Question

The co-efficient of x⁴ in (1 - x + 2x²)⁶ is

• A. 185
• B. 155
• C. 195
• D. 145

Answer 1

Answer: (C)

195

Answer 2

General term = $\frac{\angle 6}{\angle p\angle q\angle r}(1)^{p}( - x)^{q}(2x^{2})^{r}$

where p + q + r = 6.

= $\frac{\angle 6}{\angle p\angle q\mathbf{r}}( - 1)^{q}2^{r}x^{q + 2r}$.

If q + 2r = 4,

q = 0, r = 2, = 4

q = 2, r = 1, p = 3

q = 4, r = 0, p = 2.

Co-efficient of x⁴ =

$\frac{\angle 6}{\angle 4\angle 2\angle 0}2^{2} + \frac{\angle 6}{\angle 3\angle 2\angle 1}2 + \frac{\angle 6}{\angle 4\angle 0\angle 2}x1$ = 195.