JEE Main 2022 (Online) 29th July Evening Shift — Question Paper

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Physics

• Given below are two statements: one is labelled as Assertion A and the other is labelled…
• Two radioactive materials A and B have decay constants 25 λ and 16 λ respectively. If…
• A thermodynamic system is taken from an original state D to an intermediate state E by…
• Match List I with List II. List I | List II; A. | Torque | I. | Nms⁻¹; B. | Stress | II…
• An α particle and a proton are accelerated from rest through the same potential…
• The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is…
• Light enters from air into a given medium at an angle of 45° with interface of the…
• A juggler throws balls vertically upwards with same initial velocity in air. When the…
• The velocity of a small ball of mass 0.3 g and density 8 g / cc when dropped in a…
• Two bodies of masses m₁=5 kg and m₂=3 kg are connected by a light string going over a…
• A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is…
• Read the following statements : (A) Volume of the nucleus is directly proportional to…
• The torque of a force 5 î+3 ĵ-7 k̂ about the origin is τ. If the force acts on a…
• A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g…
• Two identical thin metal plates has charge q₁ and q₂ respectively such that q₁>q₂. The…
• Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The…
• A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y…
• The vertical component of the earth's magnetic field is 6 × 10⁻⁵ T at any place where…
• An unpolarised light beam of intensity 2 I₀ is passed through a polaroid P and then…
• A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It…
• An object of mass 1 kg is taken to a height from the surface of earth which is equal to…
• A ball is released from a height h. If t₁ and t₂ be the time required to complete first…
• A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as…
• A metal wire of length 0.5 m and cross-sectional area 10⁻⁴ m² has breaking stress 5 ×…
• If momentum of a body is increased by 20%, then its kinetic energy increases by
• The metallic bob of simple pendulum has the relative density 5. The time period of this…
• Two identical metallic spheres A and B when placed at certain distance in air repel each…
• A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak…
• The root mean square speed of smoke particles of mass 5 × 10⁻¹⁷ kg in their Brownian…

Chemistry

• Which of the following 3d-metal ion will give the lowest enthalpy of hydration (Δ_(hyd)…
• 1.80 g of solute A was dissolved in 62.5 cm³ of ethanol and freezing point of the…
• Given below are the critical temperatures of some of the gases: Gas | Critical…
• The number of stereoisomers formed in a reaction of (±)Ph(C=O) C(OH)(CN) Ph with HCN is…
• Given below are two statements. Statement I : The compound is optically active…
• Consider the following sulphur based oxoacids. H₂ SO₃, H₂ SO₄, H₂ S₂ O₈ and H₂S₂ O₇…
• In liquation process used for tin (Sn), the metal :
• A compound 'X' is a weak acid and it exhibits colour change at pH close to the…
• For a cell, Cu(s)|Cu²⁺(0.001 M) ∥ Ag⁺(0.01 M)| Ag(s) the cell potential is found to be…
• Sum of oxidation state (magnitude) and coordination number of cobalt in Na[Co(bpy) Cl₄]…
• The Hinsberg reagent is
• Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which…
• A 1.84 mg sample of polyhydric alcoholic compound 'X' of molar mass 92.0 g/mol gave…
• Consider the reaction 4 HNO₃(1)+3 KCl(s) → Cl₂( g)+NOCl(g)+2 H₂ O(g)+3 KNO₃( s) The…
• When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely…
• Given below are the quantum numbers for 4 electrons. A. n=3,l=2, m₁=1, mₛ=+1 / 2 B…
• Assuming 1 μ g of trace radioactive element X with a half life of 30 years is absorbed…
• Dinitrogen is a robust compound, but reacts at high altitudes to form oxides. The oxide…
• C(s)+O₂( g) → CO₂( g)+400 kJ ; C(s)+1/2 O₂( g) → CO(g)+100 kJ When coal of purity 60% is…
• 200 mL of 0.01 M HCl is mixed with 400 mL of 0.01 M H₂ SO₄. The pH of the mixture is…
• Compound 'A' undergoes following sequence of reactions to give compound 'B'. The correct…
• Given below are two statements. Statement I : Stannane is an example of a molecular…
• Which of the following is NOT a natural polymer?
• Consider, PF₅, BrF₅, PCl₃, SF₆,[ICl₄]⁻, ClF₃ and IF₅. Amongst the above…
• The number of chlorine atoms in bithionol is __________.
• Portland cement contains 'X' to enhance the setting time. What is 'X'?
• Correct structure of γ-methylcyclohexane carbaldehyde is
• Given below are two statements. One is labelled as Assertion A and the other is labelled…
• When ethanol is heated with conc. H₂ SO₄, a gas is produced. The compound formed, when…

