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AMU MCA Previous Year Questions (PYQs)

AMU MCA Maxima And Minima PYQ

AMU MCA PYQ
The function $f(x,y) = 2x^4 - 3x^2y + y^2$ has:





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2025 PYQ

Solution

At $(0,0)$, first partial derivatives vanish and second derivative test confirms a minimum.
AMU MCA PYQ
The sum of two numbers is $10$. Their product will be maximum when they are





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2016 PYQ

Solution

Let numbers be $x$ and $10-x$ Product $= x(10-x) = 10x - x^2$ Maximum at vertex: $x = \frac{10}{2} = 5$ Numbers: $5,5$
AMU MCA PYQ
The maximum value of $\frac{\log x}{x}$ is





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2016 PYQ

Solution

Let $f(x)=\frac{\log x}{x}$ $f'(x)=\frac{1-\log x}{x^2}$ Set $f'(x)=0 \Rightarrow \log x=1 \Rightarrow x=e$ Maximum value $= \frac{\log e}{e}=\frac{1}{e}$
AMU MCA PYQ
The greatest value of $f(x,y)=xy$ on ellipse $ \frac{x^2}{8}+\frac{y^2}{2}=1 $





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2021 PYQ

Solution

Using Lagrange multipliers, maximum occurs at $ x=2,\ y=1 $ So $ xy=2 $
AMU MCA PYQ
The minimum value of $9^x + 9^{1-x}$, $x \in R$ is





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2016 PYQ

Solution

Let $a=9^x$ ⇒ expression $= a + \frac{9}{a}$ Minimum at $a=3$ Value $= 3 + 3 = 6$

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