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Assertion: The general… (Class 12 Maths SQP 2026-27, Q20)

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MathsCBSE Class 12 · Sample paper, session 2026-27 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics sample paper 2026-27: question 20

From the official CBSE sample question paper for 2026-27, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedDifferential Equations

Assertion: The general solution of a differential equation represents a family of curves.
Reason: The derivative of an arbitrary constant is zero.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. (C)Assertion (A) is true but Reason (R) is false.
  4. (D)Assertion (A) is false but Reason (R) is true.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

What does an arbitrary constant do to a curve?

Hint 2

How are the constants eliminated when forming the differential equation?

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. The general solution contains arbitrary constants, so it represents a family of curves.

  2. Differentiating eliminates these constants because the derivative of a constant is zero. This is why one equation describes the whole family, so the Reason explains the Assertion.

    1 mark

Answer: Option (A)

Where the marks are

  • Recognises both statements as true and linked (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Differential Equations, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.