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JEE Main 2022 29 Jul Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202229 Jul, Evening shift

Physics 26Chemistry 18Mathematics 29

Physics

Q50A capacitor of capacitance 500 μ F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC…Electromagnetic Induction and Alternating Currents
Q52Two radioactive materials A and B have decay constants 25 λ and 16 λ respectively. If initially they have the same number of nuclei, then the ratio of the…Atoms and Nuclei
Q55A modulating signal 2 sin (6.28 × 10⁶) t is added to the carrier signal 4 sin (12.56 × 10⁹) t for amplitude modulation. The combined signal is passed through…Communication Systems
Q59Nearly 10% of the power of a 110 ~W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1…Electromagnetic Waves
Q67A metal wire of length 0.5 ~m and cross-sectional area 10⁻⁴ ~m² has breaking stress 5 × 10⁸ Nm⁻². A block of 10 ~kg is attached at one end of the string and…Properties of Solids and Liquids
Q68The speed of a transverse wave passing through a string of length 50 ~cm and mass 10 ~g is 60 ~ms⁻¹. The area of cross-section of the wire is 2.0 ~mm² and its…Properties of Solids and Liquids
Q69A tube of length 50 ~cm is filled completely with an incompressible liquid of mass 250 ~g and closed at both ends. The tube is then rotated in horizontal…Properties of Solids and Liquids
Q70The velocity of a small ball of mass 0.3 ~g and density 8 ~g / cc when dropped in a container filled with glycerine becomes constant after some time. If the…Properties of Solids and Liquids
Q72The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 ~s. If the metallic bob is immersed in water, then the…Oscillations and Waves
Q5913A circuit element X when connected to an a.c. supply of peak voltage 100 ~V gives a peak current of 5 ~A which is in phase with the voltage. A second element…Electromagnetic Induction and Alternating Currents
Q6126Read the following statements: (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mass number…Atoms and Nuclei
Q6189Two identical thin metal plates has charge q₁ and q₂ respectively such that q₁>q₂. The plates were brought close to each other to form a parallel plate…Electrostatics
Q6247If momentum of a body is increased by 20%, then its kinetic energy increases byRotational Motion
Q6520Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Alloys such as constantan and manganin are…Current Electricity
Q6521A 1 ~m long wire is broken into two unequal parts X and Y. The X part of the wire is streched into another wire W. Length of W is twice the length of X and…Current Electricity
Q6577An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:Dual Nature of Matter and Radiation
Q6930Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is…Electrostatics
Q7117Light enters from air into a given medium at an angle of 45^(°) with interface of the air-medium surface. After refraction, the light ray is deviated through…Optics
Q7234An object of mass 1 ~kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the…Gravitation
Q7408The root mean square speed of smoke particles of mass 5 × 10⁻¹⁷ ~kg in their Brownian motion in air at NTP is approximately. [Given k=1.38 × 10⁻²³ JK⁻¹ ]Kinetic Theory of Gases
Q7630The vertical component of the earth's magnetic field is 6 × 10⁻⁵ ~T at any place where the angle of dip is 37^(°). The earth's resultant magnetic field at…Magnetic Effects of Current and Magnetism
Q7868A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball…Kinematics
Q7869A ball is released from a height h. If t₁ and t₂ be the time required to complete first half and second half of the distance respectively. Then, choose the…Kinematics
Q8112The torque of a force 5 i+3 j-7 k about the origin is τ. If the force acts on a particle whose position vector is 2 i+2 j+k, then the value of τ will beRotational Motion
Q8345Match List I with List II. List I List II A. Torque I. Nms ⁻¹ B. Stress II. J kg ⁻¹ C. Latent Heat III. Nm D. Power IV. Nm ⁻² Choose the correct answer from…Units and Measurements
Q8465An unpolarised light beam of intensity 2 I₀ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its…Optics

