NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The greatest integer less than 2 + 1 6 is equal to

Options

A196
B197
C198
D199

Correct answer

B. 197

Step-by-step solution

2 + 1 6 + 2 - 1 6 = 2 6 C 0 2 3 + 6 C 2 2 2 + 6 C 4 2 1 + 6 C 6 2 0 2 + 1 6 + 2 - 1 6 = 2 8 + 60 + 30 + 1 = 19 8 2 + 1 6 = 198 - 2 - 1 6 as 2 - 1 ≈ 0.414 ⇒ 2 - 1 6 ∈ 0,1 ⇒ 2 + 1 6 = 198 - f , f ∈ 0,1 ⇒ integral part of 2 + 1 6 = 197

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