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Q1: (22)4 + (101)3 - (20)5 = (x)4 + (4)x+1 where x > 4. The value of x is

A 6

B 4

C 12

D 8

ANS:C - 12

(22)4 + (10)10 - (10)10 = (22)4 Since x > 4, i.e. all the number systems with base greater than 4. All these will contain symbol '4' which will have same value in all bases. Converting 4 into base '4' system  (4)10  (10)4 Now (22)4 = (x)4 + (10)4 ∴ (x)4 = (22)4 - (10)4 = (12)4 ∴ x = 12.



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