1.9 The binomial theorem Quiz

1. Find the coefficient of $x^3$ in $(1+3x)^5$.

• A. $10$
• B. $90$
• C. $270$
• D. $30$

2. Find the value of $\binom{9}{2}$.

• A. $18$
• B. $36$
• C. $72$
• D. $81$

3. Find the constant term in $\left(2x + \frac1x\right)^4$.

• A. $6$
• B. $24$
• C. $16$
• D. $4$

4. Which is the correct third term of $(a-b)^6$?

• A. $15a^4b^2$
• B. $-15a^4b^2$
• C. $15a^3b^3$
• D. $6a^4b^2$

5. The coefficient of $x$ in $(1+ax)^7$ is 21. Find $a$.

• A. $\frac13$
• B. $14$
• C. $3$
• D. $\frac17$