JEE Main 2023 (Online) 25th January Morning Shift — Question Paper

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Physics

• A ray of light is incident from air on a glass plate having thickness √3 cm and…
• A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius…
• If P⃗=3î+√3ĵ+2k̂ and Q⃗=4î+√3ĵ+2.5k̂ then, the unit vector in the direction of P⃗× Q⃗ is…
• In the given circuit, the equivalent resistance between the terminal A and B is…
• An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and…
• The ratio of the density of oxygen nucleus (₈¹⁶O) and helium nucleus (₂⁴He) is
• An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under…
• In an LC oscillator, if values of inductance and capacitance become twice and eight…
• I_(CM) is the moment of inertia of a circular disc about an axis (CM) passing through…
• T is the time period of simple pendulum on the earth's surface. Its time period becomes…
• The root mean square velocity of molecules of gas is
• A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to…
• An LCR series circuit of capacitance 62.5 nF and resistance of 50 Ω, is connected to an…
• The wavelength of the radiation emitted is λ₀ when an electron jumps from the second…
• Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV…
• A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across…
• In Young's double slits experiment, the position of 5ᵗʰ bright fringe from the central…
• A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room…
• Given below are two statements : one is labelled as Assertion A and the other is…
• A parallel plate capacitor has plate area 40 cm² and plates separation 2 mm. The space…
• An electromagnetic wave is transporting energy in the negative z direction. At a certain…
• Match List I with List II List I | List II; A. | Surface tension | I. | kg m⁻¹ s⁻¹; B. |…
• A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long…
• A uniform electric field of 10 N/C is created between two parallel charged plates (as…
• A car travels a distance of 'x' with speed v₁ and then same distance 'x' with speed v₂…
• Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its…
• As shown in the figure, in an experiment to determine Young's modulus of a wire, the…
• The distance between two consecutive points with phase difference of 60° in a wave of…

Chemistry

• The density of a monobasic strong acid (Molar mass 24.2 g/mol) is 1.21 kg/L. The volume…
• The radius of the 2ⁿᵈ orbit of Li²⁺ is x. The expected radius of the 3ʳᵈ orbit of Be³⁺ is
• Match the List-I with List-II : List-I Cations | List-II Group reagents; A. | Pb²⁺,Cu²⁺…
• The correct order in aqueous medium of basic strength in case of methyl substituted…
• How many of the following metal ions have similar value of spin only magnetic moment in…
• The compound which will have the lowest rate towards nucleophilic aromatic substitution…
• Which of the following conformations will be the most stable?
• The variation of the rate of an enzyme catalyzed reaction with substrate concentration…
• A cubic solid is made up of two elements X and Y. Atoms of X are present on every…
• '25 volume' hydrogen peroxide means
• The number of paramagnetic species from the following is _____________…
• Inert gases have positive electron gain enthalpy. Its correct order is :
• The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the…
• The total number of lone pairs of electrons on oxygen atoms of ozone is __________.
• For the first order reaction A → B, the half life is 30 min. The time taken for 75%…
• Reaction of thionyl chloride with white phosphorus forms a compound [A], which on…
• Match items of Row I with those of Row II. Row I : Row II : (i) α-D-(-)-Fructofuranose…
• Compound A reacts with NH₄Cl and forms a compound B. Compound B reacts with H₂O and…
• Given below are two statements : one is labelled as Assertion A and the other is…
• Consider the cell Pt(s)|H₂(g) (1 atm)|H + (aq,[H + ] = 1)||Fe³⁺(aq),Fe²⁺(aq)|Pt(s) Given…
• Match List I with List II List I Elements | List II Colour imparted to the flame; A. | K…
• Which one of the following reactions does not occur during extraction of copper?
• Which of the following statements is incorrect for antibiotics?
• An athlete is given 100 g of glucose (C₆H₁₂O₆) for energy. This is equivalent to 1800kJ…
• In the cumene to phenol preparation in presence of air, the intermediate is
• A litre of buffer solution contains 0.1 mole of each of NH₃ and NH₄Cl. On the addition…
• In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate…

Mathematics

• Let f:(0,1)→ℝ be a function defined f(x) = 1/(1 - e⁻ˣ), and g(x) = ( f( - x) - f(x) )…
• If aᵣ is the coefficient of x¹⁰⁻ʳ in the Binomial expansion of (1 + x)¹⁰, then Σᵣ₌₁¹⁰…
• Let A₁,A₂,A₃ be the three A.P. with the same common difference d and having their first…
• Let y(x) = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 + x¹⁶). Then y' - y'' at x = - 1 is equal to
• Let z₁=2+3i and z₂=3+4i. The set S = { z ∈ ℂ:| z - z₁ |² - | z - z₂ |² = | z₁ - z₂ |² }…
• For some a, b, c ∈ℕ, let f(x) = ax - 3 and g(x)=xᵇ+c,x∈ℝ. If (fog)⁻¹(x) = ( (x - 7)/2…
• Let y = y(x) be the solution curve of the differential equation dy/dx = y/x( 1 + xy²(1 +…
• The points of intersection of the line ax + by = 0,(a ≠ b) and the circle x² + y² - 2x =…
• The minimum value of the function f(x) = ∫₀² e^(|x - t|)dt is :
• The distance of the point (6,-2√2) from the common tangent y=mx+c,m > 0, of the curves…
• If the sum of all the solutions of tan ⁻¹( 2x/(1 - x²) ) + cot ⁻¹( (1 - x²)/2x ) = π/3…
• Let x=2 be a local minima of the function f(x)=2x⁴-18x²+8x+12,x∈(-4,4). If M is local…
• Let f(x)=∫ 2x/(x²+1)(x²+3)dx. If f(3)=1/2(logₑ5-logₑ6), then f(4) is equal to
• Let M be the maximum value of the product of two positive integers when their sum is 66…
• Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of…
• The value of lim _(n → ∞) (1 + 2 - 3 + 4 + 5 - 6 + ..... + (3n - 2) + (3n - 1) -…
• The constant term in the expansion of ( 2x + 1/x⁷ + 3x² )⁵ is ___________.
• Let S₁ and S₂ be respectively the sets of all a ∈ ℝ - { 0} for which the system of…
• Let a⃗, b⃗ and c⃗ be three non zero vectors such that b⃗ . c⃗ = 0 and a⃗ × (b⃗ × c⃗ ) =…
• The vertices of a hyperbola H are (± 6, 0) and its eccentricity is √5/2. Let N be the…
• Let x,y,z > 1 and A = [ 1, log ₓy, log ₓz; log _yx, 2, log _yz; log _zx, log _zy, 3 ]…
• If the area enclosed by the parabolas P₁:2y=5x² and P₂:x²-y+6=0 is equal to the area…
• Consider the lines L₁ and L₂ given by L₁:(x - 1)/2 = (y - 3)/1 = (z - 2)/2 L₂:(x - 2)/1…
• The distance of the point P(4, 6, -2) from the line passing through the point (-3, 2, 3)…
• The vector a⃗ = - î + 2ĵ + k̂ is rotated through a right angle, passing through the…
• Let the equation of the plane passing through the line x - 2y - z - 5 = 0 = x + y + 3z -…
• Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum…
• The mean and variance of the marks obtained by the students in a test are 10 and 4…

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