JEE (Advanced) 2025 Paper-2

The density (in g cm$$^{-3}$$) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is ______.

Use: Atomic mass of metal = 105.6 amu and Avogadro's constant = $$6 \times 10^{23}$$ mol$$^{-1}$$

The solubility of barium iodate in an aqueous solution prepared by mixing 200 mL of 0.010 M barium nitrate with 100 mL of 0.10 M sodium iodate is $$X \times 10^{-6}$$ mol dm$$^{-3}$$. The value of $$X$$ is ______.

Use: Solubility product constant ($$K_{sp}$$) of barium iodate = $$1.58 \times 10^{-9}$$

Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from 10 mg g$$^{-1}$$ and 16 mg g$$^{-1}$$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be 4 mg g$$^{-1}$$ and 10 mg g$$^{-1}$$, respectively. At this temperature, the concentration (in mg g$$^{-1}$$) of adsorbed phenol from 20 mg g$$^{-1}$$ aqueous solution of phenol will be ______.

Use: $$\log_{10} 2 = 0.3$$

Consider a reaction $$A + R \to Product$$. The rate of this reaction is measured to be $$k[A][R]$$. At the start of the reaction, the concentration of $$R$$, $$[R]_0$$, is 10-times the concentration of $$A$$, $$[A]_0$$. The reaction can be considered to be a pseudo first order reaction with assumption that $$k[R] = k'$$ is constant. Due to this assumption, the relative error (in %) in the rate when this reaction is 40% complete, is ______.

[$$k$$ and $$k'$$ represent corresponding rate constants]

At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density = 1.00 g cm$$^{-3}$$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is 2.00 g dm$$^{-3}$$, the molar mass of the macromolecule is $$X \times 10^4$$ g mol$$^{-1}$$. The value of $$X$$ is ______.

Use: Universal gas constant (R) = 8.3 J K$$^{-1}$$ mol$$^{-1}$$ and acceleration due to gravity (g) = 10 m s$$^{-2}$$

An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is $$\frac{X}{F} \times 10^3$$ volts, where $$F$$ is the Faraday constant. The value of $$X$$ is ______.

Use: Standard Gibbs energies of formation at 298 K are: $$\Delta_f G^o_{CO_2} = -394$$ kJ mol$$^{-1}$$; $$\Delta_f G^o_{water} = -237$$ kJ mol$$^{-1}$$; $$\Delta_f G^o_{butane} = -18$$ kJ mol$$^{-1}$$

The sum of the spin only magnetic moment values (in B.M.) of [Mn(Br)$$_6$$]$$^{3-}$$ and [Mn(CN)$$_6$$]$$^{3-}$$ is ______.

A linear octasaccharide (molar mass = 1024 g mol$$^{-1}$$) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The amount of 2-deoxyribose formed is 58.26% (w/w) of the total amount of the monosaccharides produced in the hydrolyzed products. The number of ribose unit(s) present in one molecule of octasaccharide is ______.

Use: Molar mass (in g mol$$^{-1}$$): ribose = 150, 2-deoxyribose = 134, glucose = 180; Atomic mass (in amu): H = 1, O = 16