Practice Questions

Q60.If CuH2O4 2 + absorbs a light of wavelength 600 nm for d - d transition, then the value of octahedral crystal field splitting energy for CuH2O6 2 + will be____ × 10-21 J [Nearest integer] (Given : h = 6 . 63 × 10-34Js and c = 3 . 08 × 108 ms-1)

Q60.Optical activity of an enantiomeric mixture is +12. 6° and the specific rotation of (+) isomer is +30°. The optical purity is____ %

Q60.Total number of relatively more stable isomer(s) possible for octahedral complex Cuen2SCN2 will be____ 1

Q60.Among the following the number of curves not in accordance with Freundlich adsorption isotherm is |x+3|−1 ∈[−6, 3] −{−2, 2} : T = {x ∈Z : x2 −7|x| + 9 ≤0}. Then the number of

Q60. If the initial pressure of a gas is 0. 03 atm, the mass of the gas adsorbed per gram of the adsorbent is____ ×10−2 g

Q60.In the given reaction (Where Et is -C2H5) The number of chiral carbon/s in product A is

Q60.The difference between spin only magnetic moment values of [Co (H2O)6] Cl2 and [Cr (H2O)6] Cl3 is

Q60.Number of complexes which will exhibit synergic bonding amongst, [Cr (CO)6], [Mn (CO)5] and [Mn2 (CO)10] is

Q61.Let O be the origin and A be the point z1 = 1 + 2i . If B is the point z2, Re (z2) < 0 , such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true? (1) arg z2 = π −tan−1 3 (2) arg(z1 −2z2) = −tan−1 34 (3) |z2| = √10 (4) |2z1 −z2| = 5

Q61.If the sum of the squares of the reciprocals of the roots α and β of the equation 3x2 + λx −1 = 0 is 15 , then 6(α3 + β3)2 is equal to (1) 46 (2) 36 (3) 24 (4) 18

Q61.The area of the polygon, whose vertices are the non-real roots of the equation z = iz2 is (1) 3√3 (2) 3√3 2 4 (3) √3 (4) √3 4 2

Q61.If α, β are the roots of the equation x2 −(5 + 3√log3 −5√log5 3)x 3(3(log3 −1) the equation, whose roots are α + β1 and β + α1 , (1) 3x2 −20x −12 = 0 (2) 3x2 −10x −4 = 0 (3) 3x2 −10x + 2 = 0 (4) 3x2 −20x + 16 = 0

Q61.Let α be a root of the equation 1 + x2 + x4 = 0. Then the value of α1011 + α2022 −α3033 is equal to: (1) 1 (2) α (3) 1 + α (4) 1 + 2α

Q61.Let A = {z ∈C : z−1z+1 < 1} and B = {z ∈C : arg( z+1z−1 ) = 2π3 }. Then A ∩B is (1) a portion of a circle centred at (0, −1√3 ) that (2) a portion of a circle centred at (0, −1√3 ) that lies in the second and third quadrants only lies in the second quadrant only (3) an empty set (4) a portion of a circle of radius 2 that lies in the √3 third quadrant only

Q61.If 𝑧≠0 be a complex number such that 𝑧- 𝑧= 2, then the maximum value of 𝑧 is (1) √2 (2) 1 (3) √2 - 1 (4) √2 + 1

Q61.The number of points of intersection |z −(4 + 3i)| = 2| and |z| + |z −4| = 6, z ∈C is (1) 1 (2) 2 (3) 3 (4) 4

Q61.Let 𝑆1 = 𝑧1 ∈𝐶: 𝑧1 - 3 = 2 and 𝑆2 = 𝑧2 ∈𝐶: 𝑧2 - 𝑧2 + 1 = 𝑧2 + 𝑧2 - 1 . Then, for 𝑧1 ∈𝑆1 and 𝑧2 ∈𝑆2, the least value of 𝑧2 - 𝑧1 is (1) 0 (2) 1 2 3 5 (3) (4) 2 2

Q61.Let α and β be the roots of the equation x2 + (2i −1) = 0 . Then, the value of α8 + β8 is equal to (1) 50 (2) 250 (3) 1250 (4) 1550

Q61.If 𝛼, 𝛽, 𝛾, 𝛿 are the roots of the equation 𝑥4 + 𝑥3 + 𝑥2 + 𝑥+ 1 = 0, then 𝛼2021 + 𝛽2021 + 𝛾2021 + 𝛿2021 is equal to (1) 4 (2) 1 (3) -4 (4) -1

Q61.Let 𝐴= 𝑥∈𝑅: 𝑥+ 1 < 2 and 𝐵= 𝑥∈𝑅: 𝑥- 1 ≥2. Then which one the following statements is NOT true? (1) 𝐴- 𝐵= -1, 1 (2) 𝐵- 𝐴= 𝑅- -3, 1 (3) 𝐴∩𝐵= ( - 3, - 1] (4) 𝐴∪𝐵= 𝑅- [1, 3 )

Q61.If A = ∑∞n=1 (3+(−1)n)n and B = ∑∞n=1 (3+(−1)n)n , then B is equal to (1) 11 (2) 1 9 (3) −119 (4) −113 Q62. 16 sin(20°) sin(40°) sin(80°) is equal to (1) √3 (2) 2√3 (3) 3 (4) 4√3 y2

Q61.The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is (1) 72 (2) 48 (3) 24 (4) 60

Q61.The sum of all real roots of equation (e2x −4)(6e2x −5ex + 1) = 0 is (1) ln 4 (2) −ln 3 (3) ln 3 (4) ln 5

Q61.Let S = {x |x|−2 ≥0} and elements in S ∩T is JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper (1) 7 (2) 5 (3) 4 (4) 3

Q61.Let f(x) be a quadratic polynomial such that f(−2) +f(3) = 0. If one of the roots of f(x) = 0 is −1, then the sum of the roots of f(x) = 0 is equal to (1) 11 (2) 7 3 3 (3) 12 (4) 14 3 3