Wednesday, 3 June 2020

UGC NET Computer Science December 2019 | Question 62

Question 62
Given following equation:
(142)b + (112)b-2 = (75)8, find base b.
  1. 1. 3
  2. 2. 6
  3. 3. 7
  4. 4. 5
Explanation
Given equation:
(142)b + (112)b-2 = (75)8

Evalute right side of the equation:
7*81+5*80 = 56 + 5 = 61

Evalute left side of the equation:
1*b2 + 4*b1 + 2*b0 + 1*(b-2)2 + 1*(b-2)1 + 2(b-2)0
= b2 + 4*b + 2 + (b-2)2 + (b-2) + 2
evaluate (b-2)2 by using formula (a-b)2 = a2 + b2 - 2ab
= b2 + 4b + 2 + (b2 + 4 - 4b) + b
= 2*b2 + 6 + b

Equate both right and left side evaluations
61 = 2*b2 + 6 + b
0 = 2*b2 + b - 55
55 = b(2b +1)

We can easily guess that after replacing the b with 5, above eqation satisfies.

55 = 5(10+1)

So, option 4 is correct answer

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