Question

Assertion :The number of terms in ${(a+b+c)}^8$ is 55. Reason: The number of terms in the expansion of ${(a+b+c)}^n$ is $\frac{1}{2}(n+1)(n+2).$

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

Answer 1

The correct option is D Assertion is false but Reason is true.

Total number of terms in $(a+b+c{)}^n$ will be $\frac{(n+1)(n+2)}{2!}$.
Substituting $n=8$

we get
$=\frac{9.10}{2!}$
$=9.5$
$=45$
Hence assertion is false, although reason is correct.