (I) 10.0 (B) Phenol (II) 15.9 (C) m-Nitrophenol (III) 7.1 (D) p-Nitrophenol…Organic Compounds Containing Oxygen
Q184Match List I with List II List - I (Bio Polymer) List - II (Monomer) (A) Starch (I) nucleotide (B) Cellulose (II) α -glucose (C) Nucleic acid (III) β -glucose…Biomolecules
Q575A reagent which gives brilliant red precipitate with Nickel ions in basic medium isCoordination Compounds
Q794The correct IUPAC name of K₂ MnO₄ isd- and f-Block Elements
Q837Which of the following acts as a strong reducing agent? (Atomic number: Ce=58, Eu=63, Gd=64, Lu=71)d- and f-Block Elements
Q903Which of the following statements are correct about Zn, Cd and Hg ? A. They exhibit high enthalpy of atomization as the d-subshell is full. B. Zn and Cd do…d- and f-Block Elements
Q1153Alkyl halide is converted into alkyl isocyanide by reaction withOrganic Compounds Containing Halogens
Q1498On passing a gas, ' X ', through Nessler's regent, a brown precipitate is obtained. The gas ' X ' isp-Block Elements
Q1583Given below are two statements: Statement I: Fluorine has most negative electron gain enthalpy in its group. Statement II: Oxygen has least negative electron…Classification of Elements and Periodicity in Properties
Q1622The element having the highest first ionization enthalpy isClassification of Elements and Periodicity in Properties
Q1663Anomalous behavior of oxygen is due to itsClassification of Elements and Periodicity in Properties
Q1764Chromatographic technique/s based on the principle of differential adsorption is / are A. Column chromatography B. Thin layer chromatography C. Paper…Purification and Characterisation of Organic Compounds
Q2169Match List I with List II List - I (Spectral Series for Hydrogen) List - II (Spectral Region/Higher Energy State) (A) Lyman (I) Infrared region (B) Balmer…Atomic Structure

Mathematics

Q26Let O be the origin, and M and N be the points on the lines (x-5)/4=(y-4)/1=(z-5)/3 and (x+8)/12=(y+2)/5=(z+11)/9 respectively such that MN is the shortest…Three Dimensional Geometry
Q29Let the area of the region \(x, y): 0 ≤ x ≤ 3,0 ≤ y ≤ min ²+2,2 x+2 be A. Then 12 ~A is equal to _ _ _ _ _.Integral Calculus
Q30Remainder when 64³2³² is divided by 9 is equal to _ _ _ _.Binomial Theorem and Its Simple Applications
Q31Let α, β be the roots of the equation x²-√(6) x+3=0 such that Im(α)>Im(β). Let a, b be integers not divisible by 3 and n be a natural number such that…Complex Numbers and Quadratic Equations
Q33Let the slope of the line 45 x+5 y+3=0 be 27 r₁+(9 r₂)/2 for some r₁, r₂ R. Then lim x → 3 (∫₃ˣ (8 t²)/((3 r₂ x)/2-r₂ x²-r₁ x³-3 x) d t) is equal to _ _ _ _ _.Integral Calculus
Q34If ∫ (π)/6 ^((π)/3) √(1- sin 2 x) d x=α+β √(2)+γ √(3), where α, β and γ are rational numbers, then 3 α+4 β-γ is equal to _ _ _ _ _.Integral Calculus
Q39Let f(x)=√(lim r → x \(2 r²[(f(r))²-f(x) f(r)])/(r²-x²)-r³ e^((f(r))/r)\) be differentiable in (-∞, 0) (0, ∞) and f(1)=1. Then the value of ea, such that…Limit, Continuity and Differentiability
Q41Let for any three distinct consecutive terms a, b, c of an A.P, the lines a x+b y+c=0 be concurrent at the point P and Q(α, β) be a point such that the system…Matrices and Determinants
