NIMCET 2019 Question Paper with solutions

Question : 97 of 120

Marks: +1, -0

The base (or radix ) of the number system such that the following equation holds 312/20 = 13.1 is

Solution:

Let 'x' be the base or radix of the number system
The equation is

{3⋅x^2+1⋅x^1+2⋅x^0}/{2⋅x^1 + 0⋅x^0}

=1⋅x^{I}+3⋅x^{II}+1⋅x^{-1}

\;\;{3x^{2}+x+2}/{2⋅x}=x+3+1/x

\;\;{3x^{2}+x+2}/{2x}=\;\;{x^{2}+3x+11}/{x}

3x^{2}+x+2=2x^{2}+6x+2

x^{2}+(-5x)=0

x(x-5)+0

x=0x=5

As base or radix of a number system cannot be zero, here

x=5

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