JEE Main202313 Apr 2023Morning ShiftMathematicsBinomial TheoremActual

Fractional part of the number 4 2022 15 is equal to

Options

A8 15
B4 15
C14 15
D1 15

Correct answer

D. 1 15

Step-by-step solution

Given that 4 2022 15 We know that a + x n = C 0 n a n x 0 + C 1 n a n - 1 x 1 + . . . . . + C n n a 0 x n ⇒ 4 2022 15 = 16 1011 15 = 15 + 1 1011 15 = C 0 1011 15 1011 + C 1 1011 15 1010 + . . . . . + C 1011 1011 15 0 15 = C 0 1011 15 1011 + C 1 1011 15 1010 + . . . . . + C 1010 1011 15 1 15 + 1 15 ∴ Fractional part of 4 2022 15 = 1 15 Hence this is the required option.

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