JEE Main 2021 (Online) 31st August Morning Shift — Question Paper

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Physics

• A uniform heavy rod of weight 10 kg ms⁻², cross-sectional area 100 cm² and length 20 cm…
• The electric field in an electromagnetic wave is given by E = (50 NC⁻¹) sinω (t - x/c)…
• In an ac circuit, an inductor, a capacitor and a resistor are connected in series with X…
• Consider a galvanometer shunted with 5Ω resistance and 2% of current passes through it…
• A wire having a linear mass density 9.0 × 10⁻⁴ kg/m is stretched between two rigid…
• For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by…
• Two plane mirrors M₁ and M₂ are at right angle to each other shown. A point source 'P'…
• A moving proton and electron have the same de-Broglie wavelength. If K and P denote the…
• A square shaped wire with resistance of each side 3Ω is bent to form a complete circle…
• The masses and radii of the earth and moon are (M₁, R₁) and (M₂, R₂) respectively. Their…
• Two particles A and B having charges 20μC and -5μC respectively are held fixed with a…
• When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases…
• Match List - I with List - II. List - I | List - II; (a) | Torque | (i) | MLT⁻¹; (b) |…
• The voltage drop across 15Ω resistance in the given figure will be ______________ V.
• A particle of mass 1 kg is hanging from a spring of force constant 100 Nm⁻¹. The mass is…
• Angular momentum of a single particle moving with constant speed along circular path :
• Which of the following equations is dimensionally incorrect? Where t = time, h = height…
• A body of mass M moving at speed V₀ collides elastically with a mass 'm' at rest. After…
• A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B…
• Choose the correct waveform that can represent the voltage across R of the following…
• A coil having N turns is wound tightly in the form of a spiral with inner and outer…
• A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a…
• A small square loop of side 'a' and one turn is placed inside a larger square loop of…
• An object is placed at the focus of concave lens having focal length f. What is the…
• A capacitor of 50 μF is connected in a circuit as shown in figure. The charge on the…
• A block moving horizontally on a smooth surface with a speed of 40 ms⁻¹ splits into two…
• A reversible engine has an efficiency of 1/4. If the temperature of the sink is reduced…
• A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10…
• In the following logic circuit the sequence of the inputs A, B are (0, 0), (0, 1), (1…

Chemistry

• Monomer of Novolac is :
• Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic…
• Select the graph that correctly describes the adsorption isotherms at two temperatures…
• According to the following figure, the magnitude of the enthalpy change of the reaction…
• In the structure of the dichromate ion, there is a :
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• A₃B₂ is a sparingly soluble salt of molar mass M (g mol⁻¹) and solubility x g L⁻¹. The…
• For a first order reaction, the ratio of the time for 75% completion of a reaction to…
• The total number of reagents from those given blow, that can convert nitrobenzene into…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing…
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Ge(Z = 32) in its ground state electronic configuration has x completely filled orbitals…
• The number of hydrogen bonded water molecule(s) associated with stoichiometry CuSO₄.5H₂O…
• The denticity of an organic ligand, biuret is :
• Choose the correct name for compound given below :
• The number of halogen/(s) forming halic (V) acid is ___________.
• Given below are two statements : Statement I : The process of producing syn-gas is…
• Consider the sulphides HgS, PbS, CuS, Sb₂S₃, As₂S₃ and CdS. Number of these sulphides…
• The molarity of the solution prepared by dissolving 6.3 g of oxalic acid (H₂C₂O₄.2H₂O)…
• The major component/ingredient of Portland Cement is :
• The correct order of reactivity of the given chlorides with acetate in acetic acid is :
• The major products A and B in the following set of reactions are :
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Which one of the following compounds contains β-C₁-C₄ glycosidic linkage?
• Consider the following cell reaction : Cd₍ₛ₎ + Hg₂SO₄₍ₛ₎ + 9/5H₂O₍ₗ₎ ⇌ CdSO₄.9/5H₂O₍ₛ₎ +…

Mathematics

• If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α…
• The number of real roots of the equation e⁴ˣ + 2e³ˣ - eˣ - 6 = 0 is :
• If ( 3⁶/4⁴ )k is the term, independent of x, in the binomial expansion of ( x/4 - 12/x²…
• If xφ (x) = ∫₅ˣ (3t² - 2φ '(t))dt, x > -2, and φ(0) = 4, then φ(2) is __________.
• If the following system of linear equations 2x + y + z = 5 x - y + z = 3 x + y + az = b…
• Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If ∫₀ˣ…
• If 'R' is the least value of 'a' such that the function f(x) = x² + ax + 1 is increasing…
• lim _(x → 0) (sin ²( π cos ⁴x ))/x⁴ is equal to :
• The length of the latus rectum of a parabola, whose vertex and focus are on the positive…
• If the variable line 3x + 4y = α lies between the two circles (x - 1)² + (y - 1)² = 1…
• The function f(x) = | x² - 2x - 3 | . e^(| 9x² - 12x + 4 |) is not differentiable at…
• cosec18° is a root of the equation :
• Which of the following is not correct for relation R on the set of real numbers ?
• The number of six letter words (with or without meaning), formed using all the letters…
• Let the equation of the plane, that passes through the point (1, 4, -3) and contains the…
• A point z moves in the complex plane such that arg ( (z - 2)/(z + 2) ) = π/4, then the…
• The integral ∫ 1/∜(x-1)³(x+2)⁵ dx is equal to : (where C is a constant of integration)
• Let [t] denote the greatest integer ≤ t. Then the value of 8.∫_(- 1/2)¹ ([2x] + |x|)dx…
• If the function f(x) = { 1/xlog ₑ( (1 + x/a)/(1 - x/b) ), ,, x < 0; k, ,, x = 0; (cos ²x…
• The sum of 10 terms of the series 3/(1² × 2²) + 5/(2² × 3²) + 7/(3² × 4²) + .... is :
• An electric instrument consists of two units. Each unit must function independently for…
• Three numbers are in an increasing geometric progression with common ratio r. If the…
• The line 12x cos θ + 5y sin θ = 60 is tangent to which of the following curves?
• The mean of 10 numbers 7 × 8, 10 × 10, 13 × 12, 16 × 14, ....... is ____________.
• If dy/dx = (2ˣ⁺ʸ - 2ˣ)/2ʸ, y(0) = 1, then y(1) is equal to :
• If aᵣ = cos 2rπ/9 + i sin 2rπ/9, r = 1, 2, 3, ....., i = √(- 1), then the determinant |…
• The square of the distance of the point of intersection of the line (x - 1)/2 = (y -…
• Let a⃗ and b⃗ be two vectors such that | 2a⃗ + 3b⃗ | = | 3a⃗ + b⃗ | and the angle…

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