NIMCET 2017 Question Paper with solutions

Changing (123) base 5 into base 10.
= 1 x $5^2$ + 2 x $5^1$ + 3 x $5^0$
= 1 x 25 + 2 x 5 + 3 x $1^0$
= 25 + 10 + 3 = 38 .,, (i)
Changing x8 base y in decimal
= x*${\mathit{y}}^1$ + 8*${\mathit{y}}^0$
= xy + 8 ... (ii)
From Eqs. (i) and (ii), we get
xy+ 8= 38
xy = 30
So, possible combinations = (1, 30), (2,15), (3,10)
but we have 8 present in x8, so base y > 8
Therefore, total soltuion = 3