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)

-0

The scalar product of vectors $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and a unit vector along the sum of vectors $$\bar{b}=2 \hat{i}-4 \hat{j}+5 \hat{k}$$ and $$\bar{c}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}$$ is one, then the value of $$\lambda$$ is

$$-2$$

$$-3$$

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

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

$$\frac{-\log \left(x^2+\mathrm{a}^2\right)}{x}+\frac{1}{\mathrm{a}} \tan ^{-1} \frac{x}{\mathrm{a}}+\mathrm{c}$$, 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

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