JEE Main 2023 (Online) 13th April Morning Shift — Question Paper

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Physics

• In the given figure, an inductor and a resistor are connected in series with a battery…
• The rms speed of oxygen molecule in a vessel at particular temperature is (1+5/x)^(1/2)…
• A solid sphere is rolling on a horizontal plane without slipping. If the ratio of…
• From the given transfer characteristic of a transistor in CE configuration, the value of…
• Two trains 'A' and 'B' of length 'l' and '4 l' are travelling into a tunnel of length…
• The difference between threshold wavelengths for two metal surfaces A and B having work…
• The elastic potential energy stored in a steel wire of length 20 m stretched through 2…
• A potential V₀ is applied across a uniform wire of resistance R. The power dissipation…
• Which graph represents the difference between total energy and potential energy of a…
• The radius of 2ⁿᵈ orbit of He⁺ of Bohr's model is r₁ and that of fourth orbit of Be³⁺ is…
• Under isothermal condition, the pressure of a gas is given by P=a V⁻³, where a is a…
• When a resistance of 5 Ω is shunted with a moving coil galvanometer, it shows a full…
• A thin infinite sheet charge and an infinite line charge of respective charge densities…
• Which of the following Maxwell's equation is valid for time varying conditions but not…
• Different combination of 3 resistors of equal resistance R are shown in the figures. The…
• A fish rising vertically upward with a uniform velocity of 8 ms⁻¹, observes that a bird…
• A bullet of 10 g leaves the barrel of gun with a velocity of 600 m / s. If the barrel of…
• A vessel of depth 'd' is half filled with oil of refractive index n₁ and the other half…
• Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an…
• The ratio of powers of two motors is (3 √x)/(√x+1), that are capable of raising 300 kg…
• A planet having mass 9 Me and radius 4 Rₑ, where Me and Re are mass and radius of earth…
• A disc is rolling without slipping on a surface. The radius of the disc is R. At t=0…
• A body of mass (5± 0.5) kg is moving with a velocity of (20± 0.4) m/s. Its kinetic…
• ₉₂²³⁸A → ₉₀²³⁴B + ₂⁴D + Q In the given nuclear reaction, the approximate amount of…
• Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear…
• At a given point of time the value of displacement of a simple harmonic oscillator is…
• The figure shows a liquid of given density flowing steadily in horizontal tube of…
• The source of time varying magnetic field may be (A) a permanent magnet (B) an electric…

Chemistry

• KMnO₄ is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute…
• Match the following Column A | Column B; (a) | Nylon 6 | (I) | Natural Rubber; (b) |…
• Which one of the following is most likely a mismatch ?
• In the reaction given below 'B' is
• The pair of lanthanides in which both elements have high third - ionization energy is :
• 20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown…
• 2-Methyl propyl bromide reacts with C₂ H₅ O⁻ and gives 'A' whereas on reaction with C₂…
• t_(87.5) is the time required for the reaction to undergo 87.5 % completion and t₅₀ is…
• Among the following compounds, the one which shows highest dipole moment is
• An organic compound gives 0.220 g of CO₂ and 0.126 g of H₂ O on complete combustion. If…
• Given below are two statements : Statement I : Permutit process is more efficient…
• Which of the following statements are not correct? A. The electron gain enthalpy of F is…
• A₂+B₂ → 2 AB . Δ H_f⁰=-200 kJ mol⁻¹ AB, A₂ and B₂ are diatomic molecules. If the bond…
• The incorrect statement from the following for borazine is :
• What happens when a lyophilic sol is added to a lyophobic sol?
• The mismatched combinations are A. Chlorophyll - Co B. Water hardness - EDTA C…
• Be(OH)₂ reacts with Sr(OH)₂ to yield an ionic salt. Choose the incorrect option related…
• The energy of an electron in the first Bohr orbit of hydrogen atom is -2.18 × 10⁻¹⁸ J…
• In which of the following processes, the bond order increases and paramagnetic character…
• Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water…
• A metal surface of 100 cm² area has to be coated with nickel layer of thickness 0.001…
• 25.0 mL of 0.050 M Ba(NO₃)₂ is mixed with 25.0 mL of 0.020 M NaF . K_(Sp) of BaF₂ is 0.5…

