MCQ 11 Mark
Assertion (A): The expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason (R): If $x=-1$, then the above expansion is zero.
Reason (R): If $x=-1$, then the above expansion is zero.
- ABoth A and R are true and R is the correct
- BBoth A and R are true but R is not the explanation of A . correct explanation of A.
- CA is true but $R$ is false.
- DA is false but $R$ is true.
Answer
View full question & answer→(b) Both A and R are true but R is not the correct explanation of A.
Explanation: Assertion:
$(1+x)^{ n }=n_{c_0}+n_{c_1} x+n_{c 2} x^2 \ldots+n_{c_n} x^n$
Reason:
$\begin{array}{l}(1+(-1))^{ n }=n_{c_0} 1^n+n_{c_1}(1)^{n-1}(-1)^1+n_{c_2}(1)^{n-2}(-1)^2+\ldots+{ }^n c_n(1)^{n-n}(-1)^n \\ =n_{c_8}-n_{c_1}+n_{c_2}-n_{c 3}+\ldots(-1)^{ n } n_{c_n}\end{array}$
Each term will cancel each other
$\therefore(1+(-1))^{ n }=0$
Reason is also the but not the correct explanation of Assertion.
Explanation: Assertion:
$(1+x)^{ n }=n_{c_0}+n_{c_1} x+n_{c 2} x^2 \ldots+n_{c_n} x^n$
Reason:
$\begin{array}{l}(1+(-1))^{ n }=n_{c_0} 1^n+n_{c_1}(1)^{n-1}(-1)^1+n_{c_2}(1)^{n-2}(-1)^2+\ldots+{ }^n c_n(1)^{n-n}(-1)^n \\ =n_{c_8}-n_{c_1}+n_{c_2}-n_{c 3}+\ldots(-1)^{ n } n_{c_n}\end{array}$
Each term will cancel each other
$\therefore(1+(-1))^{ n }=0$
Reason is also the but not the correct explanation of Assertion.