JEE Main 2024 (Online) 27th January Morning Shift — Question Paper

Download this paper as a PDF (16 pages, with answer key)

Physics

• The radius of third stationary orbit of electron for Bohr's atom is R. The radius of…
• Given below are two statements : Statement (I) : Planck's constant and angular momentum…
• A body of mass 1000 kg is moving horizontally with a velocity 6 m / s. If 200 kg extra…
• A plane electromagnetic wave propagating in x-direction is described by E_y=(200 Vm⁻¹)…
• Two long, straight wires carry equal currents in opposite directions as shown in figure…
• 0.08 kg air is heated at constant volume through 5° C. The specific heat of air at…
• An electric charge 10⁻⁶ μ C is placed at origin (0,0) m of X-Y co-ordinate system. Two…
• A wire of length 10 cm and radius √7 × 10⁻⁴ m connected across the right gap of a meter…
• In a nuclear fission process, a high mass nuclide (A ≈ 236) with binding energy 7.6 MeV…
• A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean…
• Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of…
• Identify the physical quantity that cannot be measured using spherometer :
• A thin metallic wire having cross sectional area of 10⁻⁴ m² is used to make a ring of…
• Two coils have mutual inductance 0.002 H. The current changes in the first coil…
• The average kinetic energy of a monatomic molecule is 0.414 eV at temperature : (Use…
• If the refractive index of the material of a prism is cot (A/2), where A is the angle of…
• A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined…
• A particle starts from origin at t=0 with a velocity 5 î m / s and moves in x-y plane…
• If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10⁹ Nm⁻²…
• Two immiscible liquids of refractive indices 8/5 and 3/2 respectively are put in a…
• A convex lens of focal length 40 cm forms an image of an extended source of light on a…
• A proton moving with a constant velocity passes through a region of space without any…
• Which of the following circuits is reverse - biased?
• Four particles each of mass 1 kg are placed at four corners of a square of side 2 m…
• Position of an ant (S in metres) moving in Y-Z plane is given by S=2 t² ĵ+5 k̂ (where t…
• The acceleration due to gravity on the surface of earth is g. If the diameter of earth…
• The charge accumulated on the capacitor connected in the following circuit is _______ μ…
• Given below are two statements : Statement (I) :Viscosity of gases is greater than that…
• A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of…
• A train is moving with a speed of 12 m / s on rails which are 1.5 m apart. To negotiate…

Chemistry

• 3-Methylhex-2-ene on reaction with HBr in presence of peroxide forms an addition product…
• Given below are two statements : Statement (I) : The 4 f and 5 f - series of elements…
• Highest enol content will be shown by:
• Among the following, total number of meta directing functional groups is (Integer based)…
• The mass of silver (Molar mass of Ag: 108 gmol⁻¹ ) displaced by a quantity of…
• Consider the following complex ions P=[FeF₆]³⁻ ; Q=[V(H₂ O)₆]²⁺ ; R=[Fe(H₂ O)₆]²⁺ The…
• The correct statement regarding nucleophilic substitution reaction in a chiral alkyl…
• Cyclohexene is ________ type of an organic compound.
• Mass of methane required to produce 22 g of CO₂ after complete combustion is _______ g…
• The number of electrons present in all the completely filled subshells having n=4 and…
• Choose the polar molecule from the following:
• If three moles of an ideal gas at 300 K expand isothermally from 30 dm³ to 45 dm³…
• Two nucleotides are joined together by a linkage known as :
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• A solution of two miscible liquids showing negative deviation from Raoult's law will…
• Yellow compound of lead chromate gets dissolved on treatment with hot NaOH solution. The…
• Consider the following data for the given reaction 2 HI_((g)) → H_(2( g))+I_(2( g)) The…
• Which of the following electronic configuration would be associated with the highest…
• IUPAC name of following compound (P) is:
• NaCl reacts with conc. H₂ SO₄ and K₂ Cr₂ O₇ to give reddish fumes (B), which react with…
• Sum of bond order of CO and NO⁺ is ________.
• Which of the following has highly acidic hydrogen?
• Given below are two statements : Statement (I) : p-nitrophenol is more acidic than…
• The electronic configuration for Neodymium is: [Atomic Number for Neodymium 60]
• Which of the following is strongest Bronsted base?
• Given below are two statements : Statement (I) : Aqueous solution of ammonium carbonate…
• Element not showing variable oxidation state is :
• From the given list, the number of compounds with +4 oxidation state of Sulphur…

