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Mathematics · 2025 · 1 mark
CBSE 2025 · Region 7 · Set 1 · Q19
Assertion (A): f ( x )= {x sin 1/x, x ≠ 0; 0, x =0} is continuous at x =0. Reason (R): When x → 0, sin 1/x is a finite value between -1 and 1.
Assertion (A) : $\displaystyle \mathrm{f}(\mathrm{x})=\left\{\begin{array}{c}\mathrm{x} \sin \frac{1}{\mathrm{x}}, \mathrm{x} \neq 0 \\ 0, \mathrm{x}=0\end{array}\right.$ is continuous at $\displaystyle \mathrm{x}=0$. Reason $\displaystyle (R): \quad$ When $\displaystyle \mathrm{x} \rightarrow 0, \sin \frac{1}{\mathrm{x}}$ is a finite value between -$\displaystyle 1$ and $\displaystyle 1$ .
Official answer
(A)
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
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CBSE Class 12 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.