NTA | UGC NET 2019 December | Question 15

 Given following equation:

(142)_b + (112)_b-2 = (75)₈. Find base b.

(A)

3

(B)

6

(C)

7

(D)

5

Answer: (D)
Explanation:

=>( 1 4 2)_b + ( 1 1 2)_{b-2 =} (7 5)₈  

=> 1xb²  + 4 X  b¹ +  2 X b⁰   + 1 (b-2)²  + 1 (b-2)¹ + 2 (b-2)⁰  =  8¹ x 7 +8⁰x 5

=>  b² + 4b +2 + b² – 4b + 4 + b – 2 + 2 = 56 + 5

=> 2b² + b – 55 = 0

=> 2b² -10b + 11b – 55 = 0

=> 2b(b-5)+ 11(b-5) = 0

So after solving this we get b = 5.

Quiz of this Question
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