UPCET / UPSEE Parametric — practice questions

Explore 2 free Parametric questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Parametric questions and exercises with answers

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If $x = a t^2$, $y = 2 a t$ (parametric), then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →Given $x = a(\theta - \sin\theta)$, $y = a(1 - \cos\theta)$ (cycloid). Then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →

Worked practice questions

If $x = a t^2$, $y = 2 a t$ (parametric), then $\dfrac{dy}{dx}$ equals:

$2t$
$1/(2t)$
$t$
$1/t$

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Correct answer: D. $1/t$

$dx/dt = 2at$, $dy/dt = 2a$. $dy/dx = (dy/dt)/(dx/dt) = 2a/(2at) = 1/t$. (This parametrises a parabola $y^2 = 4ax$; slope at parameter $t$ is $1/t$.)

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Given $x = a(\theta - \sin\theta)$, $y = a(1 - \cos\theta)$ (cycloid). Then $\dfrac{dy}{dx}$ equals:

$\cos\theta$
$\tan(\theta/2)$
$\sin\theta$
$\cot(\theta/2)$

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Correct answer: D. $\cot(\theta/2)$

$dx/d\theta = a(1 - \cos\theta) = 2a\sin^2(\theta/2)$. $dy/d\theta = a\sin\theta = 2a\sin(\theta/2)\cos(\theta/2)$. Ratio = $\cos(\theta/2)/\sin(\theta/2) = \cot(\theta/2)$.