Practice Questions

Q60.An athlete is given 100 g of glucose (C6H12O6) for energy. This is equivalent to 1800 kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is _____g (Nearest integer) Assume that there is no other way of consuming stored energy. Given : The enthalpy of evaporation of water is 45 kJ mol−1 Molar mass of C, H&O are 12.1 and 16 g mol−1 .

Q60.Number of moles of AgCl formed in the following reaction is _____ . JEE Main 2023 (24 Jan Shift 1) JEE Main Previous Year Paper

Q60.Total number of tripeptides possible by mixing of valine and proline is ________ .

Q60.In potassium ferrocyanide, there are ______ pairs of electrons in the t2g set of orbitals. 2𝑧- 3𝑖

Q60.Number of cyclic tripeptides formed with 2 amino acids A and B is: (1) 2 (2) 3 (3) 5 (4) 4

Q61.Let m and n be the numbers of real roots of the quadratic equations x2 −12x + [x] + 31 = 0 and x2 −5 x + 2 −4 = 0 respectively, where [x] denotes the greatest integer ≤x. Then m2 + mn + n2 is equal to

Q61.Let S = {α : log2(92α−4 + 13) −log2( 25 ⋅32α−4 + 1) = 2}. Then the maximum value of β for which the equation x2 −2(∑α∈s α) 2x + ∑a∈s (α + 1)2β = 0 has real roots, is _____ .

Q61.If the value of real number α > 0 for which x2 −5αx + 1 = 0 and x2 −αx −5 = 0 have a common real roots is 3 then β is equal to ________ √2β

Q61.The number of points, where the curve f(x) = e8x −e6x −3e4x −e2x + 1, x ∈R cuts x-axis, is equal to............ ¯¯¯¯

Q61.Let a ∈R and let α, β be the roots of the equation x2 + 60 41 x + a = 0. If α4 + β4 = −30, then the product of all possible values of a is _____ .

Q61.The number of real roots of the equation x|x| −5|x + 2| + 6 = 0 , is (1) 5 (2) 4 (3) 6 (4) 3 ¯ ¯

Q61.Let 𝛼, 𝛽 be the roots of the equation 𝑥2 - √2𝑥+ 2 = 0 Then 𝛼14 + 𝛽14 is equal to (1) -64 (2) -64√2 (3) -128 (4) -128√2

Q61.If the solution of the equation 1, 𝑥∈0, 𝜋 is sin-1𝛼+ √𝛽 , where 𝛼, 𝛽 are integers, logcos𝑥cot𝑥+ 4logsin𝑥tan𝑥= 2 2 then 𝛼+ 𝛽 is equal to: (1) 3 (2) 5 (3) 6 (4) 4 -2

Q61.Let 𝑝, 𝑞∈ℝ and (1 - √3𝑖) 200 = 2199 (𝑝+ 𝑖𝑞), 𝑖= √-1. Then, 𝑝+ 𝑞+ 𝑞2 and 𝑝- 𝑞+ 𝑞2 are roots of the equation. (1) 𝑥2 + 4𝑥- 1 = 0 (2) 𝑥2 - 4𝑥+ 1 = 0 (3) 𝑥2 + 4𝑥+ 1 = 0 (4) 𝑥2 - 4𝑥- 1 = 0

Q61.Let w = zz + k1z + k2iz + λ(1 + i), k1, k2 ∈R. . Let Re(w) = 0 be the circle C of radius 1 in the first quadrant touching the line y = 1 and the y−axis. If the curve Im(w) = 0 intersects C at A and B, then 30(AB)2 is equal to _______. JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q61.Let α1, α2, … , α7α1, α2, … , α7 be the roots of the equation x7 + 3x5 −13x3 −15x = 0 and |α1| ≥|α2| ≥… ≥|α7|. Then, α1α2 −α3α4 + α5α6 is equal to _______ ¯

Q62.The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is _______.

Q62.For three positive integers 𝑝, 𝑞, 𝑟, 𝑥𝑝𝑞2 = 𝑦𝑞𝑟= 𝑧𝑝2𝑟 and 𝑟= 𝑝𝑞+ 1 such that 1 3, 3log𝑦𝑥, 3 log𝑧𝑦, 7log𝑥𝑧 are in A.P. with common difference 2. The 𝑟- 𝑝- 𝑞 is equal to (1) 2 (2) 6 (3) 12 (4) -6

Q62.Let α = 8 −14i, A = {z ∈C : z2−(¯z)2−112iαz−α¯z = 1} and B = {z ∈C : |z + 3i| = 4} Then, ∑z∈A∩B(Re z −Imz) is equal to ________

Q62.If the set {Re ( 2−3z+5zz−z+zz ) : z ∈C, Re z = 3} is equal to the interval (α, β], then 24(β −α) is equal to (1) 36 (2) 27 (3) 30 (4) 42

Q62.For α, β, z ∈C and λ > 1 , if √λ −1 is the radius of the circle |z −α|2 + |z −β|2 = 2λ, then |α −β| is equal to _____.

Q62.The number of ways of selecting two numbers a and b, a ∈{2, 4, 6, … … , 100} and b ∈{1, 3, 5, … … , 99} such that 2 is the remainder when a + b is divided by 23 is (1) 186 (2) 54 (3) 108 (4) 268 JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q62.Let 𝑆= 𝑧∈ℂ: ¯𝑧= 𝑖𝑧2 + Re ( ¯𝑧) . Then ∑𝑧∈𝑆| 𝑧| 2 is equal to (1) 5 (2) 4 2 (3) 7 (4) 3 2

Q63.Let x and y be distinct integers where 1 ≤x ≤25 and 1 ≤y ≤25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5 , is _____ .

Q63.If all the six digit numbers x1x2x3x4x5x6 with 0 < x1 < x2 < x3 < x4 < x5 < x6 are arranged in the increasing order, then the sum of the digits in the 72th number is _______.