If energy, E = Gphqcr, where G is the universal gravitational constant, h is the Planck's constant and c is the velocity of light, then the values of p, q and r are, respectively:

Dimension of Energy, E = [ML2T-2]
Dimension of gravitational constant, G = [M-1L3T-2]
Dimension of Planck's constant, h = [ML2T-1]
Dimension of speed of light, c = [M0LT-1]
Given : E = Gphqcr
∴ [ML2T-2] = [M-1L3T-2]p × [ML2T-1]q × [M0LT-1]r
⇒ [ML2T-2] = [M-p+qL3p+2q+rT-2p-q-r]
Equating both sides, we get:
-p + q = 1 (1)
3p + 2q + r = 2 (2)
-2p - q - r = -2 (3)
Adding (2) and (3), we get:
p + q = 0.. (4)
Solving (1) and (4),
⇒ p = -1/2 and q = 1/2
Now from (2),
3 × (-1/2) + 2 × (1/2) + r = 2
⇒ r = 5/2