Class 9 Mathematics Chapter 9: Propositions and their Converses — practice questions with answers
Free practice for Class 9 Mathematics, Chapter 9: Propositions and their Converses. Try the solved questions below, then take a free test with instant marking and explanations.
58 questions16 easy, 27 medium, 15 hardNCERT · CBSE · State boards
Sample questions with solutions
Q1. What is a proposition in mathematics?
- A statement that is either true or false
- A question
- An instruction
- An opinion that cannot be checked
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Answer: A. A statement that is either true or false
Why: e.g. ‘If two sides of a triangle are equal, the opposite angles are equal.’ [p.1]
Why: e.g. ‘If two sides of a triangle are equal, the opposite angles are equal.’ [p.1]
Q2. What is the converse of ‘If X then Y’?
- If Y then X
- If not X then not Y
- X and Y
- Y implies not X
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Answer: A. If Y then X
Why: The parts swap places. [p.1]
Why: The parts swap places. [p.1]
Q3. Write the converse of ‘If it rains, then the road is wet.’
- If the road is wet, then it has rained.
- If it does not rain, the road is dry.
- It rains and the road is wet.
- If the road is dry, it did not rain.
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Answer: A. If the road is wet, then it has rained.
Why: The converse need not be true. [p.1]
Why: The converse need not be true. [p.1]
Q4. What is a counterexample?
- An example that shows a proposition is false
- An example that proves a proposition true
- A calculation error
- A type of graph
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Answer: A. An example that shows a proposition is false
Why: One counterexample is enough to disprove a claim. [p.1–2]
Why: One counterexample is enough to disprove a claim. [p.1–2]
Q5. Which number is a counterexample to ‘If a number is a multiple of 3, then it is a multiple of 6’?
- 15
- 12
- 18
- 24
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Answer: A. 15
Why: 15 is odd, so not a multiple of 6. [p.2]
Why: 15 is odd, so not a multiple of 6. [p.2]
Q6. Find the value of 2^(2^3) + 1 (a Fermat number).
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Answer: 257 (± 0)
Why: 2^8 + 1 = 257, which is prime. [p.2]
Why: 2^8 + 1 = 257, which is prime. [p.2]
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Frequently asked questions
How many practice questions are there for Class 9 Mathematics Chapter 9: Propositions and their Converses?
58 questions (16 easy, 27 medium, 15 hard). A few are solved on this page; the free test shows the answer and explanation for every question after you submit.
Is this chapter from the NCERT book?
Yes — it follows the NCERT Class 9 Mathematics syllabus, used by CBSE and many state boards.