JEE Main 2023 (Online) 24th January Evening Shift — Question Paper

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Physics

• An α-particle, a proton and an electron have the same kinetic energy. Which one of the…
• Given below are two statements: one is labelled as Assertion A and the other is labelled…
• A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of…
• A long solenoid is formed by winding 70 turns cm⁻¹. If 2.0 A current flows, then the…
• Given below are two statements: Statement I : Acceleration due to earth's gravity…
• When a beam of white light is allowed to pass through convex lens parallel to principal…
• A body of mass 1kg begins to move under the action of a time dependent force F⃗ = ( tî +…
• The electric field and magnetic field components of an electromagnetic wave going…
• A uniform solid cylinder with radius R and length L has moment of inertia I₁, about the…
• If a copper wire is stretched to increase its length by 20%. The percentage increase in…
• Let γ₁ be the ratio of molar specific heat at constant pressure and molar specific heat…
• The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop…
• The energy released per fission of nucleus of ²⁴⁰X is 200 MeV. The energy released if…
• The velocity time graph of a body moving in a straight line is shown in the figure. The…
• The electric potential at the centre of two concentric half rings of radii R₁ and R₂…
• A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end…
• A parallel plate capacitor with air between the plate has a capacitance of 15pF. The…
• A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12…
• A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass…
• The logic gate equivalent to the given circuit diagram is :
• A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The…
• Three identical resistors with resistance R = 12Ω and two identical inductors with self…
• A cell of emf 90 V is connected across series combination of two resistors each of 100Ω…
• If two vectors P⃗=î+2mĵ+mk̂ and Q⃗=4î-2ĵ+mk̂ are perpendicular to each other. Then, the…
• A metallic rod of length 'L' is rotated with an angular speed of 'ω' normal to a uniform…
• If the distance of the earth from Sun is 1.5 × 10⁶ km. Then the distance of an imaginary…
• In an Isothermal change, the change in pressure and volume of a gas can be represented…
• Given below are two statements: one is labelled as Assertion A and the other is labelled…
• A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water…

Chemistry

• Identify the correct statements about alkali metals. A. The order of standard reduction…
• The number of units, which are used to express concentration of solutions from the…
• The total pressure observed by mixing two liquids A and B is 350 mm Hg when their mole…
• If the pKa of lactic acid is 5, then the pH of 0.005 M calcium lactate solution at 25°C…
• In which of the following reactions the hydrogen peroxide acts as a reducing agent?
• Total number of tripeptides possible by mixing of valine and proline is ___________
• Which will undergo deprotonation most readily in the basic medium?
• Given below are two statements, one is labelled as Assertion A and the other is labelled…
• Sum of π-bonds present in peroxodisulphuric acid and pyrosulphuric acid is ___________
• K₂Cr₂O₇ paper acidified with dilute H₂SO₄ turns green when exposed to :
• Which of the following cannot be explained by crystal field theory?
• Given below are two statements: Statement I : Pure Aniline and other arylamines are…
• One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The…
• Which one amongst the following are good oxidizing agents? A. Sm²⁺ B. Ce²⁺ C. Ce⁴⁺ D…
• Choose the correct representation of conductometric titration of benzoic acid vs sodium…
• What is the number of unpaired electron(s) in the highest occupied molecular orbital of…
• The hybridization and magnetic behaviour of cobalt ion in [Co(NH₃)₆]³⁺ complex…
• A student has studied the decomposition of a gas AB₃ at 25°C. He obtained the following…
• The number of s-electrons present in an ion with 55 protons in its unipositive state is
• The metal which is extracted by oxidation and subsequent reduction from its ore is :
• Choose the correct colour of the product for the following reaction.
• Match List I with List II List-I Type | List-II Name; A. | Antifertility drug | i) |…
• The number of statement/s which are the characteristics of physisorption is __________…
• Given below are two statements, one is labelled as Assertion A and the other is labelled…

Mathematics

• If the system of equations x+2y+3z=3 4x+3y-4z=4 8x+4y-λ z=9+μ has infinitely many…
• The equations of the sides AB, BC and CA of a triangle ABC are : 2x+y=0,x+py=21a,(a± 0)…
• Let α⃗ = 4î + 3ĵ + 5k̂ and β⃗ = î + 2ĵ - 4k̂. Let β⃗ ₁ be parallel to α⃗ and β⃗ ₂ be…
• The number of real solutions of the equation 3( x² + 1/x² ) - 2( x + 1/x ) + 5 = 0, is
• The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6…
• The minimum number of elements that must be added to the relation R = {(a, b), (b, c)…
• If f(x) = x³ - x²f'(1) + xf''(2) - f'''(3),x ∈ ℝ, then
• If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the…
• Let f(x) be a function such that f(x+y)=f(x).f(y) for all x,y∈ ℕ. If f(1)=3 and Σₖ₌₁ⁿ…
• Let the six numbers a₁,a₂,a₃,a₄,a₅,a₆, be in A.P. and a₁+a₃=10. If the mean of these six…
• If (1³ + 2³ + 3³ + ... up to n terms)/(1 . 3 + 2 . 5 + 3 . 7 + ... up to n terms) = 9/5…
• If f(x) = 2²ˣ/(2²ˣ + 2),x ∈ ℝ, then f( 1/2023 ) + f( 2/2023 ) + ... + f( 2022/2023 ) is…
• The locus of the mid points of the chords of the circle C₁:(x - 4)² + (y - 5)² = 4 which…
• Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls…
• The set of all values of a for which lim _(x → a) ([x - 5] - [2x + 2]) = 0, where [α]…
• Let the plane containing the line of intersection of the planes P₁ : x+(λ+4)y+z=1 and P₂…
• The number of square matrices of order 5 with entries from the set {0, 1}, such that the…
• Let f be a differentiable function defined on [ 0,π/2 ] such that f(x) > 0 and f(x) +…
• Let A be a 3 × 3 matrix such that |adj(adj(adj A))|=12⁴. Then |A⁻¹ adj A| is equal to
• Let y=y(x) be the solution of the differential equation (x²-3y²)dx+3xy dy=0,y(1)=1. Then…
• Let a⃗ = î + 2ĵ + λ k̂,b⃗ = 3î - 5ĵ - λ k̂,a⃗ . c⃗ = 7,2b⃗ . c⃗ + 43 = 0,a⃗ × c⃗ = b⃗ ×…
• The value of ( (1 + sin 2π/9 + i cos 2π/9)/(1 + sin 2π/9 - i cos 2π/9) )³ is
• If the shortest between the lines (x + √6)/2 = (y - √6)/3 = (z - √6)/4 and (x - λ)/3 =…
• If the area of the region bounded by the curves y²-2y=-x,x+y=0 is A, then 8 A is equal…
• If (³⁰C₁)² + 2(³⁰C₂)² + 3(³⁰C₃)² + ... + 30(³⁰C₃₀)² = (α 60!)/(30!)² then α is equal to :
• Let the sum of the coefficients of the first three terms in the expansion of ( x - 3/x²…
• Let S = { θ ∈ [0,2π ):tan (π cos θ ) + tan (π sin θ ) = 0}. Then Σ_(θ ∈ S) sin ²( θ +…
• ∫_(3√2/4)^(3√3/4) 48/√(9 - 4x²)dx is equal to :

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