JEE Main 2022 (Online) 28th July Morning Shift — Question Paper

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Physics

• Identify the solar cell characteristics from the following options :
• The frequency of echo will be __________ Hz if the train blowing a whistle of frequency…
• Given below are two statements : Statement I : The average momentum of a molecule in a…
• A Carnot engine has efficiency of 50 %. If the temperature of sink is reduced by 40° C…
• Four identical discs each of mass 'M' and diameter 'a' are arranged in a small plane as…
• The current sensitivity of a galvanometer can be increased by : (A) decreasing the…
• In two different experiments, an object of mass 5 kg moving with a speed of 25 ms⁻¹ hits…
• In a Young's double slit experiment, a laser light of 560 nm produces an interference…
• Two electric dipoles of dipole moments 1.2 × 10⁻³⁰ Cm and 2.4 × 10⁻³⁰ Cm are placed in…
• The force required to stretch a wire of cross-section 1 cm² to double its length will be…
• In the wave equation y=0.5 sin (2 π)/λ(400 t-x) m the velocity of the wave will be:
• The equation λ=1.227/x nm can be used to find the de-Brogli wavelength of an electron…
• As shown in the figure, a metallic rod of linear density 0.45 kg m⁻¹ is lying…
• As shown in the figure, a potentiometer wire of resistance 20 Ω and length 300 cm is…
• A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation…
• A wire of resistance R₁ is drawn out so that its length is increased by twice of its…
• If the projection of 2î+4ĵ-2k̂ on î+2ĵ+αk̂ is zero. Then, the value of α will be…
• As shown in the figure, after passing through the medium 1 . The speed of light v₂ in…
• The frequencies at which the current amplitude in an LCR series circuit becomes 1/√2…
• A NCC parade is going at a uniform speed of 9 km / h under a mango tree on which a…
• If the radius of earth shrinks by 2 % while its mass remains same. The acceleration due…
• The half life period of a radioactive substance is 60 days. The time taken for 7/8th of…
• In normal adujstment, for a refracting telescope, the distance between objective and eye…
• The equation of current in a purely inductive circuit is 5 sin (49 π t-30°). If the…
• A block of mass 'm' (as shown in figure) moving with kinetic energy E compresses a…
• The diameter of an air bubble which was initially 2 mm, rises steadily through a…
• Two capacitors, each having capacitance 40 μ F are connected in series. The space…
• The dimensions of (B²/μ₀) will be : (if μ₀ : permeability of free space and B : magnetic…
• A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate…

Chemistry

• For the given first order reaction A → B the half life of the reaction is 0.3010 min…
• In which of the following pairs, electron gain enthalpies of constituent elements are…
• The number of interhalogens from the following having square pyramidal structure is…
• Terylene polymer is obtained by condensation of :
• Which of the following has least tendency to liberate H₂ from mineral acids?
• Match List - I with List - II. List - I Reaction | List - II Catalyst; (A) | 4NH₃(g) +…
• An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm…
• On complete combustion of 0.492 g of an organic compound containing C, H and O, 0.7938 g…
• Identify the correct statement for the below given transformation. CH₃-CH₂-CH₂-CH-CH₃…
• Which of the reaction is suitable for concentrating ore by leaching process ?
• The metal salts formed during softening of hardwater using Clark's method are :
• In the given reaction, X+Y+3 Z ⇄ X YZ₃ if one mole of each of X and Y with 0.05 mol of Z…
• Match List - I with List - II. List - I | List - II; (A) | Cd(s) + 2Ni(OH)₃(s) → CdO(s)…
• Among the following marked proton of which compound shows lowest pKₐ value?
• For kinetic study of the reaction of iodide ion with H₂ O₂ at room temperature : (A)…
• Total number of relatively more stable isomer(s) possible for octahedral complex…
• Which of the following statement is incorrect ?
• Identify the incorrect statement from the following.
• Match List - I with List - II, match the gas evolved during each reaction. List - I |…
• Which of the following relation is not correct?
• Statements about Enzyme Inhibitor Drugs are given below : (A) There are Competitive and…
• Kₐ for butyric acid (C₃ H₇ COOH) is 2 × 10⁻⁵. The pH of 0.2 M solution of butyric acid…
• The number of paramagnetic species among the following is ___________. B₂, Li₂, C₂, C₂⁻…
• 150 g of acetic acid was contaminated with 10.2 g ascorbic acid (C₆ H₈ O₆) to lower down…
• The disproportionation of MnO₄²⁻ in acidic medium resulted in the formation of two…

