Q. What is the remainder when
91 × 92× 93 ×94 ×95 ×96 ×97 ×98 ×99 is divided by 1261?
a. 3
b. 2
c. 1
d. 0
Correct Answer: d. 0
Question from UPSC Prelims 2022 CSAT Paper
Explanation :
91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261.
Factors of 1261 are 13 and 97.
So, dividing the given expression by 13 × 97.
(91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99)/(13 × 97)
= 7 × 92 × 93 × 94 × 95 × 96 × 98 × 99
It means this expression is completely divisible by 1261.
Hence, option 4 is correct.
