Question

Assertion :In the expansion of $(x+x^2{)}^n$ the coefficient of eighth term and nineteenth term are equal, then $n=25$. Reason: Middle term in the expansion of $(x+a{)}^n$ has greatest binomial coefficient.

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

It is given that coefficients of 8th and 19th terms are equal.

Hence, $T_8=T_{19}$

${}^n{C}_7={}^n{C}_{18}$

${}^n{C}_{n-7}={}^n{C}_{18}$
Hence, $n-7=18$

$n=25$.

The reason is also correct since in the pascal's triangle the middle term has the maximum value. However it is not the correct explanation of the assertion.