**Q2: **

Find the value of given that the ratio between and , in the expansion of , equals the ratio between and in the expansion of .

**Q3: **

Find the ratio between the fifteenth and seventeenth terms in the expansion of .

- A
- B
- C
- D

**Q4: **

Determine the ratio of the coefficient of in to the coefficient of in . Note that for , we have .

- A
- B
- C
- D

**Q5: **

Consider the expansion of . Find the value of given that and the ratio between and is equal to .

**Q6: **

The coefficients of three consecutive terms in the expansion of are 230, 690, and 1β380 respectively. Evaluate and find their orders.

- A11, , ,
- B11, , ,
- C11, , ,
- D11, , ,

**Q7: **

Consider the expansion of . Find given that the ratio between and is .

- A
- B
- C
- D

**Q8: **

Consider the expansion of in ascending powers of . Given that the ratio between the coefficient of the fourth term and the coefficient of the second term is , determine the value of .

**Q9: **

Consider the expansion of . Determine the values of and , given that the ratio between the coefficients of and is equal to and that the ratio between the coefficients of and is equal to .

- A ,
- B ,
- C ,
- D ,

**Q10: **

The ratio between the coefficients of three consecutive terms in the expansion of is . Evaluate and find the orders of these terms.

- A22, , ,
- B44, , ,
- C22, , ,
- D44, , ,

**Q11: **

Consider the expansion of If the ratio between the middle term and the term containing is , determine the value of .

- A4
- B
- C
- D2

**Q12: **

Consider the binomial expansion of in ascending powers of . When , one of the terms in the expansion is equal to twice its following term. Find the position of these two terms.

- A ,
- B ,
- C ,
- D ,

**Q13: **

Note that . Given that the ratio between the coefficient of in the binomial expansion of and the coefficient of in the expansion of is , find the value of .

**Q14: **

Find given that the ratio between the sixth and the seventh terms in the expansion of is equal to .

- A
- B
- C
- D

**Q15: **

Find given that the ratio between the second and the third terms in the expansion of is equal to .

- A
- B
- C
- D

**Q16: **

Find given that the ratio between the ninth and the tenth terms in the expansion of is equal to .

- A
- B
- C
- D

**Q17: **

Consider the expansion of in ascending powers of . Given that the ratio between the thirteenth term and the twelfth term is , find the value of .

- A
- B
- C2
- D