JEE Main 2023 (Online) 30th January Evening Shift — Question Paper

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Physics

• A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m / s at t=0 s…
• A vehicle travels 4 km with speed of 3 km / h and another 4 km with speed of 5 km / h…
• The velocity of a particle executing SHM varies with displacement (x) as 4 v²=50-x². The…
• A current carrying rectangular loop PQRS is made of uniform wire. The length P R=Q S=5…
• As shown in figure, a cuboid lies in a region with electric field E=2 x² î-4 y ĵ+6 k̂ N…
• In an ac generator, a rectangular coil of 100 turns each having area 14 × 10⁻² m² is…
• The output Y for the inputs A and B of circuit is given by Truth table of the shown…
• In the given circuit, rms value of current (Iᵣₘₛ) through the resistor R is:
• For a simple harmonic motion in a mass spring system shown, the surface is frictionless…
• As shown in the figure, a point charge Q is placed at the centre of conducting spherical…
• A block of √3 kg is attached to a string whose other end is attached to the wall. An…
• A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the…
• An electron accelerated through a potential difference V₁ has a de-Broglie wavelength of…
• An object is allowed to fall from a height R above the earth, where R is the radius of…
• Match List I with List II : List I | List II ; A. | Torque | I. | kgm⁻¹ s⁻²; B. | Energy…
• A force is applied to a steel wire 'A', rigidly clamped at one end. As a result…
• A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute…
• A point source of 100 W emits light with 5 % efficiency. At a distance of 5 m from the…
• A radioactive nucleus decays by two different process. The half life of the first…
• A thin prism P₁ with an angle 6° and made of glass of refractive index 1.54 is combined…
• A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal…
• Given below are two statements: one is labelled as Assertion A and the other is labelled…
• The equivalent resistance between A and B is _________.
• As shown in the figure, a current of 2 A flowing in an equilateral triangle of side 4 √3…
• If the potential difference between B and D is zero, the value of x is 1/n Ω. The value…
• A faulty thermometer reads 5° C in melting ice and 95° C in stream. The correct…
• A flask contains hydrogen and oxygen in the ratio of 2: 1 by mass at temperature 27° C…
• In a Young's double slit experiment, the intensities at two points, for the path…
• Given below are two statements: one is labelled as Assertion A and the other is labelled…

Chemistry

• KMnO₄ oxidises I⁻ in acidic and neutral/faintly alkaline solutions, respectively, to :
• 1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature…
• Given below are two statements: One is labelled as Assertion A and the other is labelled…
• Consider the following equation: 2SO₂(g)+O₂(g)⇌ 2SO₃(g),Δ H=-190 kJ The number of…
• The graph of log x/m vs log p for an adsorption process is a straight line inclined at…
• Decreasing order towards SN 1 reaction for the following compounds is:
• Match List I with List II : List I (Complexes) | List II (Hybridisation) ; A. |…
• Which of the following reaction is correct?
• Chlorides of which metal are soluble in organic solvents :
• Formulae for Nessler's reagent is :
• The strength of 50 volume solution of hydrogen peroxide is ______ g / L (Nearest…
• 1 L, 0.02 M solution of [Co(NH₃)₅ SO₄] Br is mixed with 1 L, 0.02 M solution of…
• The Cl-Co-Cl bond angle values in a fac- [Co(NH₃)₃ Cl₃] complex is/are :
• Number of compounds from the following which will not dissolve in cold NaHCO₃ and NaOH…
• Boric acid is solid, whereas BF₃ is gas at room temperature because of :
• Match List I with List II : List I (Mixture) | List II (Separation Technique) ; A. |…
• In the above conversion of compound (X) to product (Y), the sequence of reagents to be…
• The wave function (Ψ) of 2 s is given by Ψ₂ₛ=1/(2 √(2 π))(1/a₀)^(1 / 2)(2-r/a₀) e^(-r /…
• Bond dissociation energy of "E-H" bond of the "H₂ E " hydrides of group 16 elements…
• An organic compound undergoes first-order decomposition. If the time taken for the 60 %…
• Lead storage battery contains 38 % by weight solution of H₂ SO₄. The van't Hoff factor…
• The electrode potential of the following half cell at 298 K X|X²⁺(0.001 M) ∥ Y²⁺(0.01…
• A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of…
• Given below are two statements: One is labelled as Assertion A and the other is labelled…
• The most stable carbocation for the following is:
• The correct order of pKₐ values for the following compounds is:
• Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of 5.0 Å…
• Maximum number of electrons that can be accommodated in shell with n=4 are:
• Given below are two statements: Statement I : During Electrolytic refining, the pure…

