Binomial Theorem – Expansion, General Term, Middle Term

Grade 11 Maths Higher — Binomial Theorem – Expansion, General Term, Middle Term: 25 practice questions with instant scoring and explanations.

1. (x + y)ⁿ = ∑ ⁿCᵣ xⁿ⁻ʳ yʳ is the:
2. The general term in the expansion of (x + a)ⁿ is:
3. The middle term(s) in the expansion of (x + y)⁶ is/are:
4. The sum of all binomial coefficients in (a + b)ⁿ is:
5. The number of terms in the expansion of (x + y)ⁿ is:
6. The coefficient of x⁵ in (x + 2)⁷ is:
7. In the expansion of (x + y)⁸, the term independent of x in (x + 1/x)⁸ is:
8. The middle term in the expansion of (2x + 1/(3x))⁶ is:
9. (2x - 3y)⁴ has coefficients:
10. The term containing x⁸ in (x² + 2/x)⁶ is:
11. The constant term in (x + 1/x²)⁹ is:
12. In the expansion of (1 + x)ⁿ, the sum of odd-placed binomial coefficients is:
13. The coefficient of a⁴b² in the expansion of (a + b)⁶ is:
14. The number of rational terms in the expansion of (2^(1/5) + 3^(1/3))¹⁵ is:
15. The greatest coefficient in the expansion of (1 + x)¹⁰ is:
16. The term independent of x in (x² + 2/(3x))⁹ is:
17. In (x + y)ⁿ, if the coefficients of the 5th and 11th terms are equal, then n =
18. The coefficient of xⁿ⁻¹ in (x + 1)ⁿ is:
19. The middle term of (x/2 + y/3)¹⁰ is:
20. In the expansion of (3 + 2x)⁶, the term containing x² is:
21. If the coefficients of xʳ and xˢ in (1 + x)⁴⁰ are equal, then r + s =
22. The number of rational terms in (2^(1/3) + 3^(1/2))¹⁸ is:
23. The constant term in (x^(1/3) + x^(-1/6))⁶ is:
24. In (a + b)ⁿ, the ratio of the 4th to the 3rd term is:
25. The coefficient of x⁴ in (1 + x)⁷ is: