Class 11 Mathematics · Chapter 8 · Test 1
Mathematical Induction
37 MCQs Covers the principle of mathematical induction: the basic case, the induction hypothesis and the conclusion.
37 questions · 30 min · 37 marks
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Sample questions
The first 5 of 37. Try each one, then tap to see the answer.
Question 1
A proof by mathematical induction (as in the textbook) involves how many steps?
- A2
- B3
- C4
- D5
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Answer: B
The three steps are the basic case and the induction hypothesis and the conclusion.
Question 2
The basic case of a proof by induction means showing that S(n) is true for:
- An = k
- Bn = k+1
- Call n
- Dthe first value of n (n = 1)
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Answer: D
The basic case checks the statement for the starting value usually n = 1.
Question 3
The induction hypothesis means:
- Aassuming S(k) is true for some positive integer k
- Bproving S(k) is true for all k
- Cshowing S(1) is true
- Dassuming S(k+1) is false
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Answer: A
We assume the statement holds for n = k and then use it to prove the next case.
Question 4
In the induction step we must show that:
- AS(1) is true
- BS(k) is false
- CS(k+1) is true whenever S(k) is true
- DS(k-1) is true
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Answer: C
The key step is S(k) implies S(k+1).
Question 5
After the basic case and the induction step are proved the conclusion is that:
- AS(n) is true only for n = 1
- BS(n) is true for all positive integers n
- CS(k+1) is false
- DS(n) is true only for even n
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Answer: B
Both conditions satisfied means S(n) is true for every n in N.
More tests in Mathematical Induction and Binomial Theorem
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