Binomial Theorem – Applications, Coefficient Problems, Greatest Term

Grade 11 Maths Higher — Binomial Theorem – Applications, Coefficient Problems, Greatest Term: 25 practice questions with instant scoring and explanations.

1. The sum 1 + 5 + 10 + 10 + 5 + 1 is equal to:
2. If the greatest term in the expansion of (1 + x)ⁿ has coefficient nCr, then the greatest term is:
3. The greatest coefficient in the expansion of (2 + 3)⁷ is:
4. The sum of the coefficients in the expansion of (x - y)ⁿ is:
5. Using the binomial theorem, (1.02)⁵ ≈
6. The value of (99)⁴ using binomial theorem is:
7. In the expansion of (1 + x)ⁿ, the ratio of the (r+1)th term to the rth term is:
8. The coefficient of x in (1 + x)ⁿ is:
9. If Tᵣ is the greatest term in the expansion of (1 + x)ⁿ, then Tᵣ₊₁/Tᵣ ≤ 1 gives:
10. The greatest term in the expansion of (3 + 2x)¹⁰ when x = 1 occurs at:
11. (1 + 2 + 2² + 2³ + ... + 2ⁿ) can be obtained from binomial expansion by:
12. The sum ⁿC₀ + 2·ⁿC₁ + 3·ⁿC₂ + ... + (n+1)·ⁿCₙ equals:
13. The number of integral terms in the expansion of (∛2 + ∜3)²⁴ is:
14. If (1 + x)ⁿ = 1 + 4x + 6x² + 4x³ + x⁴, then n =
15. The approximate value of ∜(16.81) using binomial expansion is:
16. In the expansion of (x + y)ⁿ, if a term is independent of both x and y, it is:
17. The sum ⁿC₀ - ⁿC₁ + ⁿC₂ - ⁿC₃ + ... + (-1)ⁿ·ⁿCₙ equals:
18. Using binomial theorem, ∛(1000 + 1) ≈
19. The greatest coefficient in the expansion of (x + y)⁷ is:
20. If in the expansion of (x + 1/(x^α))⁶, the term independent of x has coefficient 20, then α =
21. The value of ⁶C₀ + ⁶C₃ + ⁶C₆ + ... is:
22. In the expansion of (x - 1/x)⁶, the constant term is:
23. The ratio of the greatest term to the preceding term in (1 + 1/10)¹⁰ is:
24. Using binomial approximation, (1.01)⁵ ≈
25. The middle term in (x + y)⁶ is T₄ with coefficient: