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JEE Main 2024 1 Feb Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20241 Feb, Morning shift

Physics 27Chemistry 25Mathematics 30

Physics

Q59The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is 1000/x, where x is _ _ _ _.Atoms and Nuclei
Q61Three identical spheres each of mass 2 M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 ~m each. Taking…Rotational Motion
Q64The current in a conductor is expressed as I=3 t²+4 t³, where I is in Ampere and t is in second. The amount of electric charge that flows through a section of…Current Electricity
Q67A rectangular loop of sides 12 ~cm and 5 ~cm, with its sides parallel to the x -axis and y -axis respectively, moves with a velocity of 5 ~cm / s in the…Electromagnetic Induction and Alternating Currents
Q68Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ with each other. When suspended in water the angle…Electrostatics
Q69The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 ~cm. The focal length of the lens used is _ _ _ _ _ cm.Optics
Q73A regular polygon of 6 sides is formed by bending a wire of length 4 π meter. If an electric current of 4 π √(3) A is flowing through the sides of the…Magnetic Effects of Current and Magnetism
Q74A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was 16 ~m right of origin. The variation of…Kinematics
Q75A plane is in level flight at constant speed and each of its two wings has an area of 40 ~m². If the speed of the air is 180 ~km / h over the lower wing…Properties of Solids and Liquids
Q82A tuning fork resonates with a sonometer wire of length 1 ~m stretched with a tension of 6 ~N. When the tension in the wire is changed to 54 ~N, the same…Oscillations and Waves
Q5922A parallel plate capacitor has a capacitance C=200~ pF. It is connected to 230 ~V ac supply with an angular frequency 300~ rad / s. The rms value of…Electromagnetic Induction and Alternating Currents
Q5923In series LCR circuit, the capacitance is changed from C to 4 C. To keep the resonance frequency unchanged, the new inductance should be:Electromagnetic Induction and Alternating Currents
Q6023The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:Atoms and Nuclei
Q6181Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2 ~V. The negative ends of both are…Electrostatics
Q6291A ball of mass 0.5 ~kg is attached to a string of length 50 ~cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum…Kinematics
Q6292A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an…Kinematics
Q6479A galvanometer has a resistance of 50 ~Ω and it allows maximum current of 5 ~mA. It can be converted into voltmeter to measure upto 100 ~V by connecting in…Current Electricity
Q6589The de Broglie wavelengths of a proton and an α particle are λ and 2 λ respectively. The ratio of the velocities of proton and α particle will be:Dual Nature of Matter and Radiation
Q7169If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g=π² ~m / s², then the length of the second's pendulum at a…Gravitation
Q7321Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:Thermodynamics
Q7427The pressure and volume of an ideal gas are related as PV^(3/2)=K (Constant). The work done when the gas is taken from state A(P₁, V₁, T₁) to state B(P₂, V₂…Thermodynamics
Q7964With rise in temperature, the Young's modulus of elasticity:Properties of Solids and Liquids
Q8175A simple pendulum of length 1 ~m has a wooden bob of mass 1 ~kg. It is struck by a bullet of mass 10⁻² ~kg moving with a speed of 2 × 10² ~ms⁻¹. The bullet…Oscillations and Waves
Q8274The dimensional formula of angular impulse is:Units and Measurements
Q8317The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r=(0.35 ± 0.05) ~cm R=(100 ± 10) ~ohm l=(15 ± 0.2)~ cm The…Units and Measurements
Q836110 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the…Experimental Skills
Q8405A monochromatic light of wavelength 6000 ~ A is incident on the single slit of width 0.01 ~mm. If the diffraction pattern is formed at the focus of the convex…Optics

