MHT CET 2023 13th May Morning Shift | MHT CET Year Wise Previous Years Questions

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

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$$\int \frac{\log \left(x^2+a^2\right)}{x^2} d x=$$

$$\frac{-\log \left(x^2+\mathrm{a}^2\right)}{x}+\frac{1}{\mathrm{a}} \tan ^{-1} \frac{x}{\mathrm{a}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{-\log \left(x^2+\mathrm{a}^2\right)}{x}+\frac{2}{\mathrm{a}} \tan ^{-1} \frac{x}{\mathrm{a}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{\log \left(x^2+\mathrm{a}^2\right)}{x^2}-\frac{1}{\mathrm{a}} \tan ^{-1} \frac{x}{\mathrm{a}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{\log \left(x^2+\mathrm{a}^2\right)}{x^2}-\frac{2}{\mathrm{a}} \tan ^{-1} \frac{x}{\mathrm{a}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

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The parametric equations of the curve $$x^2+y^2+a x+b y=0$$ are

$$x=\frac{\mathrm{a}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=\frac{\mathrm{b}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

$$x=\frac{\mathrm{a}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=\frac{\mathrm{b}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

$$x=-\frac{\mathrm{a}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=-\frac{\mathrm{b}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

$$x=-\frac{\mathrm{a}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=-\frac{\mathrm{b}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides of the triangle (in units) are

3, 4, 5

4, 5, 6

5, 6, 7

2, 3, 4

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

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$$x, y, z$$ are in G.P. and $$\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$$ are in A.P., then

$$6 x=4 y=3 z$$

$$2 x=3 y=6 z$$

$$6 x=3 y=2 z$$

$$x=y=\mathrm{z}$$