JEE Main 2021 (Online) 22nd July Evening Shift — Question Paper

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Physics

• Consider a situation in which reserve biased current of a particular P-N junction…
• A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the…
• Statement I : The ferromagnetic property depends on temperature. At high temperature…
• Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on…
• In 5 minutes, a body cools from 75°C to 65°C at room temperature of 25°C. The…
• What will be the average value of energy for a monoatomic gas in thermal equilibrium at…
• Match List - I with List - II List - I | List - II; (a) | ω L > 1/(ω C) | (i) | Current…
• A nucleus with mass number 184 initially at rest emits an α-particle. If the Q value of…
• An electric dipole is placed on x-axis in proximity to a line charge of linear charge…
• A ray of light passes from a denser medium to a rarer medium at an angle of incidence i…
• A body is projected vertically upwards from the surface of earth with a velocity…
• T₀ is the time period of a simple pendulum at a place. if the length of the pendulum is…
• Three particles P, Q and R are moving along the vectors A⃗=î+ĵ, B⃗=ĵ+k̂ and C⃗=-î+ĵ…
• What will be the projection of vector A⃗=î+ĵ+k̂ on vector B⃗=î+ĵ ?
• A ray of light passing through a prism (μ = √3) suffers minimum deviation. It is found…
• Three students S₁, S₂ and S₃ perform an experiment for determining the acceleration due…
• In a circuit consisting of a capacitance and a generator with alternating emf E g = E g₀…
• An electron of mass mₑ and a proton of mass mₚ are accelerated through the same…
• The area of cross-section of a railway track is 0.01 m². The temperature variation is…
• The total charge enclosed in an incremental volume of 2 × 10⁻⁹ m³ located at the origin…
• Choose the correct option
• In a given circuit diagram, a 5 V zener diode along with a series resistance is…
• A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm² is joined with a…
• The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed…
• Intensity of sunlight is observed as 0.092 Wm⁻² at a point in free space. What will be…
• The centre of a wheel rolling on a plane surface moves with a speed v₀. A particle on…
• In an electric circuit, a cell of certain emf provides a potential difference of 1.25 V…
• A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a…
• The motion of a mass on a spring, with spring constant K is as shown in figure. The…

Chemistry

• A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been…
• The number of acyclic structural isomers (including geometrical isomers) for pentene are…
• If the concentration of glucose (C₆H₁₂O₆) in blood is 0.72 g L⁻¹, the molarity of…
• Isotope(s) of hydrogen which emits low energy β⁻ particles with t 1/2 value > 12 years…
• Given below are the statements about diborane (a) Diborane is prepared by the oxidation…
• The water having more dissolved O₂ is :
• Which one of the following 0.06 M aqueous solutions has lowest freezing point?
• Which purification technique is used for high boiling organic liquid compound…
• Value of K P for the equilibrium reaction N₂O 4(g) ⇌ 2NO 2(g) at 288 K is 47.9. The K C…
• The total number of unpaired electrons present in [Co(NH₃)₆]Cl₂ and [Co(NH₃)₆]Cl₃ is :
• Which one of the following reactions does not occur?
• Methylation of 10 g of benzene gave 9.2 g of toluene. Calculate the percentage yield of…
• Sulphide ion is soft base and its ores are common for metals. (a) Pb (b) Al (c) Ag (d) Mg
• Thiamine and pyridoxine are also known respectively as :
• N₂O_(5(g)) → 2NO_(2(g)) + 1/2O_(2(g)) In the above first order reaction the initial…
• Which of the following compounds does not exhibit resonance?
• When silver nitrate solution is added to potassium iodide solution then the sol produced…
• Which one of the following statements for D.I. Mendeleeff, is incorrect?
• Assume a cell with the following reaction Cu₍ₛ₎ + 2Ag + (1 × 10⁻³M) → Cu²⁺(0.250M) +…
• Which one of the following group-15 hydride is the strongest reducing agent?
• In the chemical reactions given above A and B respectively are :
• An organic compound A (C₆H₆O) gives dark green colouration with ferric chloride. On…
• Number of electrons that Vanadium (Z = 23) has in p-orbitals is equal to _____________
• Which of the following molecules does not show stereo isomerism?
• Match List-I with List-II List-I (Elements) | List-II (Properties); (a) | Ba | (i) |…
• Match List-I with List-II : List-I (Species) | List-II (Hybrid Orbitals); (a) | SF₄ |…
• If the standard molar enthalpy change for combustion of graphite powder is -2.48 × 10²…
• The set having ions which are coloured and paramagnetic both is :