Q42Let P(α, β) be a point on the parabola y²=4 x. If P also lies on the chord of the parabola x²=8 y whose mid point is (1, 5/4), then (α-28)(β-8) is equal to _…Coordinate Geometry
Q45Let the set C=\(x, y) x²-2^(y)=2023, x, y N. Then Σ (x, y) C (x+y) is equal to _ _ _ _ _.Complex Numbers and Quadratic Equations
Q2383Let P(3,2,3), Q(4,6,2) and R(7,3,2) be the vertices of PQR. Then, the angle QPR isThree Dimensional Geometry
Q2682The function f(x)=2 x+3(x)^(2/3), x R, hasLimit, Continuity and Differentiability
Q2734The function f(x)=x/(x²-6 x-16), x R-\-2,8Limit, Continuity and Differentiability
Q3218Let r and θ respectively be the modulus and amplitude of the complex number z=2-i(2 tan (5 π)/8), then (r, θ) is equal toComplex Numbers and Quadratic Equations
Q3645If sin (y/x)= log e |x|+(α)/2 is the solution of the differential equation x cos (y/x) (d y)/(d x)=y cos (y/x)+x and y(1)=(π)/3, then α² is equal toDifferential Equations
Q3693Let y= log e ((1-x²)/(1+x²)),-1 < x<1. Then at x=1/2, the value of 225(y^()-y^()) is equal toLimit, Continuity and Differentiability
Q4038If ∫ (sin ^(3/2) x+ cos ^(3/2) x)/(√(sin ³ x cos ³ x sin (x-θ))) d x=A √(cos θ tan x- sin θ)+B √(cos θ- sin θ cot x)+C, where C is the integration constant…Integral Calculus
Q4119Let x=m/n (m, n are co-prime natural numbers) be a solution of the equation cos (2 sin ⁻¹ x)=1/9 and let α, β(α >β) be the roots of the equation m x²-n x-m+…Trigonometry
Q4512Let A=[ ccc2 1 2 6 2 11 3 3 2 ] and P=[ lll1 2 0 5 0 2 7 1 5 ]. The sum of the prime factors of |P⁻¹ A P-2 I| is equal toMatrices and Determinants
Q4835Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal toPermutations and Combinations
Q4930An integer is chosen at random from the integers 1,2,3,, 50. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 isStatistics and Probability
Q5236If log e a, log e ~b, log e c are in an A.P. and log e a- log e 2 ~b, log e 2 ~b- log e 3 c, log e 3 c - log e a are also in an A.P, then a: b: c is equal toSequence and Series
Q5272If each term of a geometric progression a₁, a₂, a₃, with a₁=1/8 and a₂ ≠ a₁, is the arithmetic mean of the next two terms and S n =a₁+a₂+..+a n, then S₂₀-S₁₈…Sequence and Series
Q5366If R is the smallest equivalence relation on the set \1,2,3,4 such that \(1,2),(1,3) R, then the number of elements in R is _ _ _ _ _.Sets, Relations and Functions
Q5493If the mean and variance of five observations are 24/5 and 194/25 respectively and the mean of the first four observations is 7/2, then the variance of the…Statistics and Probability
Q5556Let A be the point of intersection of the lines 3 x+2 y=14,5 x-y=6 and B be the point of intersection of the lines 4 x+3 y=8,6 x+y=5. The distance of the…Coordinate Geometry
Q5557The distance of the point (2,3) from the line 2 x-3 y+28=0, measured parallel to the line √(3) x-y+1=0, is equal toCoordinate Geometry
Q5630The sum of the solutions x R of the equation (3 cos 2 x+ cos ³ 2 x)/(cos ⁶ x- sin ⁶ x)=x³-x²+6 isTrigonometry
Q5785Let a unit vector u=x i+y j+z k make angles (π)/2, (π)/3 and (2 π)/3 with the vectors 1/(√(2)) i+1/(√(2)) k, 1/(√(2)) j+1/(√(2)) k and 1/(√(2)) i+1/(√(2)) j…Vector Algebra
Q5848Let O A=a, O B=12 a+4 b and O C=b, where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then (area of the quadrilateral OA…Vector Algebra