The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is :

(Specific heat of water liquid and water vapour are 4.2 kJ K^$$-$$1 kg^$$-$$1 and 2.0 kJ K^$$-$$1 kg^$$-$$1; heat of liquid fusion and vapourisation of water are 334 kJ^$$-$$1 and 2491 kJ kg^$$-$$1, respectively). (log 273 = 2.436, log 373 = 2.572, log 383 = 2.583)

Let a, b and c be the 7^th, 11^th and 13^th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then $${a \over c}$$ equal to :

Let the equations of two sides of a triangle be 3x $$-$$ 2y + 6 = 0 and 4x + 5y $$-$$ 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is :

The number of all possible positive integral values of $$\alpha $$  for which the roots of the quadratic equation, 6x² $$-$$ 11x + $$\alpha $$ = 0 are rational numbers is :