JEE Class main Answered

units of planck's constant ,  h = J s = N m s = (kg m/ s² ) m  s = kg m² s^-2

Dimension of h = M L² T^-1

units of speed of light  c = m/s

Dimension of c = L T^-1

units of universal gravitational constant , G = N m² kg^-2 = kg m/s² m² kg^-2 = kg^-1 m³ s^-2 

Dimension of G = M^-1 L³ T^-2

Dimension of [ (hc)/(2G) ]^1/2  = [  ( M L² T^-1 ) ( L T^-1) / ( M^-1L³T^-2 ) ]^1/2  = [ M²  ] ^1/2  ≠  T

Dimension of  [ (hc) / G² ]^1/2  =  [  ( M L² T^-1 ) ( L T^-1) / ( M^-1L³T^-2 )² ]^1/2  = [ M³ L^-3 T² ] ^1/2  ≠  T

Dimension of  [ (h G) / c⁵ ]^1/2 = [  ( M L² T^-1 )  ( M^-1L³T^-2 ) / ( L T^-1)⁵ ]^1/2  =  T

We get dimension of time in [ (h G) / c⁵ ]^1/2