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JEE Main 2023 15 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202315 Apr, Morning shift

Physics 24Chemistry 23Mathematics 30

Physics

Q59A 20 ~cm long metallic rod is rotated with 210~ rpm about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a…Electromagnetic Induction and Alternating Currents
Q62The refractive index of a transparent liquid filled in an equilateral hollow prism is √(2). The angle of minimum deviation for the liquid will be _ _ _ _ _ _°.Optics
Q67An electron in a hydrogen atom revolves around its nucleus with a speed of 6.76 × 10⁶ ~ms⁻¹ in an orbit of radius 0.52 ~A^(°). The magnetic field produced at…Magnetic Effects of Current and Magnetism
Q70There is an air bubble of radius 1.0 ~mm in a liquid of surface tension 0.075~ Nm⁻¹ and density 1000 ~kg ~m⁻³ at a depth of 10 ~cm below the free surface. The…Properties of Solids and Liquids
Q71A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations…Rotational Motion
Q76The fundamental frequency of vibration of a string stretched between two rigid support is 50 ~Hz. The mass of the string is 18 ~g and its linear mass density…Oscillations and Waves
Q77A block of mass 10 ~kg is moving along x -axis under the action of force F=5 x~ N. The work done by the force in moving the block from x=2 m to 4 m will be _…Work, Energy and Power
Q6133The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:Atoms and Nuclei
Q6327The height of transmitting antenna is 180 ~m and the height of the receiving antenna is 245 ~m. The maximum distance between them for satisfactory…Communication Systems
Q6388Given below are two statements: Statement I: The equivalent resistance of resistors in a series combination is smaller than least resistance used in the…Current Electricity
Q6583The de Broglie wavelength of an electron having kinetic energy E is λ. If the kinetic energy of electron becomes E/4, then its de-Broglie wavelength will be:Dual Nature of Matter and Radiation
Q668912 ~V battery connected to a coil of resistance 6 Ω through a switch, drives a constant current in the circuit. The switch is opened in 1 ~ms. The emf induced…Electromagnetic Induction and Alternating Currents
Q6844Match List I with List II of Electromagnetic waves with corresponding wavelength range: List I List II (A) Microwave (I) 400 ~nm to 1 ~nm (B) Ultraviolet (II)…Electromagnetic Waves
Q6976The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as:Electrostatics
Q7238A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be (Given g=…Gravitation
Q7280Two identical particles each of mass ' m ' go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each…Gravitation
Q7417A flask contains Hydrogen and Argon in the ratio 2: 1 by mass. The temperature of the mixture is 30^(°) C. The ratio of average kinetic energy per molecule of…Kinetic Theory of Gases
Q7596The position vector of a particle related to time t is given by r=(10 t i+15 t² j+7 k) m The direction of net force experienced by the particle is:Laws of Motion
Q7836The position of a particle related to time is given by x=(5 t²-4 t+5) m. The magnitude of velocity of the particle at t=2 s will be:Kinematics
Q7960A wire of length ' L ' and radius ' r ' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by ' l '…Properties of Solids and Liquids
Q8171In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and displacement are opposite…Oscillations and Waves
Q8270The speed of a wave produced in water is given by v=λ^(a) g^(b) ρ^(c). Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of…Units and Measurements
Q8387A vector in x-y plane makes an angle of 30^(°) with y -axis. The magnitude of y -component of vector is 2 √(3). The magnitude of x -component of the vector…Kinematics
Q8403A single slit of width a is illuminated by a monochromatic light of wavelength 600 ~nm. The value of ' a ' for which first minimum appears at θ=30^(°) on the…Optics

