MHT CET 2025 23rd April Evening Shift | MHT CET Year Wise Previous Years Questions

MHT CET 2025 23rd April Evening Shift

MCQ (Single Correct Answer)

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If $\mathrm{f}(x)=3 x^3+2 x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \prime}(2)+\mathrm{f}^{\prime \prime \prime}(3)$ then $\mathrm{f}(x)=$ __________ .

$\frac{1}{7}\left(3 x^3-90 x^2+72 x+18\right)$

$\frac{1}{7}\left(21 x^3-90 x^2+72 x+126\right)$

$3 x^3-90 x^2+72 x+18$

$3 x^3-45 x^2+36 x+9$

MHT CET 2025 23rd April Evening Shift

MCQ (Single Correct Answer)

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If $x=\sin \theta, y=\sin ^3 \theta$, then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{6}$ is

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

MHT CET 2025 23rd April Evening Shift

MCQ (Single Correct Answer)

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If $x=\mathrm{e}^{\tan ^{-1}\left(\frac{y-x^2}{x^2}\right)}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is

MHT CET 2025 23rd April Evening Shift

MCQ (Single Correct Answer)

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The difference between the maximum value and minimum value of objective function $\mathrm{z}=3 x+5 y$ subject to constraints $x+3 y \leq 60$, $x+y \geq 10, x-y \geq 0, x, y \geq 0$ is