JEE Main 2023 (Online) 31st January Morning Shift — Question Paper

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Physics

• Which of the following correctly represents the variation of electric potential (V) of a…
• A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic…
• A free neutron decays into a proton but a free proton does not decay into neutron. This…
• A lift of mass M=500 kg is descending with speed of 2 ms⁻¹. Its supporting cable begins…
• At a certain depth "d " below surface of earth, value of acceleration due to gravity…
• Given below are two statements : One is labelled as Assertion A and the other is…
• If R, X_L, and X_C represent resistance, inductive reactance and capacitive reactance…
• The effect of increase in temperature on the number of electrons in conduction band (nₑ)…
• Spherical insulating ball and a spherical metallic ball of same size and mass are…
• A thin rod having a length of 1 m and area of cross-section 3 × 10⁻⁶ m² is suspended…
• An inductor of 0.5 mH, a capacitor of 20 μ F and resistance of 20 Ω are connected in…
• The pressure of a gas changes linearly with volume from A to B as shown in figure. If no…
• The drift velocity of electrons for a conductor connected in an electrical circuit is…
• Expression for an electric field is given by E⃗=4000 x² î V/m. The electric flux through…
• 100 balls each of mass m moving with speed v simultaneously strike a wall normally and…
• If 1000 droplets of water of surface tension 0.07 N / m, having same radius 1 mm each…
• A bar magnet with a magnetic moment 5.0 Am² is placed in parallel position relative to a…
• In the figure given below, a block of mass M=490 g placed on a frictionless table is…
• Two identical cells, when connected either in parallel or in series gives same current…
• As shown in figure, a 70 kg garden roller is pushed with a force of F⃗=200 N at an angle…
• The initial speed of a projectile fired from ground is u. At the highest point during…
• A rod with circular cross-section area 2 cm² and length 40 cm is wound uniformly with…
• For hydrogen atom, λ₁ and λ₂ are the wavelengths corresponding to the transitions 1 and…
• In a medium the speed of light wave decreases to 0.2 times to its speed in free space…
• If a source of electromagnetic radiation having power 15 kW produces 10¹⁶ photons per…
• The speed of a swimmer is 4 km h⁻¹ in still water. If the swimmer makes his strokes…
• The correct relation between γ = cₚ/cᵥ and temperature T is :
• Two polaroide A and B are placed in such a way that the pass-axis of polaroids are…
• The maximum potential energy of a block executing simple harmonic motion is 25 J. A is…

Chemistry

• A protein 'X' with molecular weight of 70,000 u, on hydrolysis gives amino acids. One of…
• The logarithm of equilibrium constant for the reaction Pd²⁺+4 Cl⁻ ⇌ PdCl₄²⁻ is…
• The correct order of basicity of oxides of vanadium is :
• Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of…
• H₂ O₂ acts as a reducing agent in :
• The methods NOT involved in concentration of ore are A. Liquation B. Leaching C…
• Adding surfactants in non polar solvent, the micelles structure will look like
• Match items of column I and II Column I (Mixture of compounds) | Column II (Separation…
• For reaction : SO₂( g)+1/2O₂( g)⇌ SO₃( g) Kₚ=2× 10¹² at 27°C and 1 atm pressure. The K_c…
• The oxidation state of phosphorus in hypophosphoric acid is + _____________.
• When Cu²⁺ ion is treated with KI, a white precipitate, X appears in solution. The…
• Cobalt chloride when dissolved in water forms pink colored complex X which has…
• The correct order of melting points of dichlorobenzenes is
• The enthalpy change for the conversion of 1/2 Cl₂( g) to Cl⁻(aq) is (-) ___________ kJ…
• Choose the correct set of reagents for the following conversion. trans (Ph-CH=CH-CH₃) →…
• An organic compound 'A' with emperical formula C₆ H₆ O gives sooty flame on burning. Its…
• Which one of the following statements is correct for electrolysis of brine solution?
• Which transition in the hydrogen spectrum would have the same wavelength as the Balmer…
• The correct increasing order of the ionic radii is
• On complete combustion, 0.492 g of an organic compound gave 0.792 g of CO₂. The % of…
• A → B The rate constants of the above reaction at 200 K and 300 K are 0.03 min⁻¹ and…
• At 27° C, a solution containing 2.5 g of solute in 250.0 mL of solution exerts an…
• Nd²⁺ = __________
• Consider the above reaction and identify the product B.
• Which of the following artificial sweeteners has the highest sweetness value in…
• How many of the transformations given below would result in aromatic amines?

