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JEE Main 2024 27 Jan Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202427 Jan, Evening shift

Physics 27Chemistry 21Mathematics 30

Physics

Q53A series LCR circuit with L=100/(π) mH, C=(10⁻³)/(π) F and R=10 Ω, is connected across an ac source of 220 ~V, 50 ~Hz supply. The power factor of the circuit…Electromagnetic Induction and Alternating Currents
Q55If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be (α)/(7 R), where α= _ _ _ _.Atoms and Nuclei
Q61Two charges of -4 μ C and +4 μ C are placed at the points A(1,0,4) m and B(2,-1,5) m located in an electric field E=0.20 i ~V / cm. The magnitude of the…Electrostatics
Q63The electric potential at the surface of an atomic nucleus (z=50) of radius 9 × 10⁻¹³ ~cm is _ _ _ _ _ × 10⁶ ~V.Electrostatics
Q69A body falling under gravity covers two points A and B separated by 80 ~m in 2 ~s. The distance of upper point A from the starting point is _ _ _ _ m (use…Kinematics
Q70The reading of pressure metre attached with a closed pipe is 4.5 × 10⁴ ~N / m². On opening the valve, water starts flowing and the reading of pressure metre…Properties of Solids and Liquids
Q72A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of…Rotational Motion
Q76A parallel beam of monochromatic light of wavelength 5000 A^(o) is incident normally on a single narrow slit of width 0.001 ~mm. The light is focused by…Optics
Q78A closed organ pipe 150 ~cm long gives 7 beats per second with an open organ pipe of length 350 ~cm, both vibrating in fundamental mode. The velocity of sound…Oscillations and Waves
Q5944Primary side of a transformer is connected to 230 ~V, 50 ~Hz supply. Turns ratio of primary to secondary winding is 10: 1. Load resistance connected to…Electromagnetic Induction and Alternating Currents
Q6058The atomic mass of ₆ C¹² is 12.000000 ~u and that of ₆ C¹³ is 13.003354 ~u. The required energy to remove a neutron from ₆ C¹³, if mass of neutron is 1.008665…Atoms and Nuclei
Q6480A current of 200 μ A deflects the coil of a moving coil galvanometer through 60^(°). The current to cause deflection through (π)/10 radian is:Current Electricity
Q6524Wheatstone bridge principle is used to measure the specific resistance (S₁) of given wire, having length L, radius r. If X is the resistance of wire, then…Current Electricity
Q6664The threshold frequency of a metal with work function 6.63 ~eV is:Dual Nature of Matter and Radiation
Q6820An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity 6 × 10⁸ ~W / m² falls normally on the object and it is absorbed…Electromagnetic Waves
Q6978Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Work done by electric field on moving…Electrostatics
Q7218Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The angular speed of the moon in its…Gravitation
Q7428The equation of state of a real gas is given by (P+a/(V²))(V-b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal…Thermodynamics
Q7429The total kinetic energy of 1 mole of oxygen at 27^(°) C is: [Use universal gas constant (R)=8.31 ~J / mole K]Thermodynamics
Q7502During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of Cp/Cv for the gas is:Thermodynamics
Q7561Given below are two statements: Statement (I): The limiting force of static friction depends on the area of contact and independent of materials. Statement…Laws of Motion
Q7965Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The property of body, by virtue of…Properties of Solids and Liquids
Q8113A heavy iron bar of weight 12 ~kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60^(°) with the…Rotational Motion
Q8176A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle…Oscillations and Waves
Q8362Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In Vernier calliper if positive zero…Experimental Skills
Q8469When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of:Optics
Q8593A bullet is fired into a fixed target looses one third of its velocity after travelling 4 ~cm. It penetrates further D × 10⁻³ ~m before coming to rest. The…Work, Energy and Power

