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JEE Main 2023 10 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202310 Apr, Morning shift

Physics 22Chemistry 25Mathematics 30

Physics

Q58The decay constant for a radioactive nuclide is 1.5 × 10 ⁻⁵ s ⁻¹. Atomic weight of the substance is 60 g mole ⁻¹, (N A =6×10²³). The activity of 1.0 μ g of…Atoms and Nuclei
Q6110 resistors each of resistance 10 Ω can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent…Current Electricity
Q65Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities σ,-σ and σ respectively. The…Electrostatics
Q69If the earth suddenly shrinks to 1/64 th of its original volume with its mass remaining the same, the period of rotation of earth becomes 24/x h. The value of…Gravitation
Q72The current required to be passed through a solenoid of 15 cm length and 60 turns in order of demagnetise a bar magnet of magnetic intensity 2.4×10³~Am⁻¹ is _…Magnetic Effects of Current and Magnetism
Q78A transverse harmonic wave on a string is given by y(x,t) = 5 sin (6t + 0.003x) where x and y are in cm and t in sec. The wave velocity is _ _ _ _ _ _ _ m s ⁻¹.Oscillations and Waves
Q5920Given below are two statements: Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series…Electromagnetic Induction and Alternating Currents
Q6020The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular…Atoms and Nuclei
Q6229A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together…Rotational Motion
Q6377A carrier wave of amplitude 15 V is modulated by a sinusoidal base band signal of magnitude 3 V. The ratio of maximum amplitude to minimum amplitude in an…Communication Systems
Q6586The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is λ₁. If the temperature of the gas is increased to 600 K, then the de Broglie…Dual Nature of Matter and Radiation
Q6712Given below are two statements: Statement I: If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes…Electromagnetic Induction and Alternating Currents
Q6815The energy of an electromagnetic wave contained in a small volume oscillates withElectromagnetic Waves
Q7087An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm…Optics
Q7165Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=R/2 from the surface of earth, if its weight on the surface of…Gravitation
Q7213Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r 3r respectively. The ratio of orbital speeds of the satellites…Gravitation
Q7320Match List I with List II: List I List II (A) 3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms…Kinetic Theory of Gases
Q7499Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally…Thermodynamics
Q7803The range of the projectile projected at an angle of 15° with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45° with…Kinematics
Q7997Given below are two statements: Statement I: Pressure in a reservoir of water is same at all points at the same level of water. Statement II: The pressure…Properties of Solids and Liquids
Q8174A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is x=A/2 and it moves along positive x-axis. The displacement…Oscillations and Waves
Q8313A physical quantity P is given as P = (a²b³)/(c d) The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage…Units and Measurements