Chemistry

Q5For a reversible reaction A B, the Δ H forward reaction = 20 ~kJ ~mol⁻¹. The activation energy of the uncatalysed forward reaction is 300 ~kJ ~mol⁻¹. When the…Chemical Kinetics
Q7The homoleptic and octahedral complex of Co²⁺ and H₂ O has _ _ _ _ _ u npaired electron(s) in the t 2g set of orbitals.Coordination Compounds
Q8In Chromyl chloride, the oxidation state of chromium is (+) _ _ _ _ _ _ _ _.d- and f-Block Elements
Q9The total change in the oxidation state of manganese involved in the reaction of KMnO₄ and potassium iodide in the acidic medium is _ _ _ _ _ _.d- and f-Block Elements
Q10The number of correct statements from the following is _ _ _ _. (A) Conductivity always decreases with decrease in concentration for both strong and weak…Redox Reactions and Electrochemistry
Q18The vapour pressure of 30%(w / v) aqueous solution of glucose is _ _ _ _ _ mm ~Hg at 25^(°) C. [Given: The density of 30% (w/v), aqueous solution of glucose…Solutions
Q19The volume (in mL) of 0.1 M ~AgNO₃ required for complete precipitation of chloride ions present in 20 ~mL of 0.01 M solution of [Cr(H₂ O)₅ Cl] Cl₂ as silver…Some Basic Concepts in Chemistry
Q21The total number of isoelectronic species from the given set is _ _ _ _ _ _. O²⁻, F⁻, Al, Mg²⁺, Na⁺, O⁺, Mg, Al³⁺, FAtomic Structure
Q2220 ~mL of 0.5 M ~NaCl is required to coagulate 200 ~mL of As₂ S₃ solution in 2 hours. The coagulating value of NaCl is _ _ _ _ _ _.Surface Chemistry
Q2330.4 ~kJ of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is 28.4 ~J ~K⁻¹ ~mol⁻¹ at 1 atm. The melting…Chemical Thermodynamics
Q138Which of the following statement is correct for paper chromatography?Some Basic Principles of Organic Chemistry
Q242Which is not true for arginine?Biomolecules
Q270Consider the following statements: (A) NF₃ molecule has a trigonal planar structure. (B) Bond length of N₂ is shorter than O₂. (C) Isoelectronic molecules or…Chemical Bonding and Molecular Structure
Q316The number of P-O-P bonds in H₄ P₂ O₇,(HPO₃)₃ and P₄ O₁₀ are respectively:Chemical Bonding and Molecular Structure
Q640The complex with highest magnitude of crystal field splitting energy (Δ₀) is:Coordination Compounds
Q1046The possibility of photochemical smog formation will be minimum at:Environmental Chemistry
Q1315Which of the following statement(s) is/are correct? (A) The pH of 1 × 10⁻⁸~ M ~HCl solution is 8. (B) The conjugate base of H₂ PO₄⁻ is HPO₄²⁻. (C) K w…Equilibrium
Q1363Which one of the following is not an example of calcination?Isolation of Elements
Q1475During water-gas shift reactionp-Block Elements
Q1706Match List I with List II: List I - (Monomer) List II - (Polymer) (A) Tetrafluoroethene (I) Orlon (B) Acrylonitrile (II) Natural rubber (C) Caprolactam (III)…Polymers
Q1903Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion (A): BeCl₂ and MgCl₂ produce characteristic…S Block Elements
Q1932Which of the following expressions is correct in case of a CsCl unit cell (edge length 'a')?Solid State
Q2126Given below are two statements: Statement I: According to Bohr's model of hydrogen atom, the angular momentum of an electron in a given stationary state is…Atomic Structure

