Correct Answer  Option 2 : x = 1, y = 1, z = 1
CONCEPT:
Principle of homogeneity of dimensions:

According to this principle, a physical equation will be dimensionally correct if the dimensions of all
the terms occurring on both sides of the equation are the same.
 This principle is based on the fact that only the physical quantities of the same kind can be
added, subtracted, or compared.
 Thus, velocity can be added to velocity but not to force.
EXPLANATION:
Given that, P = pressure, Q = Energy striking per unit area per second, C = speed of light
Let k = P^{x}Q^{y}C^{z}....(1)
Dimensions of k = [M^{0}L^{0}T^{0}]
Therefore Dimensions of \(Pressure=\frac{Force}{Area}=\frac{MLT^{2}}{L^2}\) = ML^{1}T^{2}
\(Q=\frac{Energy}{Area \times time}=\frac{MLT^{2}}{L^2}=\frac{ML^{2}T^{2}}{L^{2}T}=MT^{3}\)
\(C=LT^{1}\)
Substituting these values in equation (1)
\(M^{0}L^{0}T^{0}=[ML^{1}T^{2}]^{x}[MT^{3}]^{y}[LT^{1}]^{z}\)
Applying the principle of homogeneity of dimensions, we get
x + y = 0...(i)
x + z = 0...(ii)
2x  3y  z = 0...(iii)
solving (i),(ii),(iii), we get
x = 1,y = 1,z = 1
The correct x = 1,y = 1,z = 1