Mathematics

• Let f : R → R be defined as f(x) = { - 4/3x³ + 2x² + 3x,, x > 0; 3xeˣ,, x ≤ 0 . Then f…
• If the digits are not allowed to repeat in any number formed by using the digits 0, 2…
• Let A = [ 0, 1, 0; 1, 0, 0; 0, 0, 1 ]. Then the number of 3 × 3 matrices B with entries…
• Four dice are thrown simultaneously and the numbers shown on these dice are recorded in…
• Let A = [aᵢⱼ] be a real matrix of order 3 × 3, such that aᵢ₁ + aᵢ₂ + aᵢ₃ = 1, for i = 1…
• If the constant term, in binomial expansion of ( 2xʳ + 1/x² )¹⁰ is 180, then r is equal…
• Let [x] denote the greatest integer less than or equal to x. Then, the values of x∈R…
• The area (in sq. units) of the region bounded by the curves x² + 2y - 1 = 0, y² + 4x - 4…
• If the shortest distance between the straight lines 3(x - 1) = 6(y - 2) = 2(z - 1) and…
• If ∫₀^(100π) (sin ²x)/e^(( x/π - [ x/π ] ))dx = (α π ³)/(1 + 4π ²),α ∈ R where [x] is…
• Let y = y(x) be the solution of the differential equation ( (x + 2)e^(( (y + 1)/(x + 2)…
• Let n denote the number of solutions of the equation z² + 3z̅ = 0, where z is a complex…
• Let f : R → R be a function defined as f(x) = { 3( 1 - |x|/2 ), if, |x| ≤ 2; 0, if, |x|…
• Let Sₙ denote the sum of first n-terms of an arithmetic progression. If S₁₀ = 530, S₅ =…
• Consider the following frequency distribution : Class : | 0-6 | 6-12 | 12-18 | 18-24 |…
• Let the circle S : 36x² + 36y² - 108x + 120y + C = 0 be such that it neither intersects…
• If the domain of the function f(x) = (cos ⁻¹√(x² - x + 1))/√(sin ⁻¹( (2x - 1)/2 )) is…
• The number of solutions of sin⁷x + cos⁷x = 1, x∈ [0, 4π] is equal to
• Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x² - y² = 3. If L is also…
• Let f : R → R be defined as f(x) = { x³/(1 - cos 2x)²log ₑ( (1 + 2xe⁻²ˣ)/(1 - xe⁻ˣ)² )…
• The number of elements in the set n ∈ 1, 2, 3, ......., 100 | (11)ⁿ > (10)ⁿ + (9)ⁿ is…
• Let y = y(x) be the solution of the differential equation cos ec²xdy + 2dx = (1 + y cos…
• Let A = 0, 1, 2, 3, 4, 5, 6, 7. Then the number of bijective functions f : A → A such…
• Let a vector a⃗ be coplanar with vectors b⃗ = 2î + ĵ + k̂ and c⃗ = î - ĵ + k̂. If a⃗ is…
• Let E₁:x²/a² + y²/b² = 1,a > b. Let E₂ be another ellipse such that it touches the end…
• The values of λ and μ such that the system of equations x + y + z = 6, 3x + 5y + 5z =…
• The sum of all the elements in the set n∈ 1, 2, ....., 100 | H.C.F. of n and 2040 is 1…
• Let three vectors a⃗, b⃗ and c⃗ be such that a⃗ × b⃗ = c⃗, b⃗ × c⃗ = a⃗ and | a⃗ | = 2…
• Let L be the line of intersection of planes r⃗ .(î - ĵ + 2k̂) = 2 and r⃗ .(2î + ĵ - k̂)…

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