Saved Bookmarks
| 1. |
If the third term in the binomial expansion of (1 - x)k is (1/4)x2 then the rational value of k is1. \(\frac 12\)2. \(- \frac 34\)3. 34. None of these |
|
Answer» Correct Answer - Option 4 : None of these Concept: (1 + x)n = [nC0 + nC1 x + nC2 x2 + … +nCn xn]
Calculation: Given: (1 - x)k and the third term of the expansion is (-1/4)x2 Expansion of (1 - x)k = [kC0 - kC1 x + kC2 x2 + …] So the third term = kC2 x2 = (-1/4)x2 \(\rm \Rightarrow \frac{k!}{2!(k-2)!}=\frac 1 4\) \(\rm \Rightarrow \frac{k\times (k-1)\times (k-2)!}{2(k-2)!}=\frac 1 4\) \(\rm \Rightarrow \frac{k\times (k-1)}{2}=\frac 1 4\) \(\rm \Rightarrow k^2-k=\frac 1 2\) \(\rm \Rightarrow 2k^2-2k- 1 =0\) .....(Multiply by 2 on both the sides) \(\rm \Rightarrow k = \frac {2 \pm \sqrt {12}}{4} = \frac {1 \pm \sqrt {3}}{2}\) \(\Rightarrow \rm k = \frac {1 \pm \sqrt {3}}{2}\) Hence, option (1) is correct. |
|