Chemistry

Q2The number of stereoisomers formed in a reaction of (±)Ph(C=O) C(OH)(CN) Ph with HCN is _ _ _ _ _ _. [. where Ph is -C₆ H₅ ]Organic Compounds Containing Oxygen
Q4Consider, PF₅, BrF₅, PCl₃, SF₆,[ICl₄]⁻, ClF₃ and IF₅. Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having sp³~d² hybridisation is _…Chemical Bonding and Molecular Structure
Q5Assuming 1 μ g of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100…Chemical Kinetics
Q8For a cell, Cu(s)|Cu²⁺(0.001 M) \| Ag⁺(0.01 M)| Ag(s) the cell potential is found to be 0.43 ~V at 298 ~K. The magnitude of standard electrode potential for…Redox Reactions and Electrochemistry
Q9'x' g of molecular oxygen (O₂) is mixed with 200 ~g of neon (Ne). The total pressure of the non-reactive mixture of O₂ and Ne in the cylinder is 25 bar. The…Gaseous State
Q12When ethanol is heated with conc. H₂ SO₄, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer's…Organic Compounds Containing Oxygen
Q151.80 ~g of solute A was dissolved in 62.5 ~cm³ of ethanol and freezing point of the solution was found to be 155.1 ~K. The molar mass of solute A is _ _ _ _ g…Solutions
Q18A 1.84 mg sample of polyhydric alcoholic compound 'X' of molar mass 92.0 g/mol gave 1.344 mL of H₂ gas at STP. The number of alcoholic hydrogens present in…Some Basic Concepts in Chemistry
Q180Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Amylose is insoluble in water. Reason R…Biomolecules
Q634Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural…Coordination Compounds
Q1312200 ~mL of 0.01 M HCl is mixed with 400 ~mL of 0.01 M H₂ SO₄. The pH of the mixture is _ _ _ _ _. Given: log 2=0.30, log 3=0.48, log 5=0.70, log 7=0.84, log…Equilibrium
Q1473In liquation process used for tin (Sn), the metal:p-Block Elements
Q1474Given below are two statements. Statement I: Stannane is an example of a molecular hydride. Statement II: Stannane is a planar molecule. In the light of the…p-Block Elements
Q1703Which of the following is NOT a natural polymer?Polymers
Q1813A compound 'X' is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with CH₃ COOH. Compound 'X'…Redox Reactions and Electrochemistry
Q2078Consider the reaction 4 HNO₃(1)+3 KCl(s) → Cl₂(~g)+NOCl(g)+2 H₂ O(g)+3 KNO₃(~s) The amount of HNO₃ required to produce 110.0 ~g of KNO₃ is (Given: Atomic…Some Basic Concepts in Chemistry
Q2079C(s)+O₂(~g) → CO₂(~g)+400 ~kJ C(s)+1/2 O₂(~g) → CO(g)+100 ~kJ When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is…Some Basic Concepts in Chemistry
Q2209Given below are the quantum numbers for 4 electrons. A. n=3,l=2, ~m₁=1, ~m s =+1 / 2 B. n=4,l=1, ~m₁=0, ~m s =+1 / 2 C. n=4,l=2, ~m₁=-2, ~m s =-1 / 2 D…Atomic Structure

