UGC NET Computer Science December 2019 | Question 62

Question 62

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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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