Mathematics

• If y=y(x), x ∈(0, π / 2) be the solution curve of the differential equation (sin ² 2 x)…
• Let x₁, x₂, x₃, …, x₂₀ be in geometric progression with x₁=3 and the common ratio 1/2. A…
• If ∫₀^(√3) (15 x³)/√(1+x²+√(1+x²)³) d x=α √2+β √3, where α, β are integers, then α+β is…
• Let the matrix A=[0, 1, 0; 0, 0, 1; 1, 0, 0] and the matrix B₀=A⁴⁹+2 A⁹⁸. If Bₙ=A d…
• The remainder when 7²⁰²²+3²⁰²² is divided by 5 is :
• Let f:[0,1] → R be a twice differentiable function in (0,1) such that f(0)=3 and f(1)=5…
• The minimum value of the twice differentiable function f(x)=∫₀ˣ eˣ⁻ᵗ f′(t) dt-(x²-x+1)…
• Let S₁={z₁ ∈ C:|z₁-3|=1/2} and S₂={z₂ ∈ C:|z₂-| z₂+1||=|z₂+| z₂-1||}. Then, for z₁ ∈ S₁…
• If the tangents drawn at the points P and Q on the parabola y²=2 x-3 intersect at the…
• Let a vector a⃗ has magnitude 9. Let a vector b⃗ be such that for every (x, y) ∈ R ×…
• Let the vectors a⃗=(1+t) î+(1-t) ĵ+k̂, b⃗=(1-t) î+(1+t) ĵ+2 k̂ and c⃗=t î-t ĵ+k̂, t ∈ R…
• Out of 60 % female and 40 % male candidates appearing in an exam, 60 % candidates…
• For p, q ∈ R, consider the real valued function f(x)=(x-p)²-q, x ∈ R and q>0. Let a₁…
• The sum of all real values of x for which (3 x²-9 x+17)/(x²+3 x+10)=(5 x²-7 x+19)/(3…
• lim(x → 0)(((x+2 cos x)³+2(x+2 cos x)²+3 sin (x+2 cos x))/((x+2)³+2(x+2)²+3 sin…
• If the minimum value of f(x)=(5 x²)/2+α/x⁵, x>0, is 14 , then the value of α is equal to :
• Considering the principal values of the inverse trigonometric functions, the sum of all…
• Let the solution curve of the differential equation x d y=(√(x²+y²)+y) d x, x>0…
• Considering only the principal values of the inverse trigonometric functions, the domain…
• For α ∈ N, consider a relation R on N given by R={(x, y): 3 x+α y is a multiple of 7}…
• Let P(-2,-1,1) and Q(56/17, 43/17, 111/17) be the vertices of the rhombus PRQS. If the…
• Let S be the set of all passwords which are six to eight characters long, where each…
• The foot of the perpendicular from a point on the circle x²+y²=1, z=0 to the plane 2 x+3…
• Let A=[1, -1; 2, α] and B=[β, 1; 1, 0], α, β ∈ R. Let α₁ be the value of α which…
• Consider the sequence a₁, a₂, a₃, … such that a₁=1, a₂=2 and aₙ₊₂=2/aₙ₊₁+aₙ for n=1,2,3…
• For the hyperbola H: x²-y²=1 and the ellipse E: x²/a²+y²/b²=1, a >b>0, let the (1)…
• Let C be the centre of the circle x²+y²-x+2 y=11/4 and P be a point on the circle. A…
• Let α, β and γ be three positive real numbers. Let f(x)=α x⁵+β x³+γ x, x ∈ R and g: R →…

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