JEE Main 2022 (Online) 27th July Morning Shift — Question Paper

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Physics

• A bag is gently dropped on a conveyor belt moving at a speed of 2 m / s. The coefficient…
• A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude A₁. When…
• A microscope was initially placed in air (refractive index 1). It is then immersed in…
• An electron (mass m) with an initial velocity v⃗=v₀ î(v₀>0) is moving in an electric…
• Two cylindrical vessels of equal cross-sectional area 16 cm² contain water upto heights…
• A direct current of 4 A and an alternating current of peak value 4 A flow through…
• Two satellites A and B, having masses in the ratio 4: 3, are revolving in circular…
• Two identical positive charges Q each are fixed at a distance of '2a' apart from each…
• A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an…
• A long cylindrical volume contains a uniformly distributed charge of density ρ Cm⁻³. The…
• A torque meter is calibrated to reference standards of mass, length and time each with…
• To light, a 50 W, 100 V lamp is connected, in series with a capacitor of capacitance…
• In a meter bridge experiment, for measuring unknown resistance 'S', the null point is…
• A magnet hung at 45° with magnetic meridian makes an angle of 60° with the horizontal…
• The one division of main scale of Vernier callipers reads 1 mm and 10 divisions of…
• Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time…
• Sand is being dropped from a stationary dropper at a rate of 0.5 kgs⁻¹ on a conveyor…
• A pulley of radius 1.5 m is rotated about its axis by a force F=(12 t-3 t²) N applied…
• A square aluminum (shear modulus is 25 × 10⁹ Nm⁻²) slab of side 60 cm and thickness 15…
• Read the following statements : A. When small temperature difference between a liquid…
• What is the half-life period of a radioactive material if its activity drops to 1 / 16ᵗʰ…
• A bullet is shot vertically downwards with an initial velocity of 100 m / s from a…
• Same gas is filled in two vessels of the same volume at the same temperature. If the…
• A beam of light travelling along X-axis is described by the electric field E_y=900 sin…
• A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B…
• If K₁ and K₂ are the thermal conductivities, L₁ and L₂ are the lengths and A₁ and A₂ are…
• Two beams of light having intensities I and 4I interfere to produce a fringe pattern on…
• Two sources of equal emfs are connected in series. This combination is connected to an…
• A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is 2.0…

Chemistry

• In Carius method of estimation of halogen, 0.45 g of an organic compound gave 0.36 g of…
• 20 mL of 0.02 M K₂ Cr₂ O₇ solution is used for the titration of 10 mL of Fe²⁺ solution…
• The incorrect statement is
• According to MO theory, number of species/ions from the following having identical bond…
• 250 g solution of D-glucose in water contains 10.8 % of carbon by weight. The molality…
• The molar heat capacity for an ideal gas at constant pressure is 20.785 J K⁻¹ mol⁻¹. The…
• In the following reaction The % yield for reaction I is 60 % and that of reaction II is…
• Boiling point of a 2 % aqueous solution of a non-volatile solute A is equal to the…
• The total number of Mn=O bonds in Mn₂ O₇ is __________.
• A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on…
• Given below are two statements. Statement I : Hydrogen peroxide can act as an oxidizing…
• Given below are two statements. Statement I: O₂, Cu²⁺, and Fe³⁺ are weakly attracted by…
• The conductivity of a solution of complex with formula CoCl₃(NH₃)₄ corresponds to 1 : 1…
• Given below are two statements: one is labelled as Assertion A and, the other is…
• Given below are two statements. One is labelled as Assertion A and the other is labelled…
• Which oxoacid of phosphorous has the highest number of oxygen atoms present in its…
• Given below are two statements. Statement I : Iron (III) catalyst, acidified K₂ Cr₂ O₇…
• Given below are two statements. One is labelled as Assertion A and the other is labelled…
• Which of the following methods are not used to refine any metal? A. Liquation B…
• In the titration of KMnO₄ and oxalic acid in acidic medium, the change in oxidation…
• Given below are two statements. Statement I: The chlorides of Be and Al have Cl-bridged…
• Optical activity of an enantiomeric mixture is +12.6° and the specific rotation of (+)…
• Match List I with List II. List I | List II; (A) | Benzenesulphonyl chloride | (I) |…
• 2 NO+2 H₂ → N₂+2 H₂ O The above reaction has been studied at 800° C. The related data…
• Amongst the following, the number of oxide(s) which are paramagnetic in nature is Na₂ O…

