M∝c
M∝√G
L∝h
L∝√G
h=ML²T⁻¹
c=LT⁻¹
G=M⁻¹L³T⁻²
L=hᵃcᵇGᵈ
M⁰L¹T⁰=MᵃL²ᵃT⁻ᵃLᵇT⁻ᵇM⁻ᵈL³ᵈT⁻²ᵈ
Equating coefficients of M, L and T
a-d=0, 2a+b+3d=1, -a-b-2d=0
a=1/2, d=1/2, b=-1/2
L∝√(h/c)
L∝√G
Similarly using dimensional analysis for second case
M=hᵃcᵇGᵈ
M¹L⁰T⁰=MᵃL²ᵃT⁻ᵃLᵇT⁻ᵇM⁻ᵈL³ᵈT⁻²ᵈ
a-d=1, 2a+b+3d=0, -a-b-2d=0
a=1/2, d=-1/2, b=-1/2
M∝√(h/c)
M∝1/√G
M∝c
Correct options are A, C and D.