If the dimensions of length are expressed as $G^xc^yh^z$; where G, c and h are the universal gravitational constant, speed of light and Planck’s constant respectively, then
(a) $x=\frac{1}{2},y=\frac{1}{2}$
(b) $x=\frac{1}{2},z=\frac{1}{2}$
(c) $y=\frac{1}{2},z=\frac{3}{2}$
(d) $y=-\frac{3}{2},z=\frac{1}{2}$

b, d

The correct answer is Option (3) → b, d

lenght $l = G^x\, c^y\, h^z$

or $M^0LT^0 = [M^{–1}L^3T^{–2}]^x [LT^{–1}]^y [ML^2T^{–1}]^z$

After comparing, we get

$x = 1/2, y = –3/2, z = 1/2$