Practice Questions

Q56.The standard free energy change ΔG° for 50% dissociation of N2O4 into NO2 at 27 °C and 1 atm pressure is -x J mol-1. The value of x is - . . . . . J. (Nearest Integer) [Given : R = 8 . 31 J K-1 mol-1, log1 . 33 = 0 . 1239 ln10 = 2 . 3]

Q57.Resistance of a conductivity cell (cell constant 129 m−1 ) filled with 74. 5 ppm solution of KCl is 100 Ω (labelled as solution 1). When the same cell is filled with KCl solution of 149 ppm, the resistance is 50 Ω (labelled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is i.e. ∧1 = x × 10−3 . The ∧2 value of x is____Given, molar mass of KCl is 74. 5 g mol−1 )

Q57.The distance between Na+ and Cl- ions in solid NaCl of density 43 . 1 gcm-3 is . . . . . × 10-10 m. (Nearest Integer) (Given : NA = 6 . 02 × 1023 mol-1)

Q58.Amongst FeCl3 . 3H2O, K3FeCN6 and CoNH36Cl3, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is B.M. [nearest integer]

Q58.The number of terminal oxygen atoms present in the product B obtained from the following reaction is FeCr2 O4 + Na2 CO3 + O2 →A + Fe2 O3 + CO2 A + H+ →B + H2O + Na+

Q58.The quantity of electricity in Faraday needed to reduce 1 mol of Cr2 O2−7 to Cr3+ is

Q58.Total number of isomers (including stereoisomers) obtain on monochlorination of methylcyclohexane is

Q59.Consider the following metal complexes : CoNH3 3 + CoClNH35 2 + 3 - Co ( CN ) 6 CoNH35H2O3 + The spin-only magnetic moment value of the complex that absorbs light with shortest wavelength is B.M. (Nearest integer)

Q60.Reaction of [Co (H2O)6]2+ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in t2g -orbitals of the product is 1 (−1)n A

Q60.A sample of 4. 5 mg of an unknown monohydric alcohol, R −OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3. 1 mL. The molecular weight of the unknown alcohol is g/ mol. p is _______.

Q61.Let a circle 𝐶 in complex plane pass through the points 𝑧1 = 3 + 4𝑖, 𝑧2 = 4 + 3𝑖 and 𝑧3 = 5𝑖. If 𝑧≠𝑧1 is a point on 𝐶 such that the line through 𝑧 and 𝑧1 is perpendicular to the line through 𝑧2 and 𝑧3, then arg𝑧 is equal to 2 (1) tan-124 - 𝜋 (2) tan-1 - 𝜋 7 √5 (3) tan-13 - 𝜋 (4) tan-13 - 𝜋 4 JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper 1 1 1 𝐾

Q61.For z ∈C if the minimum value of ( z −3√2 + z −p√2i ) is 5√2 , then a value of (1) 3 (2) 72 (3) 4 (4) 92

Q62.The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives atleast 4 and atmost 7 candies, C3 receives atleast 2 and atmost 6 candies, is equal to (1) 205 (2) 615 (3) 510 (4) 430 JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper

Q62.Consider two G.Ps. 2, 22, 23, … and 4, 42, 43, … of 60 and n terms respectively. If the geometric mean of all 225 the 60 + n terms is (2) 8 , then ∑nk=1 k(n −k) is equal to: (1) 560 (2) 1540 (3) 1330 (4) 2600 n(S) + ∑θ∈S(sec( π4 + 2θ) cosec ( π4 + 2θ)) is equal

Q62.Let 𝑆= 𝑧= 𝑥+ 𝑖𝑦: 𝑧- 1 + 𝑖≥𝑧, 𝑧< 2, 𝑧+ 𝑖= 𝑧- 1. Then the set of all values of 𝑥, for which 𝑤= 2𝑥+ 𝑖𝑦∈𝑆 for some 𝑦∈ℝ, is 1 1 1 (2) - (1) -√2, 4 2√2 √2, (3) -√2, 1 (4) - 1 1 2 √2, 2√2

Q62.Let for some real numbers α and β, a = α −iβ . If the system of equations 4ix + (1 + i)y = 0 and ¯8(cos 2π3 + i sin 2π3 )x + ay = 0 has more than one solution then αβ is equal to (1) 2 −√3 (2) 2 + √3 (3) −2 + √3 (4) −2 −√3

Q62.Let (z) represent the principal argument of the complex number z. The, |z| = 3 and arg(z −1) −arg(z + 1) = π4 intersect: (1) Exactly at one point (2) Exactly at two points (3) Nowhere (4) At infinitely many points.

Q63.Consider the sequence 𝑎1, 𝑎2, 𝑎3, … … such that 𝑎1 = 1, 𝑎2 = 2 and 𝑎𝑛+ 2 = + 𝑎𝑛 for 𝑛= 1, 2, 3, … 𝑎𝑛+ 1 1 1 1 1 𝑎1 + 𝑎2 𝑎2 + 𝑎3 𝑎3 + 𝑎4 𝑎30 + 𝑎31 If · · … = 2𝛼61𝐶31 then 𝛼 is equal to 𝑎3 𝑎4 𝑎5 𝑎32 (1) -30 (2) -31 (3) -60 (4) -61

Q63.Let 𝑎𝑛𝑛=∞ 0 be a sequence such that 𝑎0 = 𝑎1 = 0 and 𝑎𝑛+ 2 = 3𝑎𝑛+ 1 - 2𝑎𝑛+ 1, ∀𝑛≥0. Then 𝑎25𝑎23 - 2𝑎25𝑎22 - 2𝑎23𝑎24 + 4𝑎22𝑎24 is equal to (1) 483 (2) 528 (3) 575 (4) 624 Q64. ∑𝑟=20 1 𝑟2 + 1𝑟! is equal to (1) 22! - 21! (2) 22! - 221! (3) 21! - 220! (4) 21! - 20!

Q63.The value of cos( 2π7 ) + cos( 4π7 ) + cos( 6π7 ) is equal to (1) −1 (2) −12 (3) −13 (4) −14

Q63.The sum of the infinite series 1 + 65 + 1262 + 2263 + 3564 + 5165 + 7066 + … is equal to: (1) 425 (2) 429 216 216 (3) 288 (4) 280 125 125

Q63.Let S = {θ ∈[0, 2π] : 82 sin2 θ + 82 cos2 θ = 16} . Then to: (1) 0 (2) −2 (3) −4 (4) 12

Q63.If the constant term in the expansion of (3x3 −2x2 + x5 ) is 2k. l, where l is an odd integer, then the value of k is equal to (1) 6 (2) 7 (3) 8 (4) 9

Q64.Let a line L pass through the point of intersection of the lines bx + 10y −8 = 0 and 2x −3y = 0, b ∈R −{ 34 }. If the line L also passes through the point (1, 1) and touches the circle 17(x2 + y2) = 16, then x2 y2 the eccentricity of the ellipse 5 + b2 = 1 is (1) 2 (2) √5 √35 (3) 1 (4) √5 √25

Q64.Let the hyperbola H : x2 −y2 = 1 pass through the point . A parabola is drawn whose focus is a2 b2 (2√2, −2√2) same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H . If the length of the latus rectum of the parabola is e times the length of the latus rectum of H , where e is the eccentricity of H , then which of the following points lies on the parabola? (1) (2√3, 3√2) (2) (3√3, −6√2) (3) (√3, −√6) (4) (3√6, 6√2)