Mathematics

• If ∫ √(sec 2x-1)dx=α logₑ|cos 2x+β+√(cos 2x(1+cos 1/βx))|+ constant, then β-α is equal…
• A bag contains six balls of different colours. Two balls are drawn in succession with…
• Let S be the set of all values of a₁ for which the mean deviation about the mean of 100…
• The number of ways of selecting two numbers a and b, a ∈{2,4,6, … ., 100} and b ∈{1,3,5…
• If the functions f(x)=x³/3+2 b x+(a x²)/2 and g(x)=x³/3+a x+b x², a ≠ 2 b have a common…
• For α, β ∈ ℝ, suppose the system of linear equations x-y+z=5 ; 2 x+2 y+α z=8 ; 3 x-y+4…
• The 8ᵗʰ common term of the series S₁=3+7+11+15+19+… . . ; ; S₂=1+6+11+16+21+… . . is :
• Let x=(8 √3+13)¹³ and y=(7 √2+9)⁹. If [t] denotes the greatest integer ≤ t, then :
• The solution of the differential equation (d y)/(d x)=-((x²+3 y²)/(3 x²+y²)), y(1)=0 is :
• A vector v⃗ in the first octant is inclined to the x-axis at 60°, to the y-axis at 45…
• If P is a 3 × 3 real matrix such that Pᵀ=a P+(a-1) I, where a>1, then :
• If the value of real number a>0 for which x²-5 a x+1=0 and x²-a x-5=0 have a common real…
• If a plane passes through the points (-1, k, 0),(2, k,-1),(1,1,2) and is parallel to the…
• lim(n → ∞) 3/n{4+(2+1/n)²+(2+2/n)²+…+(3-1/n)²} is equal to :
• The parabolas : a x²+2 b x+c y=0 and d x²+2 e x+f y=0 intersect on the line y=1. If a…
• 50ᵗʰ root of a number x is 12 and 50ᵗʰ root of another number y is 18 . Then the…
• Let a line L pass through the point P(2,3,1) and be parallel to the line x+3 y-2…
• Let f, g and h be the real valued functions defined on ℝ as f(x)={x/|x|,, x ≠ 0; 1,, x=0…
• Let λ ∈ ℝ, a⃗=λ î+2 ĵ-3 k̂, b⃗=î-λ ĵ+2 k̂. If ((a⃗+b⃗) ×(a⃗ × b⃗)) ×(a⃗-b⃗)=8 î-40 ĵ-24…
• Let A be the area of the region {(x,y):y≥ x²,y≥ (1-x)²,y≤ 2x(1-x)}. Then 540 A is equal…
• Let A be a point on the x-axis. Common tangents are drawn from A to the curves x²+y²=8…
• Let P(a₁, b₁) and Q(a₂, b₂) be two distinct points on a circle with center C(√2, √3)…
• Let a⃗ and b⃗ be two vectors, Let |a⃗|=1,|b⃗|=4 and a⃗ · b⃗=2. If c⃗=(2 a⃗ × b⃗)-3 b⃗…
• Let a, b, c>1, a³, b³ and c³ be in A.P., and log ₐ b, log _c a and log _b c be in G.P…
• Let q be the maximum integral value of p in [0,10] for which the roots of the equation…
• The range of the function f(x)=√(3-x)+√(2+x) is :
• The number of seven digits odd numbers, that can be formed using all the seven digits 1…
• Let A={1,2,3,5,8,9}. Then the number of possible functions f: A → A such that f(m ·…

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