Chemistry

Q5The number of bent-shaped molecule/s from the following is _ _ _ _ _ N ₃^-, NO ₂^-, I ₃^-, O ₃, SO ₂Chemical Bonding and Molecular Structure
Q6The sum of lone pairs present on the central atom of the interhalogen IF ₅ and IF ₇ is _ _ _ _ _Chemical Bonding and Molecular Structure
Q7The number of correct statement/s involving equilibria in physical processes from the following is _ _ _ _ (A) Equilibrium is possible only in a closed system…Equilibrium
Q8A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min. If both the reactions are occurring then the time…Chemical Kinetics
Q10In potassium ferrocyanide, there are _ _ _ _ pairs of electrons in the t 2g set of orbitals.Coordination Compounds
Q13FeO₄²⁻ + 2.2V F e³⁺ + 0.70V F e²⁺ - 0.45V F e⁰ E_ FeO₄²⁻/F e²⁺ ^θ is x × 10⁻³ V. The value of x is _ _ _ _ _Redox Reactions and Electrochemistry
Q15At constant temperature, a gas is at a pressure of 940.3 mm Hg. The pressure at which its volume decreases by 40% is _ _ _ _ _ mm Hg. (Nearest integer)Gaseous State
Q19In the following reactions, the total number of oxygen atoms in X and Y is _ _ _ _ _ _. Na ₂ O + H ₂ O → 2X Cl ₂ O ₇ + H ₂ O → 2Yp-Block Elements
Q21Suitable reaction condition for preparation of Methyl phenyl ether isOrganic Compounds Containing Oxygen
Q22If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed freezing point will be _ _ _ _ _ _% higher…Solutions
Q24The number of incorrect statement/s about the black body from the following is _ _ _ _ _ (A) Emit or absorb energy in the form of electromagnetic radiation…Atomic Structure
Q139Using column chromatography, mixture of two compounds 'A' and 'B' was separated. 'A' eluted first, this indicates 'B' hasSome Basic Principles of Organic Chemistry
Q215The one that does not stabilize 2° and 3° structures of proteins isBiomolecules
Q319The compound which does not exist isChemical Bonding and Molecular Structure
Q644The octahedral diamagnetic low spin complex among the following is:Coordination Compounds
Q787Prolonged heating is avoided during the preparation of ferrous ammonium sulphate to:d- and f-Block Elements
Q896Which of the following statements are correct? (A) The M ³⁺ /M ²⁺ reduction potential for iron is greater than manganese. (B) The higher oxidation states of…d- and f-Block Elements
Q1076Match List I with List II List I Industry List II Waste Generated (A) Steel plants (I) Gypsum (B) Thermal power plants (II) Fly ash (C) Fertilizer industries…Environmental Chemistry
Q1150The pair from the following pairs having both compounds with net non-zero dipole moment isOrganic Compounds Containing Halogens
Q1264Given below are two reactions, involved in the commercial production of dihydrogen (H ₂). The two reactions are carried out at temperature "T ₁ " and "T ₂ "…Hydrogen
Q1365Which of the following is used as a stabilizer during the concentration of sulphide ores?Isolation of Elements
Q1712Match List I with List II List I Polymer List II Type/Class (A) Nylon-2-Nylon-6 (I) Thermosetting polymer (B) Buna-N (II) Biodegradable polymer (C)…Polymers
Q1740Given below are two statements: Statement I: Aqueous solution of K ₂ Cr ₂ O ₇ is preferred as a primary standard in volumetric analysis over Na ₂ Cr ₂ O ₇…Principles Related to Practical Chemistry
Q2082The number of molecules and moles in 2.8375 litres of O ₂ at STP are respectivelySome Basic Concepts in Chemistry
Q2361Given (A) 2CO(g)+O₂(g)→ 2CO₂(g) Δ H₁⁰=-x~kJ~mol⁻¹ (B) C(graphite)+O₂(g)→ CO₂(g) Δ H₂⁰=-y~kJ~mol⁻¹ Δ H⁰ for the reaction C(graphite)+1/2O₂(g)→ CO(g) is:Chemical Thermodynamics

