Goodmarks
Sign in

Maths · Simple applications

Assertion The expression ! \) is minimum for Reason The expression attains maxim

Assertion The expression \( n !(10-n) ! \) is minimum for \( n=5 \) Reason The expression \( ^{2 m} C_{r} \) attains maximum value for \( \boldsymbol{m}=\boldsymbol{r} \)

  • A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
  • B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
  • C. (A)is true but (R) is false
  • D. (A)is false but (R) is true

Step-by-step solution

The expression n!(10-n)! is minimized when the binomial coefficient C(10,n) is maximized, which occurs at n=5 (since 10 is even). The reason states that for 2m choose r, the maximum occurs at r=m, which is a standard property. For m=5, this gives maximum at r=5, explaining the assertion. Hence both are true and reason correctly explains assertion.
Practise more in this unitView MCQsSign up for full question bank

Related MCQs