PU E 2026 Mathematical Induction and Binomial Theorem Free Quiz 1

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PU E 2026 Mathematical Induction and Binomial Theorem Free Quiz 1

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General 10 MCQs

1. What does mathematical induction prove statements for?

A. All positive integers B. All real numbers C. All complex numbers D. All rational numbers

2. What are the two steps of mathematical induction?

A. Only base case B. Base case and inductive step C. Only inductive step D. Conclusion

3. What is the sum of squares of first n natural numbers?

A. n(n+1)/2 B. n(n+1)(2n+1)/6 C. [n(n+1)/2]² D. n(n+1)(2n+1)/6

4. What is the sum of cubes of first n natural numbers?

A. [n(n+1)/2]² B. n(n+1)/2 C. n(n+1)(2n+1)/6 D. n²(n+1)²/4

5. What is the inductive step in mathematical induction?

A. Prove for n = 1 B. Assume for n = k, prove for n = k+1 C. Assume for n = k+1 D. Conclude the statement

6. What is the binomial theorem?

A. Σ (ⁿCᵣ) aⁿ⁻ʳ bʳ B. Σ (ⁿPᵣ) aⁿ⁻ʳ bʳ C. Σ (ⁿCᵣ) aʳ bⁿ⁻ʳ D. Σ (ⁿPᵣ) aʳ bⁿ⁻ʳ

7. How many terms are in the expansion of (a + b)ⁿ?

A. n B. n + 1 C. 2n D. n²

8. What is the general term in (a + b)ⁿ?

A. Tᵣ = ⁿCᵣ aⁿ⁻ʳ bʳ B. Tᵣ₊₁ = ⁿPᵣ aⁿ⁻ʳ bʳ C. Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ D. Tᵣ₊₁ = ⁿCᵣ aʳ bⁿ⁻ʳ

9. What is the sum of binomial coefficients in (1 + x)ⁿ?

A. 2ⁿ B. n C. n² D. 2n

10. What are the binomial coefficients?

A. ⁿPᵣ B. ⁿCᵣ C. n! D. r!

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