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

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JEE Main 202427 Jan, Morning shift

Physics 25Chemistry 21Mathematics 30

Physics

Q54In a nuclear fission process, a high mass nuclide (A ≈ 236) with binding energy 7.6 ~MeV / Nucleon dissociated into middle mass nuclides (A ≈ 118), having…Atoms and Nuclei
Q60Two coils have mutual inductance 0.002 ~H. The current changes in the first coil according to the relation i=i₀ sin ω t, where i₀=5 ~A and ω=50 π rad/s. The…Electromagnetic Induction and Alternating Currents
Q63A thin metallic wire having cross sectional area of 10⁻⁴ ~m² is used to make a ring of radius 30 ~cm. A positive charge of 2 π ~C is uniformly distributed…Electrostatics
Q72A particle starts from origin at t=0 with a velocity 5 i ~m / s and moves in x-y plane under action of a force which produces a constant acceleration of (3…Kinematics
Q74If average depth of an ocean is 4000 ~m and the bulk modulus of water is 2 × 10⁹ ~Nm⁻², then fractional compression (Δ V)/V of water at the bottom of ocean is…Properties of Solids and Liquids
Q76A particle executes simple harmonic motion with an amplitude of 4 ~cm. At the mean position, velocity of the particle is 10 ~cm / s. The distance of the…Oscillations and Waves
Q6024The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:Atoms and Nuclei
Q6253Two bodies of mass 4 ~g and 25 ~g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is:Rotational Motion
Q6254A body of mass 1000 ~kg is moving horizontally with a velocity 6 ~m / s. If 200 ~kg extra mass is added, the final velocity (in m / s) is:Rotational Motion
Q6293A train is moving with a speed of 12 ~m / s on rails which are 1.5 ~m apart. To negotiate a curve radius 400 ~m, the height by which the outer rail should be…Kinematics
Q6389A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be:Current Electricity
Q6527A wire of length 10 ~cm and radius √(7) × 10⁻⁴ ~m connected across the right gap of a meter bridge. When a resistance of 4.5 Ω is connected on the left gap by…Current Electricity
Q6714A rectangular loop of length 2.5 ~m and width 2 ~m is placed at 60^(°) to a magnetic field of 4 ~T. The loop is removed from the field in 10 ~sec. The average…Electromagnetic Induction and Alternating Currents
Q6819A plane electromagnetic wave propagating in x -direction is described by E y =(200 Vm⁻¹) sin [1.5 × 10⁷ t-0.05 x]; The intensity of the wave is: (Use ε₀=8.85…Electromagnetic Waves
Q7023An electric charge 10⁻⁶ μ C is placed at origin (0,0) m of X-Y co-ordinate system. Two points P and Q are situated at (√(3), √(3)) m and (√(6), 0) m…Electrostatics
Q7053A convex lens of focal length 40 ~cm forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by…Optics
Q7073Identify the physical quantity that cannot be measured using spherometer:Optics
Q7126If the refractive index of the material of a prism is cot (A/2), where A is the angle of prism then the angle of minimum deviation will beOptics
Q7170The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then…Gravitation
Q7322The average kinetic energy of a monatomic molecule is 0.414 ~eV at temperature: (Use K B =1.38 × 10⁻²³ ~J / mol-K)Kinetic Theory of Gases
Q74660.08 ~kg air is heated at constant volume through 5^(°) C. The specific heat of air at constant volume is 0.17 ~kcal / kg^(°) C and J=4.18 joule/ ~cal. The…Thermodynamics
Q7764A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic…Magnetic Effects of Current and Magnetism
Q7823Position of an ant (S in metres) moving in Y - Z plane is given by S=2 t² j+5 k (where t is in second). The magnitude and direction of velocity of the ant at…Kinematics
Q8031Given below are two statements: Statement (I):Viscosity of gases is greater than that of liquids. Statement (II): Surface tension of a liquid decreases due to…Properties of Solids and Liquids
Q8275Given below are two statements: Statement (I): Planck's constant and angular momentum have same dimensions. Statement (II): Linear momentum and moment of…Units and Measurements