Chemistry

Q5The number of non-polar molecules from the following is _ _ _ _ _. HF, H₂ O, SO₂, H₂, CO₂, CH₄, NH₃, HCl, CHCl₃, BF₃Chemical Bonding and Molecular Structure
Q6Time required for completion of 99.9% of a First order reaction is _ _ _ _ times of half life (t 1 / 2) of the reaction.Chemical Kinetics
Q8The Spin only magnetic moment value of square planar complex [Pt(NH₃)₂ Cl(NH₂ CH₃)] Cl is _ _ _ _ B.M. (Nearest integer) (Given atomic number for Pt=78)Coordination Compounds
Q11Total number of ions from the following with noble gas configuration is _ _ _ _ _. Sr²⁺(z=38), Cs⁺(z=55), La²⁺(z=57), Pb²⁺(z=82), Yb²⁺(z=70) and Fe²⁺(z=26)d- and f-Block Elements
Q14The hydrogen electrode is dipped in a solution of pH=3 at 25^(°) C. The potential of the electrode will be _ _ _ _ _ × 10⁻² ~V. ((2.303 RT)/F=0.059 ~V)Redox Reactions and Electrochemistry
Q161 mole of PbS is oxidised by " X " moles of O₃ to get " Y " moles of O₂. X+Y= _ _ _ _ _.p-Block Elements
Q20Volume of 3 M ~NaOH (formula weight 40 ~g ~mol⁻¹) which can be prepared from 84 ~g of NaOH is _ _ _ _ _ × 10⁻¹ dm³.Some Basic Concepts in Chemistry
Q219.3 ~g of aniline is subjected to reaction with excess of acetic anhydride to prepare acetanilide. The mass of acetanilide produced if the reaction is 100%…Some Basic Concepts in Chemistry
Q22For a certain thermochemical reaction M → N at T=400 ~K, Δ H^()=77.2 ~kJ ~mol⁻¹, Δ S=122 ~JK⁻¹, log equilibrium constant (log K) is _ _ _ _ _ × 10⁻¹.Chemical Thermodynamics
Q35Phenolic group can be identified by a positive:Organic Compounds Containing Oxygen
Q106The incorrect statement regarding conformations of ethane is:Some Basic Principles of Organic Chemistry
Q218Which structure of protein remains intact after coagulation of egg white on boiling?Biomolecules
Q573Identity the incorrect pair from the following:Coordination Compounds
Q747Identify from the following species in which d² sp³ hybridization is shown by central atom:Coordination Compounds
Q836Given below are two statements: Statement (I): In the Lanthanoids, the formation Ce⁺⁴ is favoured by its noble gas configuration. Statement (II): Ce⁺⁴ is a…d- and f-Block Elements
Q902Choose the correct option having all the elements with d¹⁰ electronic configuration from the following:d- and f-Block Elements
Q919Which of the following statements is not correct about rusting of iron?Redox Reactions and Electrochemistry
Q1517Given below are two statements: Statement (I): Oxygen being the first member of group 16 exhibits only -2 oxidation state. Statement (II): Down the group 16…p-Block Elements
Q1734The technique used for purification of steam volatile water immiscible substances is:Purification and Characterisation of Organic Compounds
Q1799Which of the following cannot function as an oxidising agent?Redox Reactions and Electrochemistry
Q2050The quantity which changes with temperature is:Some Basic Concepts in Chemistry