Mathematics

• If the plane P passes through the intersection of two mutually perpendicular planes 2…
• For k ∈ ℝ, let the solutions of the equation cos (sin ⁻¹(x cot (tan ⁻¹(cos (sin ⁻¹…
• The area of the smaller region enclosed by the curves y²=8x+4 and x²+y²+4√3x-4=0 is…
• If the circle x²+y²-2 g x+6 y-19 c=0, g, c ∈ ℝ passes through the point (6,1) and its…
• Let A=(1, 2; -2, -5). Let α, β ∈ ℝ be such that α A²+β A=2 I. Then α+β is equal to
• Let f(x)=2 x²-x-1 and S={n ∈ ℤ:|f(n)| ≤ 800}. Then, the value of Σ_(n ∈ S) f(n) is equal…
• If the length of the latus rectum of the ellipse x²+4 y²+2 x+8 y-λ=0 is 4 , and l is the…
• Let the minimum value v₀ of v=|z|²+|z-3|²+|z-6 i|², z ∈ ℂ is attained at z=z₀. Then |2…
• Let the line (x-3)/7=(y-2)/-1=(z-3)/-4 intersect the plane containing the lines…
• Let f, g: ℕ-{1} → ℕ be functions defined by f(a)=α, where α is the maximum of the powers…
• Let y=y₁(x) and y=y₂(x) be two distinct solutions of the differential equation (d y)/(d…
• Let A(1,1),B(-4,3),C(-2,-5) be vertices of a triangle ABC,P be a point on side BC, and…
• An ellipse E: x²/a²+y²/b²=1 passes through the vertices of the hyperbola H…
• Let S be the sample space of all five digit numbers. It p is the probability that a…
• Let a⃗=α î+ĵ+β k̂ and b⃗=3 î-5 ĵ+4 k̂ be two vectors, such that a⃗ × b⃗=-î+9 ĵ+12 k̂…
• Suppose a₁, a₂, …, aₙ, .. be an arithmetic progression of natural numbers. If the ratio…
• Let f: ℝ → ℝ be a function defined as f(x)=a sin (π[x]/2)+[2-x], a ∈ ℝ where [t] is the…
• The mean and variance of 10 observations were calculated as 15 and 15 respectively by a…
• Let P(a, b) be a point on the parabola y²=8 x such that the tangent at P passes through…
• Let a function f: ℝ → ℝ be defined as : f(x)= ∫₀ˣ(5-|t-3|) d t, x>4 ; x²+b x , x ≤ 4…
• Let S={z ∈ ℂ: z²+z̄=0}. Then Σ_(z ∈ S)(Re(z)+Im(z)) is equal to ______________.
• Let R₁ and R₂ be two relations defined on ℝ by a R₁ b ⇔ a b ≥ 0 and a R₂ b ⇔ a ≥ b Then,
• Let S be the set containing all 3 × 3 matrices with entries from {-1,0,1}. The total…
• Let a⃗=2 î-ĵ+5 k̂ and b⃗=α î+β ĵ+2 k̂ . If ((a⃗ × b⃗) × î) · k̂=23/2 , then |b⃗ × 2 ĵ|…
• Let M and N be the number of points on the curve y⁵-9 x y+2 x=0, where the tangents to…
• The remainder when (2021)²⁰²²+(2022)²⁰²¹ is divided by 7 is
• Let y=y(x) be the solution curve of the differential equation sin ( 2x² )log ₑ( tan x²…

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