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Applied Mathematics · 2025 · 1 mark
CBSE 2025 · Central · Set 4 · Q20
Assertion (A): The differential equation representing the family of curves y = m x, m being an arbitrary constant, is x dy/(d x)- y =0. Reason (R):…
Assertion (A): The differential equation representing the family of curves $\displaystyle \mathrm{y}=\mathrm{m} x$, m being an arbitrary constant, is
$$x \frac{\mathrm{dy}}{\mathrm{d} x}-\mathrm{y}=0 .
$$
Reason (R): For a family of curves, the differential equation is obtained by differentiating the equation of family of curves with respect to $\displaystyle x$ and then eliminating the arbitrary constant, if any.
Official answer
(A)
Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
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CBSE Class 12 Applied Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.