If the dimensions of length are expressed as G × C y h z , where G , C and h are the universal gravitational constant, speed of light and Planck's constant respectively, then

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L = [ M − 1 L 3 T − 2 ] x [ L T − 1 ] y [ M L 2 T − 1 ] z M 0 L T 0 = M − x + z L 3 x + y + 2 z T − 2 x − y − 2 − x + z = 0 ; 3 x + y + 2 z = 1 ; 2 x + y + z = 0 x = z ; 2 z = 1 3 x + y = 0 z = 1/2 x = 2 1 ​ and y = − 2 3 ​ ​

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