Mathematics

• A coin is biased so that the head is 3 times as likely to occur as tail. This coin is…
• Fractional part of the number 4²⁰²²/15 is equal to
• The distance of the point (-1,2,3) from the plane r⃗ ·(î-2 ĵ+3 k̂)=10 parallel to the…
• Let the equation of plane passing through the line of intersection of the planes x+2 y+a…
• Let the tangent and normal at the point (3 √3, 1) on the ellipse x²/36+y²/4=1 meet the…
• If S={x ∈ ℝ: sin ⁻¹((x+1)/√(x²+2 x+2))-sin ⁻¹(x/√(x²+1))=π/4}, then Σx ∈ s(sin ((x²+x+5)…
• Let a⃗=î+4 ĵ+2 k̂, b⃗=3 î-2 ĵ+7 k̂ and c⃗=2 î-ĵ+4 k̂. If a vector d⃗ satisfies d⃗ ×…
• Let PQ be a focal chord of the parabola y²=36 x of length 100 , making an acute angle…
• Let α be the constant term in the binomial expansion of (√x-6/x^(3/2))ⁿ, n ≤ 15. If the…
• Among (S1): lim n → ∞ 1/n²(2+4+6+… …+2 n)=1 (S2) : lim n → ∞ 1/n¹⁶(1¹⁵+2¹⁵+3¹⁵+……
• The area of the region enclosed by the curve f(x)=max{sin x,cos x},-π≤ x≤ π and the…
• ∫0^∞ 6/(e³ˣ+6 e²ˣ+11 eˣ+6) d x=
• The number of seven digit positive integers formed using the digits 1,2,3 and 4 only and…
• Let for x ∈ ℝ, S₀(x)=x, Sₖ(x)=Cₖ x+k ∫₀ˣ Sₖ₋₁(t) d t, where C₀=1, Cₖ=1-∫₀¹ Sₖ₋₁(x) d x…
• max 0 ≤ x ≤ π{x-2 sin x cos x+1/3 sin 3 x}=
• The number of symmetric matrices of order 3, with all the entries from the set…
• For the system of linear equations 2 x+4 y+2 a z=b x+2 y+3 z=4 2 x-5 y+2 z=8 which of…
• For the differentiable function f: ℝ-{0} → ℝ, let 3 f(x)+2 f(1/x)=1/x-10, then…
• The set of all a ∈ ℝ for which the equation x|x-1|+|x+2|+a=0 has exactly one real root…
• Let y=y₁(x) and y=y₂(x) be the solution curves of the differential equation (d y)/(d…
• Let the mean of the data x | 1 | 3 | 5 | 7 | 9; Frequency (f) | 4 | 24 | 28 | α | 8 be…
• The sum to 20 terms of the series 2 · 2²-3²+2 · 4²-5²+2 · 6²-… … is equal to __________.
• Let a⃗=3 î+ĵ-k̂ and c⃗=2 î-3 ĵ+3 k̂. If b⃗ is a vector such that a⃗=b⃗ × c⃗ and…
• Let w=z z̄+k₁ z+k₂ i z+λ(1+i), k₁, k₂ ∈ ℝ. Let Re(w)=0 be the circle C of radius 1 in…
• For x ∈ ℝ, two real valued functions f(x) and g(x) are such that, g(x)=√x+1 and f °…
• Let m₁ and m₂ be the slopes of the tangents drawn from the point P(4,1) to the hyperbola…
• Let B=[1, 3, α; 1, 2, 3; α, α, 4], α > 2 be the adjoint of a matrix A and |A|=2. Then…
• Let the image of the point (5/3, 5/3, 8/3) in the plane x-2 y+z-2=0 be P. If the…
• Let s₁, s₂, s₃, …, s₁₀ respectively be the sum to 12 terms of 10 A.P. s whose first…

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