Practice Questions

Q57.Consider the cell PtsH2g, 1atmH+aq, 1M | Fe3 + aq, Fe2 + aq Pt s When the potential of the cell is 0 . 712 V at 298 K, the ratio Fe2 + / Fe3 + is (Nearest integer) + + + + 2 . 303RT Given: Fe3 + e- = Fe2 , E°Fe3 , Fe2 Pt = 0 . 771 = 0 . 06 V F

Q57.In an electrochemical reaction of lead, at standard temperature, if EPb2o + / Pb = n Volt, then the value of E°Pb2 + / Pb4 + is given by m – xn. The value of x is _______. EPb4o + / Pb (Nearest integer)

Q57.For the given reaction The, total number of possible products formed by tertiary carbocation of A is _______. JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q57.Number of isomeric aromatic amines with molecular formula C8H11N, which can be synthesized by Gabriel Phthalimide synthesis is _____.

Q57.At 298 K, a 1 litre solution containing 10 mmol of Cr2O72 - and 100mmol of Cr3 + shows a pH of 3 . 0. 2 - + 2 . 303RT Given : Cr2O7 →Cr3 ; E0 = 1 . 330 V and F = 0 . 059 V The potential for the half cell reaction is x × 10-3 V . The value of x is _____ .

Q58.The specific conductance of 0 . 0025M acetic acid is 5 × 10-5 S cm-1 at a certain temperature. The dissociation constant of acetic acid is ___________ × 10-7.(Nearest integer) Consider limiting molar conductivity of CH3COOH as 400 S cm2 mol-1

Q58.For the adsorption of hydrogen on platinum, the activation energy is 30 kJ mol – 1 and for the adsorption of hydrogen on nickel, the activation energy is 41 . 4 kJ mol – 1 . The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at 300 K is _______ (Nearest integer) Given: In10 = 2 . 3 R = 8 . 3 J K-1 mol-1

Q59.The volume (in mL) of 0. 1 M AgNO3 required for complete precipitation of chloride ions present in 20 mL of 0. 01 M solution of [Cr (H2O)5 Cl] Cl2 as silver chloride is_______

Q60.Number of isomeric compounds with molecular formula C9H10O which (i) do not dissolve in NaOH (ii) do not dissolve in HCl. (iii) do not give orange precipitate with 2, 4 - DNP (iv) on hydrogenation give identical compound with molecular formula C9H12O is

Q60. The ratio x/y on completion of the above reaction is ______ . JEE Main 2023 (11 Apr Shift 1) JEE Main Previous Year Paper 𝑥- 7 2

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 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.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 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.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 _______ ¯

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

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.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.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

Q64.Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____ .

Q64.The total number of 4 -digit numbers whose greatest common divisor with 54 is 2 , is

Q64.Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed? = p1 p2 p3 . . . pm , where

Q64.The sum 12 −2. 32 + 3. 52 −4. 72 + 5. 92 −… . . +15. 292 is _____ . , is

Q65.Let a1 = b1 = 1 and an = an−1 + (n −1), bn = bn−1 + an−1, ∀n ≥2. If S = ∑10n=1( 2nbn ) and T = ∑8n=1 2n−1n then 27(2S −T) is equal to

Q68.Let the sixth term in the binomial expansion of (√2log2(10−3x) If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an A.P., then the sum of the squares of all possible values of x is _____ .