Assuming x to be so small that x3 and higher powers of x can be neglected, then value ofE=1−32x5(2+3x)6, is

A
$64 + 96 x + 720 x^{2}$
B
$65 + 97 x + 721 x^{2}$
C
$64 - 96 x + 720 x^{2}$
D
$64 + 96 x - 720 x^{2}$

Solution:

We have

$\begin{array}{l} {(1 - \frac{3}{2} x)}^{5} (2 + 3 x)^{6} = 2^{6} {(1 - \frac{3}{2} x)}^{5} {(1 + \frac{3}{2} x)}^{6} \\ = 2^{6} (1 + \frac{3}{2} x) {[(1 - \frac{3}{2} x) (1 + \frac{3}{2} x)]}^{5} \\ = 2^{6} (1 + \frac{3}{2} x) {(1 - \frac{9}{4} x^{2})}^{5} \\ = 2^{6} (1 + \frac{3}{2} x) (1 - \frac{45}{4} x^{2}) \end{array}$

$= 2^{6} (1 + \frac{3}{2} x - \frac{45}{4} x^{2}) = 64 + 96 x - 720 x^{2}$

Assuming x to be so small that $x^{3}$ and higher powers of x can be neglected, then value of
$E = {(1 - \frac{3}{2} x)}^{5} (2 + 3 x)^{6}$ , is

Solution:

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