Mathematics

Q24The lines (x-2)/2=y/(-2)=(z-7)/16 and (x+3)/4=(y+2)/3=(z+2)/1 intersect at the point P. If the distance of P from the line (x+1)/2=(y-1)/3=(z-1)/1 is l, then…Three Dimensional Geometry
Q26If the area of the region \(x, y): 0 ≤ y ≤ min \2 x, 6 x-x² is A, then 12 ~A is equal to _ _ _ _.Integral Calculus
Q27The coefficient of x²⁰¹² in the expansion of (1-x)²⁰⁰⁸(1+x+x²)²⁰⁰⁷ is equal to _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q28Consider a circle (x-α)²+(y-β)²=50, where α, β>0. If the circle touches the line y+x=0 at the point P, whose distance from the origin is 4 √(2), then (α+β)²…Coordinate Geometry
Q29Let the complex numbers α and 1/(α) lie on the circles |z-z₀|²=4 and |z-z₀|²=16 respectively, where z₀=1+i. Then, the value of 100|α|² is _ _ _ _ _.Complex Numbers and Quadratic Equations
Q31Let f(x)=∫₀ˣ g(t) log e ((1-t)/(1+t)) dt, where g is a continuous odd function. If ∫ -π / 2 ^(π / 2)(f(x)+(x² cos x)/(1+eˣ)) d x=((π)/(α))²-α, then α is equal…Integral Calculus
Q33If the solution curve, of the differential equation (d y)/(~d x)=(x+y-2)/(x-y) passing through the point (2,1) is tan ⁻¹((y-1)/(x-1))-1/(β) log e…Differential Equations
Q41Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A-x I|=0 be -1 and 3, then the sum of the diagonal…Matrices and Determinants
Q47The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in…Statistics and Probability
Q48If the sum of squares of all real values of α, for which the lines 2 x-y+3=0,6 x+3 y+1=0 and α x+2 y-2=0 do not form a triangle is p, then the greatest…Coordinate Geometry
Q2526Let the image of the point (1,0,7) in the line x/1=(y-1)/2=(z-2)/3 be the point (α, β, γ). Then which one of the following points lies on the line passing…Three Dimensional Geometry
Q2681Let g(x)=3 f(x/3)+f(3-x) and f^()(x)>0 for all x (0,3). If g is decreasing in (0, α) and increasing in (α, 3), then 8 α is:Limit, Continuity and Differentiability
Q3472For 0 < a < 1, the value of the integral ∫₀^π (d x)/(1-2 a cos x+a²) is:Integral Calculus
Q3642If y=y(x) is the solution curve of the differential equation (x²-4) d y-(y²-3 y) d x=0, x>2, y(4)=3/2 and the slope of the curve is never zero, then the value…Differential Equations
Q3833Let f: R-\(-1)/2 → R and g: R-\(-5)/2 → R be defined as f(x)=(2 x+3)/(2 x+1) and g(x)=(|x|+1)/(2 x+5). Then, the domain of the function fog is:Sets, Relations and Functions
Q3956Let e₁ be the eccentricity of the hyperbola (x²)/16-(y²)/9=1 and e₂ be the eccentricity of the ellipse (x²)/(a²)+(y²)/(b²)=1, a > b, which passes through the…Coordinate Geometry
Q4036The integral ∫ ((x⁸-x²) d x)/((x¹²+3 x⁶+1) tan ⁻¹(x³+1/(x³))) is equal to:Integral Calculus
Q4080Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying tan ⁻¹(x)+ tan ⁻¹(2 x)=(π)/4 is:Trigonometry
Q4217Consider the function f:(0,2) → R defined by f(x)=x/2+2/x and the function g(x) defined by g(x)= ll min f(t) 0<t ≤ x and 0 < x ≤ 1 3/2+x, 1 < x < 2.. Then,Limit, Continuity and Differentiability
Q4302If lim x → 0 (3+α sin x+β cos x+ log e (1-x))/(3 tan ² x)=1/3, then 2 α-β is equal to:Limit, Continuity and Differentiability
Q4471The values of α, for which | ccc1 3/2 α+3/2 1 1/3 α+1/3 2 α+3 3 α+1 0 |=0, lie in the intervalMatrices and Determinants
Q4807Let α=((4 !) !)/((4 !)^(3 !)) and β=((5 !) !)/((5 !)^(4 !)). Then:Permutations and Combinations
Q4991An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white…Statistics and Probability
Q5050If α, β are the roots of the equation, x²-x-1=0 and S n =2023 αⁿ+2024 βⁿ, then:Complex Numbers and Quadratic Equations
Q5234The 20^(th) term from the end of the progression 20,19 1/4, 18 1/2, 17 3/4,,-129 1/4 is:Sequence and Series
Q5365Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B…Sets, Relations and Functions
Q5585Let R be the interior region between the lines 3 x-y+1=0 and x+2 y-5=0 containing the origin. The set of all values of a, for which the points (a², a+1) lie…Coordinate Geometry
Q5628If 2 tan ² θ-5 sec θ=1 has exactly 7 solutions in the interval [0, (n π)/2], for the least value of n N, then Σ k=1 ⁿ k/(2^(k)) is equal to:Trigonometry
Q5703The position vectors of the vertices A, B and C of a triangle are 2 i-3 j+3 k, 2 i+2 j+3 k and -i+j+3 k respectively. Let l denotes the length of the angle…Vector Algebra
Q5845Let the position vectors of the vertices A, B and C of a triangle be 2 i+2 j+k, i+2 j+2 k and 2 i+j+2 k respectively. Let l₁, l₂ and l₃ be the lengths of…Vector Algebra