FAST-NU Advanced Mathematics — Mathematical Induction and Binomial Theorem
Mathematical Induction and Binomial Theorem is part of the Advanced Mathematics section of FAST's BS CS/Engineering admission test (usually 50 of the 120 MCQs, 50% of the marks). It breaks into 3 subtopics, and we hold 41 FAST-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (3)
How Mathematical Induction and Binomial Theorem is tested
Across the 7 FAST-pattern papers on ParhaiKrlo, Mathematical Induction and Binomial Theorem accounts for 14 questions. It appears in all 7, about 2 questions a paper. The heaviest was FAST Past Paper 07, with 2 questions.
| Paper | Questions |
|---|---|
| FAST Past Paper 07 | 2 |
| FAST Past Paper 06 | 2 |
| FAST Past Paper 05 | 2 |
| FAST Past Paper 04 | 2 |
| FAST Past Paper 03 | 2 |
| FAST Past Paper 02 | 2 |
| FAST Past Paper 01 | 2 |
Mathematical Induction and Binomial Theorem MCQs from the FAST-pattern papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · FAST Past Paper 07 · Mathematical Induction and Binomial Theorem
In the expansion of (2 − x)⁶, what is the coefficient of x³?
- A.160
- B.−20
- C.−160
- D.−320
Show answer
Answer: C. −160 — General term ⁶Cᵣ 2⁶⁻ʳ(−x)ʳ. For x³, r = 3: ⁶C₃ × 2³ × (−1)³ = 20 × 8 × (−1) = −160.
- Q2 · FAST Past Paper 06 · Mathematical Induction and Binomial Theorem
The binomial coefficients in the expansion of (a + b)³ are:
- A.1, 2, 1
- B.1, 3, 3, 1
- C.1, 3, 1
- D.3, 3, 3
Show answer
Answer: B. 1, 3, 3, 1 — (a + b)³ = a³ + 3a²b + 3ab² + b³: coefficients 1, 3, 3, 1.
- Q3 · FAST Past Paper 05 · Mathematical Induction and Binomial Theorem
In the expansion of (a + b)ⁿ, the first term is:
- A.bⁿ
- B.nab
- C.aⁿ
- D.ⁿC₁ a
Show answer
Answer: C. aⁿ — The first term is ⁿC₀ aⁿ b⁰ = aⁿ.