Chemistry

Q2Number of optical isomers possible for 2-chlorobutane _ _ _ _.Some Basic Principles of Organic Chemistry
Q4The number of molecules/ion/s having trigonal bipyramidal shape is _ _ _ _. PF₅, BrF₅, PCl₅,[Pt Cl₄]²⁻, BF₃, Fe(CO)₅Chemical Bonding and Molecular Structure
Q7The lowest oxidation number of an atom in a compound A₂ B is -2. The number of electrons in its valence shell is _ _ _ _.Chemical Bonding and Molecular Structure
Q8The ratio of (¹⁴ C)/(¹² C) in a piece of wood is 1/8 part that of atmosphere. If half life of ¹⁴ C is 5730 years, the age of wood sample is _ _ _ _ years.Chemical Kinetics
Q13The potential for the given half cell at 298 ~K is (-) _ _ _ _ _ × 10⁻² ~V 2 H (aq) ⁺+2 e⁻ H₂(~g) [H⁺]=1 M, P H₂ =2 ~atm (Given: 2.303 RT / F=0.06 ~V, log…Redox Reactions and Electrochemistry
Q15K a for CH₃ COOH is 1.8 × 10⁻⁵ and K b for NH₄ OH is 1.8 × 10⁻⁵. The pH of ammonium acetate solution will be _ _ _ _ _.Equilibrium
Q16The number of white coloured salts, among the following is (a) SrSO₄ (b) Mg(NH₄) PO₄ (c) BaCrO₄ (d) Mn(OH)₂ (e) PbSO₄ (f) PbCrO₄ (g) AgBr (h) PbI₂ (i) CaC₂ O₄…p-Block Elements
Q17Among the following oxides of p-block elements, number of oxides having amphoteric nature is _ _ _ _. Cl₂ O₇, CO, PbO₂, ~N₂ O, NO, Al₂ O₃, SiO₂, ~N₂ O₅, SnO₂p-Block Elements
Q23Consider the following reaction: 3 PbCl₂+2(NH₄)₃ PO₄ → Pb₃(PO₄)₂+6 NH₄ Cl If 72 ~mmol of PbCl₂ is mixed with 50 ~mmol of (NH₄)₃ PO₄, then the amount of…Some Basic Concepts in Chemistry
Q88Ionic reactions with organic compounds proceed through: (A) homolytic bond cleavage (B) heterolytic bond cleavage (C) free radical formation (D) primary free…Some Basic Principles of Organic Chemistry
Q246If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is:Biomolecules
Q337Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): PH₃ has lower boiling point than NH₃…Chemical Bonding and Molecular Structure
Q344Arrange the bonds in order of increasing ionic character in the molecules. LiF, K₂ O, N₂, SO₂ and ClF₃:Chemical Bonding and Molecular Structure
Q547Given below are two statements: Statement (I): The NH₂ group in Aniline is ortho and para directing and a powerful activating group. Statement (II): Aniline…Organic Compounds Containing Nitrogen
Q548Given below are two statements: Statement (I): Aminobenzene and aniline are same organic compounds. Statement (II): Aminobenzene and aniline are different…Organic Compounds Containing Nitrogen
Q651Given below are two statements: Statement (I): A solution of [Ni(H₂ O)₆]²⁺ is green in colour. Statement (II): A solution of [Ni(CN)₄]²⁻ is colourless. In the…Coordination Compounds
Q694Which of the following complex is homoleptic?Coordination Compounds
Q1151Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Haloalkanes react with KCN to form…Organic Compounds Containing Halogens
Q1733In Kjeldahl's method for estimation of nitrogen, CuSO₄ acts as:Purification and Characterisation of Organic Compounds
Q1742Given below are two statements: Statement (I): Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution. Statement…Principles Related to Practical Chemistry
Q1788In acidic medium, K₂ Cr₂ O₇ shows oxidising action as represented in the half reaction: Cr₂ O₇ ²⁻+XH⁺+Ye^() → 2 ~A+ZH₂ O X, Y, Z and A are respectively are:Redox Reactions and Electrochemistry
Q1819Which of the following reactions are disproportionation reactions? (A) Cu⁺ → Cu²⁺+Cu (B) 3 MnO₄²⁻+4 H⁺ 2 MnO₄⁻+MnO₂+2 H₂ O (C) 2 KMnO₄ K₂ MnO₄+MnO₂+O₂ (D) 2…Redox Reactions and Electrochemistry
Q1973We have three aqueous solutions of NaCl labelled as ' A ', ' B ' and ' C ' with concentration 0.1 M, 0.01 M and 0.001 M, respectively. The value of van 't…Solutions
Q2187In case of isoelectronic species the size of F⁻, Ne and Na⁺ is affected by:Atomic Structure
Q2323Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following:Chemical Thermodynamics

