Binomial theorem Quiz 1

Question 1

Find the value of $${{\left( 1.04 \right)}^{5}}$$ up to two decimal places without the actual multiplication.

Accepted Answer

$$1.22$$

Answer

$$1.82$$

Answer

$$1.28$$

Answer

$$1.24$$

Question 2

Expand $${{\left( \dfrac{{{x}^{2}}}{2}-\dfrac{2}{x} \right)}^{4}}$$.

Accepted Answer

$$\dfrac{{{x}^{8}}}{16}-{{x}^{5}}+6{{x}^{2}}-\dfrac{16}{x}+\dfrac{16}{{{x}^{4}}}$$

Answer

$$\dfrac{{{x}^{8}}}{16}-{{x}^{5}}+6{{x}^{2}}-\dfrac{16}{x}+\dfrac{16}{{{x}^{2}}}$$

Answer

$$\dfrac{{{x}^{6}}}{16}-{{x}^{5}}+6{{x}^{2}}-\dfrac{16}{x}+\dfrac{16}{{{x}^{4}}}$$

Answer

$$\dfrac{{{x}^{8}}}{16}-{{x}^{5}}+6{{x}^{2}}+\dfrac{16}{x}+\dfrac{16}{{{x}^{4}}}$$

Question 3

Find the $$8^{th}$$ term for the expression: $${{\left( 2{{x}^{2}}-\dfrac{1}{{{x}^{2}}} \right)}^{12}}$$.

Accepted Answer

$$-\dfrac{25344}{{{x}^{4}}}$$

Answer

$$-\dfrac{244}{{{x}^{4}}}$$

Answer

$$-\dfrac{25364}{{{x}^{6}}}$$

Answer

$$-\dfrac{57344}{{{x}^{4}}}$$

Question 4

Find the middle term of the binomial: $$\left( 1-\dfrac{{{x}^{2}}}{2} \right)$$.

Accepted Answer

$$-\dfrac{429}{16}{{x}^{14}}$$

Answer

$$-\dfrac{225}{16}{{x}^{14}}$$

Answer

$$-\dfrac{429}{64}{{x}^{7}}$$

Answer

$$-\dfrac{429}{32}{{x}^{14}}$$

Question 5

Find the coefficient of $${{x}^{19}}$$ for the binomial: $${{\left( 2{{x}^{3}}-3x \right)}^{9}}$$.

Accepted Answer

$$1632960$$

Answer

$$1632660$$

Answer

$$1623960$$

Answer

$$1633960$$