Mathematics

Q22If the tangent to the curve y=x³-x²+x at the point (a, b) is also tangent to the curve y = 5x² + 2x - 25 at the point (2, - 1), then |2a + 9b| is equal to _ _…Limit, Continuity and Differentiability
Q24If Σ k=1 ¹⁰ K²(10 C K)²=22000 L, then L is equal to _ _ _ _.Binomial Theorem and Its Simple Applications
Q25Let S=\(x, y) N × N: 9(x-3)²+16(y-4)² ≤ 144 and T=\(x, y) R × R:(x-7)²+(y-4)² ≤ 36. Then n(S T) is equal to _ _ _ _ _.Coordinate Geometry
Q26Let A B be a chord of length 12 of the circle (x-2)²+(y+1)²=169/4. If tangents drawn to the circle at points A and B intersect at the point P, then five times…Coordinate Geometry
Q35If [t] denotes the greatest integer ≤ t, then the number of points, at which the function f(x)=4|2 x+3|+9[x+1/2]-12[x+20] is not differentiable in the open…Limit, Continuity and Differentiability
Q37Let X=[ l1 1 1 ] and A=[ ccc-1 2 3 0 1 6 0 0 -1 ]. For k N, if X^() A^(k) X=33, then k is equal to _ _ _ _.Matrices and Determinants
Q40The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2,3,4,5,6 (repetition of digits is not allowed) and divisible…Permutations and Combinations
Q42The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution…Statistics and Probability
Q43Let α, β(α>β) be the roots of the quadratic equation x²-x-4=0. If P n =αⁿ-βⁿ, n N, then (P₁₅ P₁₆-P₁₄ P₁₆-P₁₅²+P₁₄ P₁₅)/(P₁₃ P₁₄) is equal to _ _ _ _ _.Complex Numbers and Quadratic Equations
Q48Let a and b be two vectors such that |a+b|²=|a|²+2|b|², a · b=3 and |a × b|²=75. Then |a|² is equal to _ _ _ _ _.Vector Algebra
Q2600Let Q be the foot of perpendicular drawn from the point P(1,2,3) to the plane x+2 y+z=14. If R is a point on the plane such that P R Q=60^(°), then the area…Three Dimensional Geometry
Q2601If (2,3,9),(5,2,1),(1, λ, 8) and (λ, 2,3) are coplanar, then the product of all possible values of λ is:Three Dimensional Geometry
Q3003Σ r=1 ²⁰(r²+1)(r !) is equal toBinomial Theorem and Its Simple Applications
Q3195Let S= =x+i y:|z-1+i| ≥|z|,|z|<2,|z+i|=|z-1|. Then the set of all values of x, for which w=2 x+i y S for some y R, is:Complex Numbers and Quadratic Equations
Q3267If z ≠ 0 be a complex number such that |z-1/z|=2, then the maximum value of |z| is:Complex Numbers and Quadratic Equations
Q3447If [t] denotes the greatest integer ≤ t, then the value of ∫₀¹[2 x-|3 x²-5 x+2|+1] d x is:Integral Calculus
Q3630If the solution curve of the differential equation (d y)/(d x)=(x+y-2)/(x-y) passes through the points (2,1) and (k+1,2), k>0, thenDifferential Equations
Q3631Let y=y(x) be the solution curve of the differential equation (d y)/(d x)+((2 x²+11 x+13)/(x³+6 x²+11 x+6)) y=((x+3))/(x+1), x>-1, which passes through the…Differential Equations
Q3995For I(x)=∫ (sec ² x-2022)/(sin ²⁰²² x) d x, if I((π)/4)=2¹⁰¹¹, thenIntegral Calculus
Q4068The domain of the function f(x)= sin ⁻¹((x²-3 x+2)/(x²+2 x+7)) is:Trigonometry
Q4158Let the function f(x)=\ cl (log e (1+5 x)- log e (1+α x))/x; if x ≠ 0 10; if x=0 be continuous at x=0.. Then α is equal toLimit, Continuity and Differentiability
Q4377The statement (p ⇒ q) (p ⇒ r) is NOT equivalent toMathematical Reasoning
Q4507Which of the following matrices can NOT be obtained from the matrix [ cc-1 2 1 -1 ] by a single elementary row operation ?Matrices and Determinants
Q4615If the system of equations x+y+z=6 2 x+5 y+α z=β x+2 y+3 z=14 has infinitely many solutions, then α+β is equal toMatrices and Determinants
Q4861Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a…Statistics and Probability
Q5338Let n n=0 ^(∞) be a sequence such that a₀=a₁=0 and a n+2 =3 a n+1 -2 a n +1, n ≥ 0. Then a₂₅ a₂₃-2 a₂₅ a₂₂-2 a₂₃ a₂₄+4 a₂₂ a₂₄ is equal toSequence and Series
Q5542Let A(α,-2), B(α, 6) and C((α)/4,-2) be vertices of a ABC. If (5, (α)/4) is the circumcentre of ABC, then which of the following is NOT correct about ABC ?Coordinate Geometry
Q5619Let m₁, m₂ be the slopes of two adjacent sides of a square of side a such that a²+11 a+3(m₁²+m₂²)=220. If one vertex of the square is (10(cos α- sin α)…Coordinate Geometry
Q5830Let a, b, c be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and (a × b) ·(b ×…Vector Algebra