SATHEE: Binomial Theorem 1 Question 23

Binomial Theorem 1 Question 23

25.

The coefficient of $x^{4}$ in $(\frac{x}{2} - \frac{3}{x^{2}})^{10}$ is

(1983, 1M)

(a) $\frac{405}{256}$

(b) $\frac{504}{259}$

(d) None of these

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Answer:

Correct Answer: 25. (a)

Solution:

The general term in $(\frac{x}{2} - \frac{3}{x^{2}})^{10}$ is

$t_{r + 1} = (- 1)^{r}^{10} C_{r} (\frac{x}{2})^{10 - r} (\frac{3}{x^{2}})^{r} = (- 1)^{r}^{10} C_{r} \cdot \frac{3^{r}}{2^{10 - r}} \cdot x^{10 - 3 r}$

For coefficient of $x^{4}$ , we put $10 - 3 r = 4$

$\begin{aligned} \Rightarrow & 3 r = 6 \\ \Rightarrow & r = 2 \end{aligned}$

$∴$ Coefficient of $x^{4}$ in $(\frac{x}{2} - \frac{3}{x^{2}})^{10} = (- 1)^{2} \cdot^{10} C_{2} \cdot \frac{3^{2}}{2^{8}}$

$= \frac{45 \times 9}{256} = \frac{405}{256}$

Binomial Theorem 1 Question 23

25.

Answer:

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Binomial Theorem 1 Question 23

25.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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