NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

If 1 ! 2 + 2 ! 2 + 3 ! 2 + ⋯ + 99 ! 2 + 100 ! 2 is divided by 100 , then the remainder obtained is

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Correct answer

C. 17

Step-by-step solution

5 ! = 120 ⇒ 5 ! 2 = 12 2 × 100 ⇒ 5 ! 2 , 6 ! 2 , 7 ! 2 , … … . . , 99 ! 2 all are divisible by 100 . and 1 ! 2 + 2 ! 2 + 3 ! 2 + 4 ! 2 = 1 + 4 + 36 + 576 = 617 So, when divided by 100 , the remainder obtained will be 17 .

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