ECAT Mathematics — Mathematical Induction and Binomial Theorem
Mathematical Induction and Binomial Theorem is part of the Mathematics section of the UET ECAT (30 of the 100 MCQs). It breaks into 4 subtopics, and we hold 26 ECAT-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (4)
How Mathematical Induction and Binomial Theorem is tested
Across the 7 ECAT past papers on ParhaiKrlo, Mathematical Induction and Binomial Theorem accounts for 5 questions. It appears in 5 of them, about 1 questions a paper. The heaviest was ECAT Past Paper 07, with 1 question.
| Paper | Questions |
|---|---|
| ECAT Past Paper 07 | 1 |
| ECAT Past Paper 06 | 1 |
| ECAT Past Paper 05 | 1 |
| ECAT Past Paper 04 | 1 |
| ECAT Past Paper 01 | 1 |
Mathematical Induction and Binomial Theorem MCQs from the ECAT past papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · ECAT Past Paper 07 · Mathematical Induction and Binomial Theorem
Using the binomial theorem, the fifth root of 40 approximates to:
- A.2.0
- B.2.5
- C.2.1
- D.2.4
Show answer
Answer: C. 2.1 — 40^(1/5) = 2(1 + 0.25)^(1/5) ≈ 2(1 + 0.05) = 2.1.
- Q2 · ECAT Past Paper 06 · Mathematical Induction and Binomial Theorem
The eighth term of the expansion of (2x² − 1/(2x²))¹² is:
- A.198/x⁴
- B.−198/x⁴
- C.−188/x⁸
- D.−188/x⁴
Show answer
Answer: B. −198/x⁴ — T₈ = ¹²C₇ (2x²)⁵ (−1/(2x²))⁷ = 792 × 2⁻² × (−1) × x⁻⁴ = −198/x⁴.
- Q3 · ECAT Past Paper 05 · Mathematical Induction and Binomial Theorem
The binomial expansion of an expression A gives 1 − 8x + 24x² − 32x³ + 16x⁴. The expression A is:
- A.(1 − 2x)⁴
- B.(1 − 4x)⁴
- C.(1 + 2x)⁴
- D.(1 + 4x)⁴
Show answer
Answer: A. (1 − 2x)⁴ — (1 − 2x)⁴ = 1 − 4(2x) + 6(4x²) − 4(8x³) + 16x⁴ = 1 − 8x + 24x² − 32x³ + 16x⁴.