Mathematics

Q27Let the line of the shortest distance between the lines L₁: r=(i+2 j+3 k)+λ(i-j+k) and L₂: r=(4 i+5 j+6 k)+μ(i+j-k) intersect L₁ and L₂ at P and Q…Three Dimensional Geometry
Q30If the Coefficient of x³⁰ in the expansion of (1+1/x)⁶(1+x²)⁷(1-x³)⁸; x ≠ 0 is α, then |α| equals _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q33Let P= C:|z+2-3 i| ≤ 1 and Q= C: z(1+i)+z(1-i) ≤-8. Let in P Q, |z-3+2 i| be maximum and minimum at z₁ and z₂ respectively. If |z₁|²+2|z₂|²=α+β √(2), where α…Complex Numbers and Quadratic Equations
Q35If ∫ -π / 2 ^(π / 2) (8 √(2) cos x ~d x)/((1+e^(sin x))(1+ sin ⁴ x))=α π+β log e (3+2 √(2)), where α, β are integers, then α²+β² equals:Integral Calculus
Q36If x=x(t) is the solution of the differential equation (t+1) d x=(2 x+(t+1)⁴) dt, x(0)=2, then, x(1) equals _ _ _ _ _.Differential Equations
Q42Let denote the fractional part of x and f(x)=(cos ⁻¹(1- \²) sin ⁻¹(1- \))/(\- \³), x ≠ 0. If L and R respectively denotes the left hand limit and the right…Limit, Continuity and Differentiability
Q45Let the line L: √(2) x+y=α pass through the point of the intersection P (in the first quadrant) of the circle x²+y²=3 and the parabola x²=2 y. Let the line L…Coordinate Geometry
Q47The number of elements in the set S=\(x, y, z): x, y, z Z, x+2 y+3 z=42, x, y, z 0 equals _ _ _ _ _.Permutations and Combinations
Q51Let 3,7,11,15,, 403 and 2,5,8,11,, 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to _ _ _ _ _ _.Sequence and Series
Q52Let A=\1,2,3,, 20. Let R₁ and R₂ two relation on A such that R₁=\(a, b): b is divisible by a R₂=\(a, b): a is an integral multiple of b. Then, number of…Sets, Relations and Functions
Q2523If the shortest distance between the lines (x-λ)/(-2)=(y-2)/1=(z-1)/1 and (x-√(3))/1=(y-1)/(-2)=(z-2)/1 is 1, then the sum of all possible values of λ is:Three Dimensional Geometry
Q2730If 5 f(x)+4 f(1/x)=x²-2, x ≠ 0 and y=9 x² f(x), then y is strictly increasing in:Limit, Continuity and Differentiability
Q2865The area enclosed by the curves x y+4 y=16 and x+y=6 is equal to:Integral Calculus
Q3034Let C: x²+y²=4 and C^(): x²+y²-4 λ x+9=0 be two circles. If the set of all values of λ so that the circles C and C intersect at two distinct points, is R-[a…Coordinate Geometry
Q3165Let S=|z C:| z-1 =1 and (√(2)-1)(z+z)-i(z-z)=2 √(2). Let z₁, z₂ S be such that |z₁|= max z s |z| and |z₂|= min z S |z|. Then |√(2) z₁-z₂|² equals:Complex Numbers and Quadratic Equations
Q3469The value of the integral ∫₀^(π / 4) (x ~d x)/(sin ⁴(2 x)+ cos ⁴(2 x)) equals:Integral Calculus
Q3641Let y=y(x) be the solution of the differential equation (d y)/(~d x)=2 x(x+y)³-x(x+y)-1, y(0)=1. Then, (1/(√(2))+y(1/(√(2))))² equals:Differential Equations
Q3767Let (x²)/(a²)+(y²)/(b²)=1, a>b be an ellipse, whose eccentricity is 1/(√(2)) and the length of the latusrectum is √(14). Then the square of the eccentricity…Coordinate Geometry
Q3832Let f: R → R and g: R → R be defined as f(x)=\ ll log e x, x>0 e⁻ˣ, x ≤ 0. and g(x)=\ llx, x 0 eˣ, x<0.. Then, gof: R → R is:Sets, Relations and Functions
Q3978For 0<θ<π / 2, if the eccentricity of the hyperbola x²-y² cosec² θ=5 is √(7) times eccentricity of the ellipse x² cosec² θ+y²=5, then the value of θ is:Coordinate Geometry
Q4216Let f: R → R be defined as: f(x)= (a-b cos 2 x)/(x²); x<0 x²+c x+2; 0 ≤ x ≤ 1 2 x+1; x>1 If f is continuous everywhere in R and m is the number of points…Limit, Continuity and Differentiability
Q4632If the system of equations 2 x+3 y-z=5 x+α y+3 z=-4 3 x-y+β z=7 has infinitely many solutions, then 13 α β is equal to:Matrices and Determinants
Q4665If A=[ cc√(2) 1 -1 √(2) ], B=[ ll1 0 1 1 ], C=ABA^(T) and X=A^(T) C² ~A, then det X is equal to:Matrices and Determinants
Q4834If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including…Permutations and Combinations
Q5011A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and…Statistics and Probability
Q5167Let S= R:(√(3)+√(2))ˣ+(√(3)-√(2))ˣ=10. Then the number of elements in S is:Complex Numbers and Quadratic Equations
Q5186Let 3, a, b, c be in A.P. and 3, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of a, b and c is:Sequence and Series
Q5490Let the median and the mean deviation about the median of 7 observation 170,125,230,190,210, a, b be 170 and 205/7 respectively. Then the mean deviation about…Statistics and Probability
Q5639If tan A=1/(√(x(x²+x+1))), tan B=(√(x))/(√(x²+x+1)) and tan C=(x⁻³+x⁻²+x⁻¹)^(1 / 2), 0<A, B, C<(π)/2, then A+B is equal to:Trigonometry
Q5844Let a=-5 i+j-3 k, b=i+2 j-4 k and c=(((a × b) × i) × i) × i. Then c ·(-i+j+k) is equal to:Vector Algebra