Chemistry

Q2Among the following, total number of meta directing functional groups is (Integer based) -OCH₃,-NO₂,-CN,-CH₃-NHCOCH₃, -COR,-OH,-COOH,-ClSome Basic Principles of Organic Chemistry
Q33-Methylhex-2-ene on reaction with HBr in presence of peroxide forms an addition product (A). The number of possible stereoisomers for ' A ' is _ _ _ _.Some Basic Principles of Organic Chemistry
Q6Sum of bond order of CO and NO ⁺ is _ _ _ _.Chemical Bonding and Molecular Structure
Q12The mass of silver (Molar mass of Ag: 108 ~gmol⁻¹) displaced by a quantity of electricity which displaces 5600 ~mL of O₂ at S.T.P. will be _ _ _ g.Redox Reactions and Electrochemistry
Q16From the given list, the number of compounds with +4 oxidation state of Sulphur _ _ _ _. SO₃, H₂ SO₃, SOCl₂, SF₄, BaSO₄, H₂ S₂ O₇p-Block Elements
Q20Mass of methane required to produce 22 ~g of CO₂ after complete combustion is _ _ _ g. (Given Molar mass in g mol-1 C=12.0, H=1.0, O=16.0)Some Basic Concepts in Chemistry
Q21The number of electrons present in all the completely filled subshells having n=4 and s=+1/2 is _ _ _ _. (Where n= principal quantum number and s= spin…Atomic Structure
Q22If three moles of an ideal gas at 300 ~K expand isothermally from 30 ~dm³ to 45 ~dm³ against a constant opposing pressure of 80 ~kPa, then the amount of heat…Chemical Thermodynamics
Q34Given below are two statements: Statement (I): p-nitrophenol is more acidic than m-nitrophenol and o-nitrophenol. Statement (II): Ethanol will give immediate…Organic Compounds Containing Oxygen
Q247Two nucleotides are joined together by a linkage known as:Biomolecules
Q271Choose the polar molecule from the following:Chemical Bonding and Molecular Structure
Q600Yellow compound of lead chromate gets dissolved on treatment with hot NaOH solution. The product of lead formed is a:Coordination Compounds
Q652Consider the following complex ions P=[FeF₆]³⁻ Q=[V(H₂ O)₆]²⁺ R=[Fe(H₂ O)₆]²⁺ The correct order of the complex ions, according to their spin only magnetic…Coordination Compounds
Q835The electronic configuration for Neodymium is: [Atomic Number for Neodymium 60]d- and f-Block Elements
Q901Which of the following electronic configuration would be associated with the highest magnetic moment?d- and f-Block Elements
Q1152The correct statement regarding nucleophilic substitution reaction in a chiral alkyl halide is;Organic Compounds Containing Halogens
Q1323Given below are two statements: Statement (I): Aqueous solution of ammonium carbonate is basic. Statement (II): Acidic/basic nature of salt solution of a salt…Equilibrium
Q1460Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Melting point of Boron (2453 K) is…p-Block Elements
Q1534Element not showing variable oxidation state is:p-Block Elements
Q1662Given below are two statements: Statement (I): The 4 f and 5 f - series of elements are placed separately in the Periodic table to preserve the principle of…Classification of Elements and Periodicity in Properties
Q1988A solution of two miscible liquids showing negative deviation from Raoult's law will have:Solutions