Mathematics

• Let X=[1; 1; 1] and A=[-1, 2, 3; 0, 1, 6; 0, 0, -1]. For k ∈ N, if X′ Aᵏ X=33, then k is…
• For I(x)=∫ (sec² x-2022)/(sin²⁰²² x)dx, if I(π/4)=2¹⁰¹¹, then
• The sum and product of the mean and variance of a binomial distribution are 82.5 and…
• Σᵣ₌₁²⁰(r²+1)(r !) is equal to
• If z ≠ 0 be a complex number such that |z-1/z|=2, then the maximum value of |z| is :
• If the tangent to the curve y=x³-x²+x at the point (a, b) is also tangent to the curve y…
• Let a⃗ and b⃗ be two vectors such that |a⃗+b⃗|²=|a⃗|²+2|b⃗|², a⃗ · b⃗=3 and |a⃗ ×…
• If the system of equations x+y+z=6 ; 2 x+5 y+α z=β ; x+2 y+3 z=14 has infinitely many…
• Let Q be the foot of perpendicular drawn from the point P(1,2,3) to the plane x+2…
• Let a⃗, b⃗, c⃗ be three coplanar concurrent vectors such that angles between any two of…
• Let m₁,m₂ be the slopes of two adjacent sides of a square of side a such that…
• If the solution curve of the differential equation (d y)/(d x)=(x+y-2)/(x-y) passes…
• Let S={z=x+i y:|z-1+i| ≥|z|,|z|<2,|z+i|=|z-1|}. Then the set of all values of x, for…
• If (2,3,9),(5,2,1),(1, λ, 8) and (λ, 2,3) are coplanar, then the product of all possible…
• If [t] denotes the greatest integer ≤ t, then the number of points, at which the…
• Let y=y(x) be the solution curve of the differential equation (d y)/(d x)+((2 x²+11…
• Let α, β(α>β) be the roots of the quadratic equation x²-x-4=0 . If Pₙ=αⁿ-βⁿ, n ∈ N, then…
• Let A(α,-2),B(α,6) and C(α/4,-2) be vertices of a △ ABC. If (5,α/4) is the circumcentre…
• Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2…
• Let the function f(x)={(log ₑ(1+5 x)-log ₑ(1+α x))/x, ; if x ≠ 0; 10, ; if x=0 be…
• The domain of the function f(x)=sin ⁻¹((x²-3 x+2)/(x²+2 x+7)) is :
• Let 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 ≤…
• The number of natural numbers lying between 1012 and 23421 that can be formed using the…
• If Σₖ₌₁¹⁰ K²(10_(C_K))²=22000 L , then L is equal to ________.
• Let A B be a chord of length 12 of the circle (x-2)²+(y+1)²=169/4. If tangents drawn to…
• Which of the following matrices can NOT be obtained from the matrix [-1, 2; 1, -1] by a…
• The number of elements in the set S={x ∈ ℝ: 2 cos ((x²+x)/6)=4ˣ+4⁻ˣ} is :
• If [t] denotes the greatest integer ≤ t, then the value of ∫₀¹[2 x-|3 x²-5 x+2|+1] d x…
• Let {aₙ}ₙ₌₀^∞ be a sequence such that a₀=a₁=0 and ; ; aₙ₊₂=3 aₙ₊₁-2 aₙ+1, ∀ n ≥ 0 . Then…

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