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

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Physics

• The height of liquid column raised in a capillary tube of certain radius when dipped in…
• The figure represents the momentum time (p-t) curve for a particle moving along an axis…
• A capacitor of capacitance 900 μ F is charged by a 100 V battery. The capacitor is…
• In Young's double slit experiment, two slits S₁ and S₂ are 'd' distance apart and the…
• In a series LR circuit with X_L=R, power factor P₁. If a capacitor of capacitance C with…
• Choose the correct relationship between Poisson ratio (σ), bulk modulus (K) and modulus…
• A horse rider covers half the distance with 5 m / s speed. The remaining part of the…
• If the gravitational field in the space is given as (-K/r²). Taking the reference point…
• As per the given figure, a small ball P slides down the quadrant of a circle and hits…
• As per the given figure, if dI/dt=-1 A / s then the value of V_(AB) at this instant will…
• The charge flowing in a conductor changes with time as Q(t)=α t-β t²+γ t³. Where α, β…
• The output waveform of the given logical circuit for the following inputs A and B as…
• Two isolated metallic solid spheres of radii R and 2 R are charged such that both have…
• The general displacement of a simple harmonic oscillator is x = A sin ω t. Let T be its…
• In an experiment for estimating the value of focal length of converging mirror, image of…
• Electric field in a certain region is given by E⃗=(A/x² î+B/y³ ĵ) . The SI unit of A and…
• A person has been using spectacles of power -1.0 dioptre for distant vision and a…
• Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas…
• A massless square loop, of wire of resistance 10 Ω, supporting a mass of 1 g, hangs…
• A point source of light is placed at the centre of curvature of a hemispherical surface…
• In a screw gauge, there are 100 divisions on the circular scale and the main scale moves…
• A thin uniform rod of length 2 m, cross sectional area 'A' and density 'd' is rotated…
• A small object at rest, absorbs a light pulse of power 20 mW and duration 300 ns…
• Speed of an electron in Bohr's 7ᵗʰ orbit for Hydrogen atom is 3.6 × 10⁶ m / s. The…
• The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation…
• A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g…
• The magnetic moments associated with two closely wound circular coils A and B of radius…

Chemistry

• Some amount of dichloromethane (CH₂ Cl₂) is added to 671.141 mL of chloroform (CHCl₃) to…
• A solution containing 2 g of a non-volatile solute in 20 g of water boils at 373.52 K…
• A trisubstituted compound 'A', C₁₀ H₁₂ O₂ gives neutral FeCl₃ test positive. Treatment…
• Caprolactam when heated at high temperature in presence of water, gives
• Lithium aluminium hydride can be prepared from the reaction of :
• For OF₂ molecule consider the following : A. Number of lone pairs on oxygen is 2 . B…
• Benzyl isocyanide can be obtained by : A. B. C. D. Choose the correct answer from the…
• The number of electrons involved in the reduction of permanganate to manganese dioxide…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Match List I with List II List I (molecules/ions) | List II (No. of lone pairs of e⁻ on…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• To inhibit the growth of tumours, identify the compounds used from the following : A…
• Which of the following compounds would give the following set of qualitative analysis ?…
• Match List I with List II List I (Atomic number) | List II (Block of periodic table); A…
• In the wet tests for identification of various cations by precipitation, which…
• Amongst the following compounds, which one is an antacid?
• During the qualitative analysis of SO₃²⁻ using dilute H₂ SO₄, SO₂ gas is evolved which…
• When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre…
• The alkaline earth metal sulphate(s) which are readily soluble in water is/are : A…
• Consider the cell Pt₍ₛ₎|H₂( g, 1 atm)| H⁺(aq, 1 M)|| Fe³⁺(aq), Fe²⁺(aq) | Pt(s) When the…
• 600 mL of 0.01 M HCl is mixed with 400 mL of 0.01 M H₂ SO₄. The pH of the mixture is…
• The energy of one mole of photons of radiation of frequency 2 × 10¹² Hz in J mol⁻¹ is…
• Which of the following is correct order of ligand field strength?
• If compound A reacts with B following first order kinetics with rate constant 2.011 ×…
• In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after…

Mathematics

• The line l₁ passes through the point (2, 6, 2) and is perpendicular to the plane…
• Let the solution curve y=y(x) of the differential equation (d y)/(d x)-(3 x⁵ tan…
• Suppose f: ℝ →(0, ∞) be a differentiable function such that 5 f(x+y)=f(x) · f(y), ∀ x, y…
• lim x → 0 48/x⁴ ∫0ˣ t³/(t⁶+1) d t is equal to ___________.
• If a⃗ ,b⃗ ,c⃗ are three non-zero vectors and n is a unit vector perpendicular to c⃗ such…
• If the equation of the plane passing through the point (1,1,2) and perpendicular to the…
• The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14…
• If aₙ = (- 2)/(4n² - 16n + 15), then a₁ + a₂ + .... + a₂₅ is equal to :
• Let the system of linear equations x+y+kz=2 2x+3y-z=1 3x+4y+2z=k have infinitely many…
• The number of points on the curve y=54 x⁵-135 x⁴-70 x³+180 x²+210 x at which the normal…
• Let y=x+2,4y=3x+6 and 3y=4x+1 be three tangent lines to the circle (x-h)²+(y-k)²=r²…
• If the coefficient of x¹⁵ in the expansion of (a x³+1/(b x^(1 / 3)))¹⁵ is equal to the…
• The minimum number of elements that must be added to the relation R={(a, b),(b, c)} on…
• Let f¹(x)=(3 x+2)/(2 x+3), x ∈ R-{-3/2} For n ≥ 2, define fⁿ(x)=f¹ o fⁿ⁻¹(x). If…
• Let a unit vector O P make angles α, β, γ with the positive directions of the…
• Let A=(m, n; p, q), d=|A| ≠ 0 and |A-d(A d j A)|=0. Then
• If λ₁ < λ₂ are two values of λ such that the angle between the planes P₁: r⃗(3 î-5…
• If P(h, k) be a point on the parabola x=4 y², which is nearest to the point Q(0,33)…
• Let Σn=0^∞ (n³((2 n) !)+(2 n-1)(n !))/(n !)((2 n) !)=ae+b/e+c, where a, b, c ∈ ℤ and…
• Let α be the area of the larger region bounded by the curve y²=8x and the lines y=x and…
• The coefficient of x³⁰¹ in (1 + x)⁵⁰⁰ + x(1 + x)⁴⁹⁹ + x²(1 + x)⁴⁹⁸ + ... + x⁵⁰⁰ is :
• Number of 4-digit numbers (the repetition of digits is allowed) which are made using the…
• Let z=1+i and z₁=(1+i z̄)/(z̄(1-z)+1/z). Then 12/π arg (z₁) is equal to __________.
• If [t] denotes the greatest integer ≤ t, then the value of 3(e - 1)/e∫₁² x²e^([x] +…
• If tan 15°+1/(tan 75°)+1/(tan 105°)+tan 195°=2a, then the value of (a+1/a) is :
• If an unbiased die, marked with -2,-1,0,1,2,3 on its faces, is thrown five times, then…

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