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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2023 · Mathematics · Permutation and Combination

Paragraph: Consider the sum S=0!+1!+2!+3!+4!+ +100!34 Question: If...

Paragraph: Consider the sum S=0!+1!+2!+3!+4!+…+100!34\mathrm{S}=0!+1!+2!+3!+4!+\ldots+100!34
Question: If the sum S is divided by 8 , what is the remainder?

Options

  1. A00
  2. B11
  3. C22
  4. Dcannot be determined

Correct answer

C. 22

Step-by-step solution

S=0!+1!+2!+……+100!S=0!+1!+2!+\ldots \ldots+100! Clearly all factorial from 4 to 100 have 4×24 \times 2 i.e. 8 in them hence all of these are completely divisible by 8. ∴\therefore \quad Remainder will be from 0!+1!+2!+30!+1!+2!+3 ! =1+1+2+6=10=1+1+2+6=10. After dividing 10 from 8 , remainder is 2
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