Question 62
Given following equation:
(142)b + (112)b-2 = (75)8, find base b.
Explanation
(142)b + (112)b-2 = (75)8, find base b.
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UGC NET CS December 2019 - Question 61 | UGC NET CS December 2019 - Question 63 |
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UGC NET CS December 2019 - Question 61 | UGC NET CS December 2019 - Question 63 |
Question 16 In a certain coding language. 'AEIOU' is written as 'TNHDZ'. Using the same coding language. 'BFJPV' wil...
(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