Planck’s constant h, speed of light  c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option is (are)

Mass in terms of h , c , GM∝hacbGc⇒M1∝ML2T−1aLT−1bM−1L3T−2c⇒M1∝Ma−cL2a+b+3cT−a−b−2cComparing powers,a−c=1→(1)2a+b+3c=0→(2)a+b+2c=0→(3)On solving (1), (2), (3),  a=12,b=12,c=−12∴M∝c  only →A  is correctIn the same way  Length in terms of h , c , GL∝hacbGc⇒L1∝ML2T−1aLT−1bM−1L3T−2c⇒L1∝Ma−cL2a+b+3cT−a−b−2cComparing powers,a−c=0→12a+b+3c=1→2a+b+2c=0→3After Solving a=12 , b=−32 , c=12⇒L∝h12c−32G12L∝h,L∝G→C,D  are correct