Question

The term independent of x in the expansion of
$(1−x^2+3x^3)(\frac{5}{2}x^3−\frac{1}{5x^2})11,x≠0$
is:

• A. $\frac{7}{40}$
• B. $\frac{33}{200}$
• C. $\frac{39}{200}$
• D. $\frac{11}{50}$

Answer 1

Answer: (B)

$\frac{33}{200}$

Answer 2

The correct answer is (B) : $\frac{33}{200}$
$(1−x^2+3x^3)(\frac{5}{2}x^3−\frac{1}{5x^2})^{11},x≠0$
General term of $(\frac{5}{2}x^3−\frac{1}{5x^2})^{11}$ is
$T_{r+1}=^{11}C_r(\frac{5}{2}x^3)^{11−r}(\frac{−1}{5x^2})^r$
$=^{11}C_r(\frac{5}{2})^{11−r}(\frac{−1}{5})^r x^{33−5r}$
So, term independent from x in given expression
$=^{−11}C_7(\frac{5}{2})^4(\frac{−1}{5})^7=\frac{11×10×9×8}{24}×\frac{1}{16×125 }$
$=\frac{33}{200}$