Mathematics

• If ∫₀¹ 1/(√(3+x)+√(1+x)) d x=a+b √2+c √3, where a, b, c are rational numbers, then 2 a+3…
• Let x=x(t) and y=y(t) be solutions of the differential equations (d x)/dt+a x=0 and (d…
• A fair die is tossed repeatedly until a six is obtained. Let X denote the number of…
• If 8=3+1/4(3+p)+1/4²(3+2 p)+1/4³(3+3 p)+… … ∞, then the value of p is ____________.
• The function f: N-{1} → N; defined by f(n)= the highest prime factor of n, is :
• If (a, b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1)…
• If S={z ∈ C:|z-i|=|z+i|=|z-1|}, then, n(S) is :
• Let a₁, a₂, … a₁₀ be 10 observations such that Σₖ₌₁¹⁰ aₖ=50 and Σ_(∀ k < j) aₖ ·…
• The number of common terms in the progressions 4,9,14,19, … …, up to 25ᵗʰ term and…
• Let f(x)=x³+x² f′(1)+x f^(′ ′)(2)+f^(′ ′ ′)(3), x ∈ R. Then f′(10) is equal to…
• Let the set of all a∈ R such that the equation cos 2x+a sin x=2a-7 has a solution be…
• If α satisfies the equation x²+x+1=0 and (1+α)⁷=A+B α+C α², A, B, C ≥ 0, then 5(3 A-2…
• Let the area of the region {(x,y):x-2y+4≥ 0,x+2y²≥ 0,x+4y²≤ 8,y≥ 0} be m/n, where m and…
• Let for a differentiable function f:(0, ∞) → R, f(x)-f(y) ≥ log ₑ(x/y)+x-y, ∀ x, y ∈(0…
• Let a⃗=î+2 ĵ+k̂, b⃗=3(î-ĵ+k̂). Let c⃗ be the vector such that a⃗ × c⃗=b⃗ and a⃗ · c⃗=3…
• Four distinct points (2 k, 3 k),(1,0),(0,1) and (0,0) lie on a circle for k equal to :
• If a=lim(x → 0) (√(1+√(1+x⁴))-√2)/x⁴ and b=lim _(x → 0) (sin ² x)/(√2-√(1+cos x)), then…
• If A denotes the sum of all the coefficients in the expansion of (1-3 x+10 x²)ⁿ and B…
• Consider the function. f(x)={a(7 x-12-x²)/(b|x²-7 x+12|), , x<3; 2^((sin…
• Let A=[2, 0, 1; 1, 1, 0; 1, 0, 1], B=[B₁, B₂, B₃], where B₁, B₂, B₃ are column matrics…
• Consider the matrix f(x)=[cos x, -sin x, 0; sin x, cos x, 0; 0, 0, 1]. Given below are…
• If the solution of the differential equation (2 x+3 y-2) d x+(4 x+6 y-7) d y=0, y(0)=3…
• If the shortest distance of the parabola y²=4 x from the centre of the circle x²+y²-4…
• The distance, of the point (7,-2,11) from the line (x-6)/1=(y-4)/0=(z-8)/3 along the…
• The portion of the line 4x+5y=20 in the first quadrant is trisected by the lines L₁ and…
• If the shortest distance between the lines (x-4)/1=(y+1)/2=z/-3 and…
• ⁿ⁻¹ Cᵣ=(k²-8) ⁿ Cᵣ₊₁ if and only if :
• The length of the chord of the ellipse x²/25+y²/16=1, whose mid point is (1, 2/5), is…
• Let S={1,2,3, …, 10}. Suppose M is the set of all the subsets of S, then the relation…
• The least positive integral value of α, for which the angle between the vectors α î-2…

Download all JEE Main 2024 PYQs chapter-wise as free PDFs