UGC-NET | NTA UGC NET 2019 June – II | Question 17

Consider the equation (146)​ b​ + (313)​ b-2​ = (246)​ 8​ . Which of the following is the value of b?
(A) 8
(B) 7
(C) 10
(D) 16

Answer: (B)
Explanation: First, we substitute and check the result

=> b = 7
=>(146)7 + (313)7-2 = (246)8
=> LHS = (146)7 + (317)7-2
=> (146)7 = 1 × 72 + 4 ×71 + 6 × 70 = 49 + 28 + 6 = (83)10
=> (313)5 = 3 × 52 + 1 × 5 + 7× 50 = 75 + 5 + 3 = (83)10
=> LHS = (83)10 + (83)10 = (166)10

=> RHS = (246)8
=> 2 × 82 + 4 ×81 + 6 × 80
=> 128 + 32 + 6 = (166)10

LHS = RHS equal only if b is 7.

So, option B is correct.
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