Mathematics

Q25Let for a differentiable function f:(0, ∞) → R, f(x)-f(y) log e (x/y)+x-y, x, y (0, ∞). Then Σ n=1 ²⁰ f^()(1/(n²)) is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q26Let the area of the region \(x, y): x-2 y+4 0, x+2 y² 0, x+4 y² ≤ 8, y 0 be m/n, where m and n are coprime numbers. Then m+n is equal to _ _ _ _ _ _ _.Integral Calculus
Q30If α satisfies the equation x²+x+1=0 and (1+α)⁷=A+B α+C α², A, B, C 0, then 5(3 A-2 B-C) is equal to _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q35If the solution of the differential equation (2 x+3 y-2) d x+(4 x+6 y-7) d y=0, y(0)=3, is α x+β y+3 log e |2 x+3 y-γ|=6, then α+2 β+3 γ is equal to _ _ _ _ _…Differential Equations
Q36Let f(x)=x³+x² f^()(1)+x f^()(2)+f^()(3), x R. Then f^()(10) is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q42Let A=[ lll2 0 1 1 1 0 1 0 1 ], B=[B₁, B₂, B₃], where B₁, B₂, B₃ are column matrics, and AB₁=[ l 1 0 0 ], AB₂=[ l 2 3 0 ], AB₃=[ l 3 2 1 ] If α=|B| and β is…Matrices and Determinants
Q44A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a=P(X=3), b=P(X 3) and c=P(X 6 X>3). Then (b+c)/a…Statistics and Probability
Q46If 8=3+1/4(3+p)+1/(4²)(3+2 p)+1/(4³)(3+3 p)+ ∞, then the value of p is _ _ _ _ _ _.Sequence and Series
Q50Let the set of all a R such that the equation cos 2 x+a sin x=2 a-7 has a solution be [p, q] and r= tan 9^(°)- tan 27^(°)-1/(cot 63^(°))+ tan 81^(°), then pqr…Trigonometry
Q52The least positive integral value of α, for which the angle between the vectors α i-2 j+2 k and α i+2 α j-2 k is acute, is _ _ _ _ _ _.Vector Algebra
Q2524The distance, of the point (7,-2,11) from the line (x-6)/1=(y-4)/0=(z-8)/3 along the line (x-5)/2=(y-1)/(-3)=(z-5)/6, is:Three Dimensional Geometry
Q2525If the shortest distance between the lines (x-4)/1=(y+1)/2=z/(-3) and (x-λ)/2=(y+1)/4=(z-2)/(-5) is 6/(√(5)), then the sum of all possible values of λ is:Three Dimensional Geometry
Q3012ⁿ⁻¹ C r =(k²-8) ⁿ C r+1 if and only if:Binomial Theorem and Its Simple Applications
Q3013If A denotes the sum of all the coefficients in the expansion of (1-3 x+10 x²)ⁿ and B denotes the sum of all the coefficients in the expansion of (1+x²)ⁿ, then:Binomial Theorem and Its Simple Applications
Q3114Four distinct points (2 k, 3 k),(1,0),(0,1) and (0,0) lie on a circle for k equal to:Coordinate Geometry
Q3201If S= C:|z-i|=|z+i|=|z-1|, then, n(S) is:Complex Numbers and Quadratic Equations
Q3470If ∫₀¹ 1/(√(3+x)+√(1+x)) ~d x=a+b √(2)+c √(3), where a, b, c are rational numbers, then 2 a+3 ~b-4 c is equal to:Integral Calculus
Q3471If (a, b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and I₁=∫ a ^(b) x sin (4 x-x²) d x, I₂=∫ a ^(b) sin (4 x-x²) d x, then…Integral Calculus
Q3563Let x=x(t) and y=y(t) be solutions of the differential equations (d x)/dt+a x=0 and (d y)/dt+by=0 respectively, a, b R. Given that x(0)=2; y(0)=1 and 3 y(1)=2…Differential Equations
Q3718The length of the chord of the ellipse (x²)/25+(y²)/16=1, whose mid point is (1, 2/5), is equal to:Coordinate Geometry
Q3810The function f: N-\1 → N; defined by f(n)= the highest prime factor of n, is:Sets, Relations and Functions
Q4161Consider the function. f(x)=\ cc (a(7 x-12-x²))/(b|x²-7 x+12|), x<3 2^((sin (x-3))/(x-[x])), x>3 ~b, x=3,. where [x] denotes the greatest integer less than or…Limit, Continuity and Differentiability
Q4301If a= lim x → 0 (√(1+√(1+x⁴))-√(2))/(x⁴) and b= lim x → 0 (sin ² x)/(√(2)-√(1+ cos x)), then the value of a b³ is:Limit, Continuity and Differentiability
Q4486Consider the matrix f(x)=[ ccc cos x - sin x 0 sin x cos x 0 0 0 1 ]. Given below are two statements: Statement I: f(-x) is the inverse of the matrix f(x)…Matrices and Determinants
Q4715If the shortest distance of the parabola y²=4 x from the centre of the circle x²+y²-4 x-16 y+64=0 is d, then d² is equal to:Coordinate Geometry
Q5233The number of common terms in the progressions 4,9,14,19,, up to 25^(th) term and 3,6,9,12,, up to 37^(th) term is:Sequence and Series
Q5393Let S=\1,2,3,, 10. Suppose M is the set of all the subsets of S, then the relation R=\(A, B): A B ≠ φ; A, B M is:Sets, Relations and Functions
Q5491Let a₁, a₂, a₁₀ be 10 observations such that Σ k=1 ¹⁰ a k =50 and Σ k < j a k · a j =1100. Then the standard deviation of a₁, a₂,, a₁₀ is equal to:Statistics and Probability
Q5505The portion of the line 4 x+5 y=20 in the first quadrant is trisected by the lines L₁ and L₂ passing through the origin. The tangent of an angle between the…Coordinate Geometry
Q5755Let a=i+2 j+k, b=3(i-j+k). Let c be the vector such that a × c=b and a · c=3. Then a ·((c × b)-b-c) is equal to:Vector Algebra