JEE Advanced 2026 · Paper 2

Xᵃ⁺ and Yᵇ⁺ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers n = 1 and n = 2 of Xᵃ⁺ is λ. The wavelength of light absorbed during the transition between the states with principal quantum numbers n = 2 and n = 4 of Yᵇ⁺ is 9λ. The lowest possible value of (a+b) is ____.

At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0. Assume, the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm, x/m = kC¹/ⁿ. If the plot of log₁₀(x/m) against log₁₀C gives a straight line with slope 1, the value of k in L mol⁻¹ is ____. Given: The molar mass of acetic acid is 60 g mol⁻¹. The acid dissociation constant of acetic acid is 1.0×10⁻⁵ at the given temperature. x is the mass (in grams) of acetic acid adsorbed. m is the mass (in grams) of charcoal. C is the equilibrium concentration of acetic acid in the solution after the adsorption is complete. k and n are constants for acetic acid–charcoal system at the given temperature.

In a solvent S, a compound B is partially dissociated into C and D as given below: B ⇌ 2C + 2D. B, C and D are non-volatile in nature. The molar mass of B is 10 times the molar mass of S. The standard boiling point and the standard enthalpy of vaporization of S are 400 K and 10R J mol⁻¹, respectively (R is the gas constant in J K⁻¹ mol⁻¹). A solution of B in S with an initial concentration of B as 0.25% (mass/mass) has a boiling point of 408 K at 1 bar pressure. In this solution, the mole percent of B that has been dissociated is ____.

Consider that the coordinating atoms of the ligands in cis-[Co(NH₃)₄Cl₂]Cl and mer-[Co(NH₃)₃Cl₃] octahedral complexes are at the vertices of an octahedron. The sum of total number of the triangular faces in both the complexes having one N atom and two Cl atoms at their corners is____.