Mathematics

• For all z ∈ C on the curve C₁:|z|=4, let the locus of the point z+1/z be the curve C₂…
• The value of ∫π/3^(π/2) (2+3 sin x)/(sin x(1+cos x)) d x is equal to :
• A wire of length 20 m is to be cut into two pieces. A piece of length l₁ is bent to make…
• If the domain of the function f(x)=[x]/(1+x²), where [x] is greatest integer ≤ x, is…
• If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296…
• Let α>0, be the smallest number such that the expansion of (x^(2/3)+2/x³)³⁰ has a term β…
• Let the shortest distance between the lines L: (x-5)/-2=(y-λ)/0=(z+λ)/1, λ ≥ 0 and L₁…
• If the maximum distance of normal to the ellipse x²/4+y²/b²=1, b < 2, from the origin is…
• Let the line L: (x-1)/2=(y+1)/-1=(z-3)/1 intersect the plane 2 x+y+3 z=16 at the point…
• Let A = ( 1, 0, 0; 0, 4, - 1; 0, 12, - 3 ). Then the sum of the diagonal elements of the…
• For the system of linear equations x+y+z=6 α x+β y+7 z=3 x+2 y+3 z=14 which of the…
• Let a₁, a₂, …, aₙ be in A.P. If a₅=2 a₇ and a₁₁=18, then…
• Let R be a relation on N × ℕ defined by (a, b) R (c, d) if and only if a d(b-c)=b…
• Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3…
• If sin ⁻¹α/17 + cos ⁻¹4/5 - tan ⁻¹77/36 = 0,0 < α < 13, then sin ⁻¹(sin α ) + cos ⁻¹(cos…
• The number of real roots of the equation √(x²-4 x+3)+√(x²-9)=√(4 x²-14 x+6), is :
• Let 5 digit numbers be constructed using the digits 0,2,3,4,7,9 with repetition allowed…
• Let θ be the angle between the planes P₁: r⃗ ·(î+ĵ+2 k̂)=9 and P₂: r⃗ ·(2 î-ĵ+k̂)=15…
• Let y=f(x) represent a parabola with focus (-1/2, 0) and directrix y=-1/2. Then S={x ∈…
• A bag contains 6 balls. Two balls are drawn from it at random and both are found to be…
• Let y=f(x)=sin ³(π/3(cos (π/(3 √2)(-4 x³+5 x²+1)^(3/2)))). Then, at x = 1,
• Let a circle C₁ be obtained on rolling the circle x²+y²-4 x-6 y+11=0 upwards 4 units on…
• Let for x∈ ℝ, f(x)=(x+|x|)/2 andg(x)={x,, x<0; x²,, x≥ 0. Then area bounded by the curve…
• If the variance of the frequency distribution xᵢ | 2 | 3 | 4 | 5 | 6 | 7 | 8; Frequency…
• Let a differentiable function f satisfy f(x)+∫3ˣ f(t)/t d t=√(x+1), x ≥ 3. Then 12 f(8)…
• Let α ∈ (0,1) and β = log ₑ(1 - α ). Let Pₙ(x) = x + x²/2 + x³/3 + ... + xⁿ/n,x ∈ (0,1)…
• Let a⃗=2 î+ĵ+k̂, and b⃗ and c⃗ be two nonzero vectors such that |a⃗+b⃗+c⃗|=|a⃗+b⃗-c⃗|…
• Let a⃗ and b⃗ be two vectors such that |a⃗|=√14,|b⃗|=√6 and |a⃗ × b⃗|=√48. Then (a⃗ ·…
• The remainder on dividing 5⁹⁹ by 11 is ____________.

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