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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

If 1 3 99 - 1 9 93 is divided by 162 , then the remainder is

Options

  1. A3
  2. B6
  3. C5
  4. D0

Correct answer

D. 0

Step-by-step solution

1 3 99 - 1 9 93 = odd number – odd number = even number ⇒ It is divisible by 2 . Also, 1 3 99 = 1 + 12 99 = 1 + 99 C 1 ⋅ 12 + 99 C 2 ⋅ 1 2 2 + 99 C 3 ⋅ 1 2 3 + 99 C 4 ⋅ 1 2 4 + . . . . = 1 + 99 × 12 + 99 × 98 2 ⋅ 1 2 2 + 33 99 × 49 98 × 97 3 × 2 × 1 2 3 + 81 Ι 1 = 1 + 99 × 12 + 99 × 49 ⋅ 1 2 2 + 3 × 11 × 49 × 97 × 1 2 3 + 81 Ι 1 = 1 + 99 × 12 + 81 11 × 49 × 16 + 11 × 49 × 97 × 64 + Ι 1 1 3 99 = 1 + 99 × 12 + 81 Ι 2 1 9 93 = 1 + 18 93 = 1 + 93 C 1 ⋅ 18 + 93 C 2 ⋅ 1 8 2 + . . . . = 1 + 93 × 18 + 81 Ι 3 ⇒ 1 3 99 - 1 9

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