General term and middle term — practice questions

Question 1 · difficulty L2 · understanding

The coefficient of $x^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}$, is

Question 2 · difficulty L2 · understanding

If the co-efficient of x 7 and x 8 in the expansion of $${\left( {2 + {x \over 3}} \right)^n}$$ are equal, then the value of n is equal to _____________.

Question 3 · difficulty L2 · understanding

The ratio of the coefficient of the middle term in the expansion of (1 + x) 20 and the sum of the coefficients of two middle terms in expansion of (1 + x) 19 is _____________.

Question 4 · difficulty L2 · understanding

The coefficient of $x^2$ in the expansion of $\left(2 x^2+\frac{1}{x}\right)^{10}, x \neq 0$, is :

• A. 3240
• B. 3360
• C. 3480
• D. 3600

Question 5 · difficulty L2 · understanding

In the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x>0$, if the term independent of $x$ is (221)k, then k is equal to:

• A. 84
• B. 78
• C. 168
• D. 198

Question 6 · difficulty L2 · understanding

The coefficient of $$x^{5}$$ in the expansion of $$\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}$$ is :

• A. $$\frac{26}{3}$$
• B. $$\frac{80}{9}$$
• C. 9
• D. 8

Question 7 · difficulty L3 · understanding

If $\left(1-x^3\right)^{10}=\sum\limits_{\mathrm{r}=0}^{10} \mathrm{a}_{\mathrm{r}} x^{\mathrm{r}}(1-x)^{30-2 \mathrm{r}}$, then $\frac{9 \mathrm{a}_9}{\mathrm{a}_{10}}$ is equal to $\_\_\_\_$ .

Question 8 · difficulty L3 · understanding

If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3}-x^4\right)^n, x \neq 0$, is zero, then the value of $n$ is $\_\_\_\_$ .

Question 9 · difficulty L3 · understanding

If the second, third and fourth terms in the expansion of $$(x+y)^n$$ are 135, 30 and $$\frac{10}{3}$$, respectively, then $$6\left(n^3+x^2+y\right)$$ is equal to __________.

Question 10 · difficulty L3 · understanding

If the constant term in the expansion of $$\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9$$ is $$\mathrm{p}$$, then $$108 \mathrm{p}$$ is equal to ________.