MHT CET 2023 11th May Morning Shift | MHT CET Year Wise Previous Years Questions

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

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Let $$\bar{a}, \bar{b}$$ and $$\bar{c}$$ be three unit vectors such that $$\bar{a} \times(\bar{b} \times \bar{c})=\frac{\sqrt{3}}{2}(\bar{b}+\bar{c})$$. If $$\bar{b}$$ is not parallel to $$\bar{c}$$, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

$$\frac{5 \pi}{6}$$

$$\frac{2 \pi}{3}$$

$$\frac{\pi}{6}$$

$$\frac{\pi}{3}$$

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

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The vector equation of the line $$2 x+4=3 y+1=6 z-3$$ is

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\frac{1}{2} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\overline{\mathrm{k}})$$

$$\overline{\mathrm{r}}=\left(-2 \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}+\frac{1}{2} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$$

$$\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\overline{\mathrm{k}})$$

$$\overline{\mathrm{r}}=(-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$$

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

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If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \overline{\mathrm{b}}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

$$\left(\frac{\pi}{4}\right)$$

$$\left(\frac{\pi}{3}\right)$$

$$\cos ^{-1}\left(\frac{1}{3}\right)$$

$$\cos ^{-1}\left(\frac{2}{7}\right)$$

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

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$$\int \frac{\log (\cot x)}{\sin 2 x} d x=$$

$$-\log (\cot x)^2+c$$, where c is constant of integration.

$$2(\log (\cot x))^2+c$$, where c is constant of integration.

$$\frac{-1}{4}(\log (\sin x))^2+c$$, where c is constant of integration.

$$\frac{-1}{4}(\log (\cot x))^2+\mathrm{c}$$, where c is constant of integration.