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Mathematics · 2023 · 2 marks
Continuity and DifferentiabilityDerivatives of Functions in Parametric Forms2 marksApplyvery short answer
CBSE 2023 · Region 2 · Set 1 · Q22
A particle moves along the curve 3 y = a x^3+1 such that at a point with x -coordinate 1, y -coordinate is changing twice as fast at x -coordinate.…
A particle moves along the curve $\displaystyle 3 \mathrm{y}=\mathrm{a} x^{3}+1$ such that at a point with $\displaystyle x$-coordinate $\displaystyle 1, \mathrm{y}$-coordinate is changing twice as fast at $\displaystyle x$-coordinate. Find the value of $\displaystyle \mathrm{a}$.
Marking-scheme solution
Differentiating equation $\displaystyle 3 \mathrm{y}=\mathrm{a} x^{3}+1$ with respect to ' $\displaystyle x$ ', $\displaystyle 3 \frac{d \mathrm{y}}{d x}=3 \mathrm{a} x^{2}$
Taking $\displaystyle x=1, \frac{d \mathrm{y}}{d x}=2,3(2)=3 \mathrm{a}(1)^{2} \Rightarrow \mathrm{a}=2$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.