Question

find the positive value of n for which the value of coefficient of x^2 in the expansion of (1+x)^n is 10​

Answer 1

Answer:

The answer is $n=5$

Step-by-step explanation:

Concept :

We know that general term in the expansion of $(1+x)^n$ is $^nC_r(1)^{n-1}x^r=^nC_rx^r$

So the coefficient of $x^2$ $=^nC_2$, for coefficient of x^2, r must be 2

But given $^nC_2=10$

               $\Rightarrow \frac{n(n-1)}{2}=10\\\Rightarrow n^2-n=20\\\Rightarrow n^2-n-20=0\\\Rightarrow (n-5)(n+4)=0\\\Rightarrow n=5,-4$

But we know n cannot be negative, hence $n=5$