Jamia Millia Islamia MCA Application of Derivatives Previous Year Question Paper and Solution with PDF

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Jamia Millia Islamia MCA

Jamia Millia Islamia MCA Previous Year Questions (PYQs)

Jamia Millia Islamia MCA Application Of Derivatives PYQ

Qus : 1 Jamia Millia Islamia MCA PYQ

The point of inflection for $f(x) = 3x^4 - 4x^3$ are –

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2023 PYQ

Solution

Solution: $f'(x) = 12x^3 - 12x^2$ $f''(x) = 36x^2 - 24x = 12x(3x - 2)$ Set $f''(x) = 0 \Rightarrow x = 0,\ x = \dfrac{2}{3}$ Hence, points of inflection are $x = 0$ and $x = \dfrac{2}{3}.$

Qus : 2 Jamia Millia Islamia MCA PYQ

The side of an equilateral triangle is increasing at the rate of $2\ \text{cm/s}$. The rate at which area increases when the side is $10\ \text{cm}$ will be —

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2024 PYQ

Solution

For an equilateral triangle, area $A = \dfrac{\sqrt{3}}{4}s^2$ Differentiate with respect to time $t$: $\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2}s\dfrac{ds}{dt}$ Given $\dfrac{ds}{dt} = 2$ and $s = 10$, $\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2} \times 10 \times 2 = 10\sqrt{3}$ Hence, rate = $10\sqrt{3}$ cm$^2$/s