Practice Questions

Q61.The area (in sq. units) of the region S = {z ∈C : |z −1| ≤2; (z + ¯z) + i(z −¯z) ≤2, Im(z) ≥0} is (1) 7π (2) 7π 3 4 (3) 17π (4) 3π 8 2

Q61.If z = x + iy, xy ≠0, satisfies the equation z2 + iz = 0, then z2 is equal to : (1) 9 (2) 1 (3) 4 (4) 14

Q61.The sum of all possible values of θ ∈[−π, 2π], for which 1−2i1+i coscosθθ is purely imaginary, is equal (1) 3π (2) 2π (3) 5π (4) 4π

Q61.If 2 and 6 are the roots of the equation ax2 + bx + 1 = 0, then the quadratic equation, whose roots are 2a+b1 and 1 , is : 6a+b (1) 2x2 + 11x + 12 = 0 (2) x2 + 8x + 12 = 0 (3) 4x2 + 14x + 12 = 0 (4) x2 + 10x + 16 = 0

Q61.If 𝑧 is a complex number, then the number of common roots of the equation 𝑧1985 + 𝑧100 + 1 = 0 and 𝑧3 + 2𝑧2 + 2𝑧+ 1 = 0, is equal to : (1) 1 (2) 2 (3) 0 (4) 3

Q61.If 𝛼, 𝛽 are the roots of the equation, x2 - x - 1 = 0 and Sn = 2023𝛼n + 2024𝛽n, then (1) 2 S12 = S11 + S10 (2) S12 = S11 + S10 (3) 2 S11 = S12 + S10 (4) S11 = S10 + S12 4! ! 5! ( ) (

Q61.Consider the following two statements : Statement I : For any two non-zero complex numbers z1, z2 , (|z1| + |z2|) z1 + z2 ≤2 (|z1| + |z2|), and |z1| |z2| Statement II : If x, y, z are three distinct complex numbers and a, b, c are three positive real numbers such that |y−z| a = |z−x|b = |x−y|c , then y−za2 + z−xb2 + x−yc2 = 1. Between the above two statements, (1) Statement I is correct but Statement II is (2) both Statement I and Statement II are correct. incorrect. (3) both Statement I and Statement II are incorrect. (4) Statement I is incorrect but Statement II is correct.

Q62.Let 𝛼= and 𝛽= 3! )4!.! Then : 4! 5! ( ( ) ) (1) 𝛼∈N and 𝛽∉N (2) 𝛼∉N and 𝛽∈N (3) 𝛼∈N and 𝛽∈N (4) 𝛼∉N and 𝛽∉N

Q62.Let Sa denote the sum of first n terms an arithmetic progression. If S20 = 790 and S10 = 145, then S15−S5 is : JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper (1) 395 (2) 390 (3) 405 (4) 410

Q31.An organic compound gives 0. 220 g of CO2 and 0. 126 g of H2O on complete combustion. If the % of carbon is 24 then the % of hydrogen is _________ × 10–1. (Nearest integer)

Q31.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Hydrogen is an environment friendly fuel. Reason R: Atomic number of hydrogen is 1 and it is a very light element. In the light of the above statements, choose the correct answer from the options given below (1) A is true but R is false (2) Both A and R are true but R is NOT the correct explanation of A (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A

Q31.A solution is prepared by adding 2 g of ′′X′′ to 1 mole of water. Mass percent of ′′X′′in solution is (1) 5% (2) 20% (3) 2% (4) 10% JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q31.A metal chloride contains 55. 0% of chlorine by weight. 100 mL vapours of the metal chloride at STP weigh 0. 57 g . The molecular formula of the metal chloride is (Given: Atomic mass of chlorine is 35. 5 u ) (1) MCl4 (2) MCl3 (3) MCl2 (4) MCl

Q31.Given below are two statements Statement I : According to Bohr’s model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised. Statement II : The concept of electron in Bohr’s orbit, violates the Heisenberg uncertainty principle. In the light of the above statements, choose the most appropriate answer from the options given below (1) Statement I is incorrect but Statement II is (2) Both Statement I and Statement II are correct correct (3) Both Statement I and Statement II are incorrect (4) Statement I is correct but Statement II is incorrect

Q31.Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is _______. JEE Main 2023 (24 Jan Shift 2) JEE Main Previous Year Paper A. T4 > T3 > T2 > T1 B. The black body consists of particles performing simple harmonic motion. C. The peak of the spectrum shifts to shorter wavelength as temperature increases. D. T1 = T2 = T3 ν1 ν2 ν3 E. The given spectrum could be explained using quantisation of energy

Q31.Number of hydrogen atoms per molecule of a hydrocarbon A having 85. 8% carbon is (Given : Molar mass of A = 84 g mol−1 )

Q31.Match List - I with List - II LIST-II LIST-I (Block of periodic (Atomic number) table) (A) 37 I. p-block (B) 78 II. d-block JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper (C) 52 III. f-block (D) 65 IV. s-block Choose the correct answer from the options given below: (1) A - II, B - IV, C - I, D - III (2) A - I, B - III, C - IV, D - II (3) A - IV, B - III, C - II, D - I (4) A - IV, B - II, C - I, D - III

Q31.Assume that the radius of the first Bohr orbit of hydrogen atom is 0. 6Å . The radius of the third Bohr orbit of He+ is _____ picometer. (Nearest Integer)

Q31.The shortest wavelength of hydrogen atom in Lyman series is λ. The longest wavelength in Balmer series of He+ is (1) 5 (2) 9λ 9λ 5 (3) 36λ (4) 5λ 5 9

Q31.The radius of the 2nd orbit of Li2+ is x . The expected radius of the 3rd orbit of Be3+ is (1) 9 4 x (2) 94 x (3) 27 16 x (4) 2716 x JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper

Q31.Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from n = 4 to n = 2 of He+spectrum (1) n = 2 to n = 1 (2) n = 1 to n = 3 (3) n = 1 to n = 2 (4) n = 3 to n = 4

Q31.The wave function (Ψ) of 2 s is given by 1/2 − Ψ2s = a0 1 ( a01 ) (2 r )e−r/2a0 2√2π At r = r0 , radial node is formed. Thus, r0 in terms of a0 (1) r0 = a0 (2) r0 = 4a0 (3) r0 = a02 (4) r0 = 2a0

Q31.It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power 'n' i.e. vn of X-rays emitted is plotted against atomic number Z, the following graph is obtained. The value of 'n' is JEE Main 2023 (24 Jan Shift 1) JEE Main Previous Year Paper (1) 1 (2) 2 1 (3) (4) 3 2

Q31.When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of A? (1) C11H8 (2) C11H4 (3) C5H8 (4) C9H8

Q31.The molality of a 10%(v/V) solution of di-bromine solution in CCl4 (carbon tetrachloride) is x '. x = _____ × 10−2M. (Nearest integer) [Given : molar mass of Br2 = 160 g mol−1 atomic mass of C = 12 g mol−1 atomic mass of Cl = 35. 5 g mol−1 density of dibromine = 3. 2 g cm−3 density of CCl4 = 1. 6 g cm−3]