Appendix 1: Proofs in Mathematics
CBSE · Class 12 · Mathematics
Most important questions from Appendix 1: Proofs in Mathematics for CBSE Class 12 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Sample Questions
Which method proves a statement by assuming it is false and then reaching a contradiction?
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Proof by contradiction
Proof by contradiction starts with the false assumption of the statement and derives a contradiction.
Which of the following best describes the principle of mathematical induction?
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If the base case is true and k implies k+1, then the statement is true for all n from the starting point onward
Mathematical induction uses a true starting case and a true inductive step to conclude truth for all later natural numbers.
Which number is constructed in the proof that the set of primes is infinite?
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N = (P1P2P3...Pk) + 1
The constructed number is the product of the assumed finite list of primes plus 1.
Which statement is true about the function φ(x) = |x|?
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It is continuous everywhere but not differentiable at x = 0
The absolute value function is continuous for all x, but it fails to be differentiable at x = 0.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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