Question

Assertion :The expression ${}^{40}{C}_r{.}^{60}{C}_0{+}^{40}{C}_{r-1}{.}^{60}{C}_1+...$ attains maximum value when $r=50$. Reason: ${}^{2n}{C}_r$ is maximum when $r=n$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

${}^{40}{C}_r{.}^{60}{C}_0{+}^{40}{C}_{r-1}{.}^{60}{C}_1+.............$

this is nothing but coefficient of$x^r$in $(1+x{)}^{40}(x+1{)}^{60}$

nothing but coefficient of $x^r$ in $(1+x{)}^{100}$

${}^{100}{C}_r$ is maximum when $r=50$