JEE Main 2021 (Online) 25th July Evening Shift — Question Paper

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Physics

• A heat engine has an efficiency of 1/6. When the temperature of sink is reduced by 62°C…
• Two vectors X⃗ and Y⃗ have equal magnitude. The magnitude of (X⃗ - Y⃗) is n times the…
• A 10 Ω resistance is connected across 220V - 50 Hz AC supply. The time taken by the…
• The nuclear activity of a radioactive element becomes ( 1/8 )ᵗʰ of its initial value in…
• If q f is the free charge on the capacitor plates and q b is the bound charge on the…
• Two ions having same mass have charges in the ratio 1 : 2. They are projected normally…
• The given potentiometer has its wire of resistance 10Ω. When the sliding contact is in…
• A light beam of wavelength 500 nm is incident on a metal having work function of 1.25…
• An electron moving with speed v and a photon moving with speed c, have same D-Broglie…
• In a semiconductor, the number density of intrinsic charge carries at 27°C is 1.5 ×…
• A system consists of two types of gas molecules A and B having same number density 2 ×…
• The relation between time t and distance x for a moving body is given as t = mx² + nx…
• A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass…
• From the given data, the amount of energy required to break the nucleus of aluminium…
• Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal…
• A force F⃗ = (40î + 10ĵ)N acts on a body of mass 5 kg. If the body starts from rest, its…
• When radiation of wavelength λ is incident on a metallic surface, the stopping potential…
• The instantaneous velocity of a particle moving in a straight line is given as V = α t +…
• A prism of refractive index μ and angle of prism A is placed in the position of minimum…
• The force is given in terms of time t and displacement x by the equation F = A cos Bx +…
• In the given potentiometer circuit arrangement, the balancing length AC is measured to…
• A force of F = (5y + 20)ĵ N acts on a particle. The work done by this force when the…
• Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the…
• A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600…
• A ray of light entering from air into a denser medium of refractive index 4/3, as shown…
• In a simple harmonic oscillation, what fraction of total mechanical energy is in the…
• Two ideal electric dipoles A and B, having their dipole moment p₁ and p₂ respectively…
• A 16 Ω wire is bend to form a square loop. A 9V supply having internal resistance of 1Ω…
• Consider a planet in some solar system which has a mass double the mass of earth and…

Chemistry

• Maleic anhydride can prepared by :
• Number of electrons present in 4f orbital of Ho³⁺ ion is ____________. (Given Atomic No…
• Identify the species having one π-bond and maximum number of canonical forms from the…
• The correct decreasing order of densities of the following compounds is :
• Match List I with List II : (Both having metallurgical terms) List - I | List - II; (a)…
• Identify the process in which change in the oxidation state is five :
• Which one of the following metals forms interstitial hydride easily?
• The ionic radii of F⁻ and O²⁻ respectively are 1.33Aᵒ and 1.4Aᵒ, while the covalent…
• Which one of the following metal complexes is most stable?
• [where Et ⇒ - C₂H₅ᵗBu ⇒ (CH₃)₃C -] Consider the above reaction sequence, Product "A" and…
• The spin only magnetic moments (in BM) for free Ti³⁺, V²⁺ and Sc³⁺ ions respectively are…
• When 3.00 g of a substance 'X' is dissolved in 100 g of CCl₄, it raises the boiling…
• Consider the above chemical reaction. The total number of stereoisomers possible for…
• The number of significant figures in 0.00340 is ____________.
• C₆H₅NO₂ →(Sn + HCl) “A” →(C₆H₅N(⊕)₂Cl(⊖)) P Consider the above reaction, the product "P"…
• A biodegradable polyamide can be made from :
• What is the major product "P" of the following reaction?
• Assuming that Ba(OH)₂ is completely ionised in aqueous solution under the given…
• 0.8 g of an organic compound was analyzed by Kjeldahl's method for the estimation of…
• A reaction of benzonitrile with one equivalent CH₃MgBr followed by hydrolysis produces a…
• In the following the correct bond order sequence is :
• Which among the following is the strongest acid ?
• For a chemical reaction A → B, it was found that concentration of B is increased by 0.2…
• Match List I with List II : List-I Example of colloids | List - II Classification; (a)…
• Which one of the following is correct structure for cytosine?
• An accelerated electron has a speed of 5 × 10⁶ ms⁻¹ with an uncertainty of 0.02%. The…
• A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of…
• Match List I with List II : List-I Elements | List-II Properties; (a) | Li | (i) | Poor…

Mathematics

• A fair coin is tossed n-times such that the probability of getting at least one head is…
• If [x] be the greatest integer less than or equal to x, then Σₙ₌₈¹⁰⁰ [ ( - 1)ⁿn/2 ] is…
• The sum of all those terms which are rational numbers in the expansion of (2 1/3 + 3 1/4…
• If | a⃗ | = 2,| b⃗ | = 5 and | a⃗ × b⃗ | = 8, then | a⃗ . b⃗ | is equal to :
• Let n∈N and [x] denote the greatest integer less than or equal to x. If the sum of (n +…
• If P = [ 1, 0; 1/2, 1 ], then P⁵⁰ is :
• If the lines (x - k)/1 = (y - 2)/2 = (z - 3)/3 and (x + 1)/3 = (y + 2)/2 = (z + 3)/1 are…
• If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of it…
• Let a, b and c be distinct positive numbers. If the vectors aî + aĵ + ck̂,î+k̂ and cî +…
• The lowest integer which is greater than ( 1 + 1/10¹⁰⁰ )^(10¹⁰⁰) is ______________.
• Consider the function where P(x) is a polynomial such that P'' (x) is always a constant…
• The equation of a circle is Re(z²) + 2(Im(z))² + 2Re(z) = 0, where z = x + iy. A line…
• If the co-efficient of x⁷ and x⁸ in the expansion of ( 2 + x/3 )ⁿ are equal, then the…
• The value of cot π/24 is :
• The number of distinct real roots of | sin x, cos x, cos x; cos x, sin x, cos x; cos x…
• Consider function f : A → B and g : B → C (A, B, C ⊆ R) such that (gof)⁻¹ exists, then :
• Let X be a random variable such that the probability function of a distribution is given…
• Let a curve y = f(x) pass through the point (2, (logₑ2)²) and have slope 2y/(xlog ₑx)…
• Let y = y(x) be the solution of the differential equation xdy = (y + x³ cosx)dx with…
• The number of real solutions of the equation, x² - |x| - 12 = 0 is :
• The value of the integral ∫₋₁¹ log ( x + √(x² + 1) )dx is :
• If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a⁴ + b⁴ + c⁴ is equal…
• The first of the two samples in a group has 100 items with mean 15 and standard…
• If ⁿPᵣ = ⁿPᵣ₊₁ and ⁿCᵣ = ⁿCᵣ₋₁, then the value of r is equal to :
• If the greatest value of the term independent of 'x' in the expansion of ( x sin α +…
• If f(x) = { ∫₀ˣ ( 5 + | 1 - t | )dt,, x > 2; 5x + 1,, x ≤ 2 , then
• If ( a⃗ + 3b⃗ ) is perpendicular to ( 7a⃗ - 5b⃗ ) and ( a⃗ - 4b⃗ ) is perpendicular to (…

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