JEE Main 2021 (Online) 27th August Morning Shift — Question Paper

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Physics

• If the velocity of a body related to displacement x is given by υ = √(5000 + 24x) m/s…
• A bar magnet is passing through a conducting loop of radius R with velocity υ. The…
• A uniform conducting wire of length is 24a, and resistance R is wound up as a current…
• A circuit is arranged as shown in figure. The output voltage V₀ is equal to…
• A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle…
• The variation of displacement with time of a particle executing free simple harmonic…
• For a transistor in CE mode to be used as an amplifier, it must be operated in :
• An ideal gas is expanding such that PT³ = constant. The coefficient of volume expansion…
• Electric field in a plane electromagnetic wave is given by E = 50 sin(500x - 10 × 10¹⁰…
• A rod CD of thermal resistance 10.0 KW⁻¹ is joined at the middle of an identical rod AB…
• A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C…
• First, a set of n equal resistors of 10 Ω each are connected in series to a battery of…
• In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of…
• An object is placed beyond the centre of curvature C of the given concave mirror. If the…
• The resultant of these forces OP⃗,OQ⃗,OR⃗,OS⃗ and OT⃗ is approximately .......... N…
• A uniformly charged disc of radius R having surface charge density σ is placed in the xy…
• Find the distance of the image from object O, formed by the combination of lenses in the…
• Calculate the amount of charge on capacitor of 4μF. The internal resistance of battery…
• Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h…
• Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions…
• Moment of inertia of a square plate of side l about the axis passing through one of the…
• Which of the following is not a dimensionless quantity?
• The alternating current is given by i = { √42 sin ( 2π/Tt ) + 10 }A The r.m.s. value of…
• There are 10¹⁰ radioactive nuclei in a given radioactive element, its half-life time is…
• A body of mass (2M) splits into four masses (m, M - m, m, M - m, which are rearranged to…
• In a photoelectric experiment, increasing the intensity of incident light :
• Two persons A and B perform same amount of work in moving a body through a certain…
• If E and H represents the intensity of electric field and magnetising field…
• Five identical cells each of internal resistance 1Ω and emf 5V are connected in series…

Chemistry

• Match items of List-I with those of List-II : List - I (Property) | List - II (Example)…
• Which refining process is generally used in the purification of low melting metals?
• The number of water molecules in gypsum, dead burnt plaster and plaster of Paris…
• The number of moles of CuO, that will be utilized in Dumas method for estimation…
• 1 mol of an octahedral metal complex with formula MCl₃ . 2L on reaction with excess of…
• 1 kg of 0.75 molal aqueous solution of sucrose can be cooled up to -4°C before freezing…
• 200 mL of 0.2 M HCl is mixed with 300 mL of 0.1 M NaOH. The molar heat of neutralization…
• When 10 mL of an aqueous solution of KMnO₄ was titrated in acidic medium, equal volume…
• The number of moles of NH₃, that must be added to 2L of 0.80 M AgNO₃ in order to reduce…
• The number of f electrons in the ground state electronic configuration of Np (Z = 93) is…
• The nature of oxides V₂O₃ and CrO is indexed as 'X' and 'Y' type respectively. The…
• The major product of the following reaction is : CH₃-CH(CH₃; |)-CH₂-CH₂-C(O; ∥)-Cl →((i)…
• In polythionic acid, H₂SₓO₆ (x = 3 to 5) the oxidation state(s) of sulphur is/are :
• The reaction that occurs in a breath analyser, a device used to determine the alcohol…
• The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal…
• In which one of the following molecules strongest back donation of an electron pair from…
• Acidic ferric chloride solution on treatment with excess of potassium ferrocyanide gives…
• In Carius method for estimation of halogens, 0.2 g of an organic compound gave 0.188 g…
• Which of the following is not a correct statement for primary aliphatic amines?
• Out of following isomeric forms of uracil, which one is present in RNA?
• Given below are two statements : one is labelled as Assertion (A) and the other is…
• Tyndall effect is more effectively shown by :
• Deuterium resembles hydrogen in properties but :

Mathematics

• If ∫ dx/(x²+x+1)²=atan⁻¹((2x+1)/√3)+b((2x+1)/(x²+x+1))+C, x > 0 where C is the constant…
• If x² + 9y² - 4x + 3 = 0, x, y ∈ R, then x and y respectively lie in the intervals :
• If A = x ∈ R : |x - 2| > 1, B = x ∈ R : √(x² - 3) > 1, C = x ∈ R : |x - 4| ≥ 2 and Z is…
• ∫₆¹⁶ (log ₑx²)/(log ₑx² + log ₑ(x² - 44x + 484))dx is equal to :
• If α, β are the distinct roots of x² + bx + c = 0, then lim _(x → β) (e^(2(x² + bx + c))…
• If S = { z ∈ C:(z - i)/(z + 2i) ∈ R }, then :
• If the matrix A = ( 0, 2; K, - 1 ) satisfies A(A³ + 3I) = 2I, then the value of K is :
• A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into…
• Let y = y(x) be the solution of the differential equation dy/dx = 2(y + 2 sin x - 5)x -…
• Let a⃗ = î + 5ĵ + α k̂, b⃗ = î + 3ĵ + β k̂ and c⃗ = - î + 2ĵ - 3k̂ be three vectors such…
• Let us consider a curve, y = f(x) passing through the point (-2, 2) and the slope of the…
• A number is called a palindrome if it reads the same backward as well as forward. For…
• Equation of a plane at a distance √(2/21) from the origin, which contains the line of…
• A tangent and a normal are drawn at the point P(2, -4) on the parabola y² = 8x, which…
• Σₖ₌₀²⁰ ( ²⁰Cₖ )² is equal to :
• If 0 < x < 1, then 3/2x² + 5/3x³ + 7/4x⁴ + ....., is equal to :
• The distance of the point (1, -2, 3) from the plane x - y + z = 5 measured parallel to a…
• If Uₙ = ( 1 + 1/n² )( 1 + 2²/n² )².....( 1 + n²/n² )ⁿ, then lim _(n → ∞) (Uₙ)^((- 4)/n²)…
• If y^(1/4) + y^(- 1/4) = 2x, and (x² - 1)d²y/dx² + α xdy/dx + β y = 0, then | α - β | is…
• If for x, y ∈ R, x > 0, y = log₁₀x + log₁₀x 1/3 + log₁₀x 1/9 + ...... upto ∞ terms and…
• Let the equation x² + y² + px + (1 - p)y + 5 = 0 represent circles of varying radius r ∈…
• Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of…
• When a certain biased die is rolled, a particular face occurs with probability 1/6 - x…
• If (sin ⁻¹x)² - (cos ⁻¹x)² = a; 0 < x < 1, a ≠ 0, then the value of 2x² - 1 is :
• If the minimum area of the triangle formed by a tangent to the ellipse x²/b² + y²/4a² =…
• The number of distinct real roots of the equation 3x⁴ + 4x³ - 12x² + 4 = 0 is…
• Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14…
• If the system of linear equations 2x + y - z = 3 x - y - z = α 3x + 3y + βz = 3 has…

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