Mathematics

Q24Let the plane P contain the line 2 x+y-z-3=0=5 x-3 y+4 z+9 and be parallel to the line (x+2)/2=(3-y)/(-4)=(z-7)/5. Then the distance of the point A(8,-1,-19)…Three Dimensional Geometry
Q28Consider the triangles with vertices A(2,1), B(0,0) and C(t, 4), t [0,4]. If the maximum and the minimum perimeters of such triangles are obtained at t=α and…Limit, Continuity and Differentiability
Q29If the area bounded by the curve 2 y²=3 x, lines x+y=3, y=0 and outside the circle (x-3)²+y²=2 is A, then 4(π+4 A) is equal to _ _ _ _ _ _.Integral Calculus
Q35Let an ellipse with centre (1,0) and latus rectum of length 1/2 have its major axis along x -axis. If its minor axis subtends an angle 60^(°) at the foci…Coordinate Geometry
Q36Let f(x)=∫ (d x)/((3+4 x²) √(4-3 x²)),|x|<2/(√(3)). If f(0)=0 and f(1)=1/(α β) tan ⁻¹((α)/(β)), α, β>0, then α²+β² is equal to _ _ _ _ _ _.Integral Calculus
Q42A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first…Permutations and Combinations
Q44If the line x=y=z intersects the line x sin A+y sin B+z sin C-18=0=x sin 2 A+y sin 2 B+z sin 2 C-9, where A, B, C are the angles of a triangle A B C, then…Properties of Triangle
Q47If the sum of the series (1/2-1/3)+(1/(2²)-1/(2 · 3)+1/(3²))+(1/(2³)-1/(2² · 3)+1/(2 · 3²)-1/(3³))+ (1/(2⁴)-1/(2³ · 3)+1/(2² · 3²)-1/(2 · 3³)+1/(3⁴))+ is…Sequence and Series
Q48The number of elements in the set N: 10 ≤ n ≤ 100. and 3ⁿ-3 is a multiple of 7 is _ _ _ _ _ _.Sets, Relations and Functions
Q49Let A=\1,2,3,4 and R be a relation on the set A × A defined by R=\((a, b),(c, d)): 2 a+3 b=4 c+5 d. Then the number of elements in R is _ _ _ _ _ _.Sets, Relations and Functions
Q2515Let S be the set of all values of λ, for which the shortest distance between the lines (x-λ)/0=(y-3)/4=(z+6)/1 and (x+λ)/3=y/(-4)=(z-6)/0 is 13. Then 8|Σ λ S…Three Dimensional Geometry
Q2605Let the foot of perpendicular of the point P(3,-2,-9) on the plane passing through the points (-1,-2,-3),(9,3,4),(9,-2,1) be Q(α, β, γ). Then the distance of…Three Dimensional Geometry
Q2606Let the system of linear equations -x+2 y-9 z=7 -x+3 y+7 z=9 -2 x+y+5 z=8 -3 x+y+13 z=λ has a unique solution x=α, y=β, z=γ. Then the distance of the point…Three Dimensional Geometry
Q2958Let (a+b x+c x²)¹⁰=Σ i=0 ²⁰ p i xⁱ, a, b, c N. If p₁=20 and p₂=210, then 2(a+b+c) is equal to:Binomial Theorem and Its Simple Applications
Q3100The number of common tangents, to the circles x²+y²-18 x-15 y+131=0 and x²+y²-6 x-6 y-7=0, is:Coordinate Geometry
Q3227If the set ((z-z+z z)/(2-3 z+5 z)): z C, Re(z)=3 is equal to the interval (α, β], then 24(β-α) is equal to:Complex Numbers and Quadratic Equations
Q3459If ∫₀¹ 1/((5+2 x-2 x²)(1+e^((2-4 x)))) d x=1/(α) log e ((α+1)/(β)), α, β>0, then α⁴-β⁴ is equal to:Integral Calculus
Q3559Let x=x(y) be the solution of the differential equation 2(y+2) log e (y+2) d x+(x+4-2 log e (y+2)) d y=0, y>-1 with x(e⁴-2)=1. Then x(e⁹-2) is equal to:Differential Equations
Q4069If the domain of the function f(x)= log e (4 x²+11 x+6)+ sin ⁻¹(4 x+3)+ cos ⁻¹((10 x+6)/3) is (α, β], then 36|α+β| is equal to:Trigonometry
Q4213Let [x] denote the greatest integer function and f(x)= max \1+x+[x], 2+x, x+2[x] 0 ≤ x ≤ 2. Let m be the number of points in [0,2], where f is not continuous…Limit, Continuity and Differentiability
Q4388Negation of p (q (p q)) is:Mathematical Reasoning
Q4543Let the determinant of a square matrix A of order m be m-n, where m and n satisfy 4 m+n=22 and 17 m+4 n=93. If det(n adj(adj(m A)))=3^(a) 5^(b) 6^(c) then…Matrices and Determinants
Q4799The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1,3,5,8, if repetition of digits is allowed, is:Permutations and Combinations
Q5010A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at…Statistics and Probability
Q5087The number of real roots of the equation x|x|-5|x+2|+6=0, is:Complex Numbers and Quadratic Equations
Q5184Let A₁ and A₂ be two arithmetic means and G₁, G₂, G₃ be three geometric means of two distinct positive numbers. Then G₁⁴+G₂⁴+G₃⁴+G₁² G₃² is equal to:Sequence and Series
Q5483The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40…Statistics and Probability
Q5544If (α, β) is the orthocenter of the triangle ABC with vertices A(3,-7), B(-1,2) and C(4,5), then 9 α-6 β+60 is equal to:Coordinate Geometry
Q5698Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and (A B-B C)+(A D-D C)=k F E, then k is equal to:Vector Algebra
Q5747Let S be the set of all (λ, μ) for which the vectors λ i-j+k, i+2 j+μ k and 3 i-4 j+5 k, where λ-μ=5, are coplanar, then Σ (λ, μ) S 80(λ²+μ²) is equal to:Vector Algebra