For one mole of an ideal gas, which of these statements must be true?
(a) U and H each depends only on temperature
(b) Compressibility factor z is not equal to 1
(c) C_{P, m} – C_{V, m} = R
(d) dU = C_VdT for any process

An organic compound (A) (molecular formula C₆H₁₂O₂) was hydrolysed with dil. H₂SO₄ to give a carboxylic acid (B) and an alcohol (C). ‘C’ gives white turbidity immediately when treated with anhydrous ZnCl₂ and conc. HCl. The organic compound (A) is :

Let $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function,
$$\phi \left( t \right) = {5 \over {12}} + t - {t^2}$$, then a² + b² is equal to :

If the system of equations
x - 2y + 3z = 9
2x + y + z = b
x - 7y + az = 24,
has infinitely many solutions, then a - b is equal to.........