Mathematics

Q31Let y = p(x) be the parabola passing through the points (- 1,0),(0,1) and (1,0). If the area of the region (x,y):(x + 1)² + (y - 1)² ≤ 1,y ≤ p(x) is A, then…Integral Calculus
Q33The coefficient of x⁷ in (1 - x + 2x³)¹⁰ is _ _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q40Let f:(- 2,2) → R be defined by f(x) = \ x[x], - 2 < x < 0 (x - 1)[x], 0 ≤ x ≤ 2. where [x] denotes the greatest integer function. If m and n respectively are…Limit, Continuity and Differentiability
Q41Let a, b, c be three distinct positive real numbers such that (2a)^(log e a) = (bc)^(log e b) and b^(log e 2) = a^(log e c). Then, 6a + 5bc is equal to _ _ _…Limit, Continuity and Differentiability
Q45Let a common tangent to the curves y² = 4x and (x - 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to _ _ _ _ _.Coordinate Geometry
Q46Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the…Permutations and Combinations
Q47The number of permutations, of the digits 1, 2, 3,..., 7 without repetition, which neither contain the string 153 nor the string 2467, is _ _ _ _ _ _.Permutations and Combinations
Q50The sum of all those terms, of the arithmetic progression 3, 8, 13,...., 373, which are not divisible by 3, is equal to _ _ _ _ _ _.Sequence and Series
Q51The number of elements in the set n Z:|n² - 10n + 19| < 6 is _ _ _ _ _.Sets, Relations and Functions
Q52If the mean of the frequency distribution Class: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 Frequency: | 2 | 3 | x | 5 | 4 is 28, then its variance is _ _ _ _ _.Statistics and Probability
Q2468Let two vertices of a triangle ABC be (2, 4, 6) and (0, - 2, - 5), and its centroid be (2, 1, - 1). If the image of the third vertex in the plane x+2y+4z=11…Three Dimensional Geometry
Q2469Let P be the point of intersection of the line (x + 3)/3 = (y + 2)/1 = (1 - z)/2 and the plane x+y+z=2. If the distance of the point P from the plane 3x - 4y…Three Dimensional Geometry
Q2518The shortest distance between the lines (x + 2)/1 = y/(- 2) = (z - 5)/2 and (x - 4)/1 = (y - 1)/2 = (z + 3)/0 is:Three Dimensional Geometry
Q2680A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the…Limit, Continuity and Differentiability
Q2791The slope of tangent at any point (x, y) on a curve y=y(x) is (x² + y²)/2xy,x > 0. If y(2) = 0, then a value of y(8) is:Limit, Continuity and Differentiability
Q2944If the coefficient of x⁷ in (ax - 1 b x²)¹³ and the coefficient of x⁻⁵ in (ax + 1 b x²)¹³ are equal, then a⁴b⁴ is equal to:Binomial Theorem and Its Simple Applications
Q3056A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius λ. Then the locus of the point, that divides…Coordinate Geometry
Q3162Let the complex number z = x + iy be such that (2z - 3i)/(2z + i) is purely imaginary. If x + y² = 0, then y⁴ + y² - y is equal to:Complex Numbers and Quadratic Equations
Q3561Let f be a differentiable function such that x²f(x) - x = 4∫₀ˣ tf(t)dt, f(1) = 2/3. Then 18f(3) is equal to:Differential Equations
Q3765Let the ellipse E:x² + 9y² = 9 intersect the positive x and y-axes at the points A and B respectively. Let the major axis of E be a diameter of the circle C…Coordinate Geometry
Q3879If f(x) = (tan 1°)x + log e (123) x log e (1234) - (tan 1°),x > 0, then the least value of f(f(x)) + f(f(4/x)) is:Sets, Relations and Functions
Q3996If I(x) = ∫ e^(sin ²x)(cos x sin 2x - sin x)dx and I(0) = 1, then I((π)/3) is equal to:Integral Calculus
Q4394The negation of the statement (p q) (q (r)) is:Mathematical Reasoning
Q4546If A is a 3 × 3 matrix and |A| = 2, then |3 adj (|3A|A²)| is equal to:Matrices and Determinants
Q4627For the system of linear equations 2x - y + 3z = 5 3x + 2y - z = 7 4x + 5y + α z = β, which of the following is NOT correct?Matrices and Determinants
Q4928Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2^(N) < N! is m/n, where m and n are coprime, then 4m-3n is…Statistics and Probability
Q5269Let the first term α and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the…Sequence and Series
Q566896 cos (π)/33 cos (2π)/33 cos (4π)/33 cos (8π)/33 cos (16π)/33 is equal to:Trigonometry
Q5701An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If OP = u,OR = v, and OQ = α u + β v, then α,β ² are the roots…Vector Algebra
Q5841Let O be the origin and the position vector of the point P be - i - 2 j + 3 k. If the position vectors of the points A, B and C are - 2 i + j - 3 k,2 i + 4 j…Vector Algebra