MHT CET 2025 25th April Evening Shift | MHT CET Year Wise Previous Years Questions

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

If the vectors $\overline{\mathrm{a}}=\mathrm{c}\left(\log _7 x\right) \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{b}}=\left(\log _\gamma x\right) \hat{\mathrm{i}}+3 \mathrm{c}\left(\log _\gamma x\right) \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$ make obtuse angle for any $x>0$, then c belongs to

$\left(0, \frac{3}{4}\right)$

$\left(\frac{-3}{4}, 0\right)$

$\left(\frac{-4}{3}, 0\right)$

$\left(0, \frac{4}{3}\right)$

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \sin ^{-4} x d x= $$

$\frac{8}{3}$

$-\frac{8}{3}$

$\frac{2}{3}$

$-\frac{2}{3}$

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

The altitude through vertex $A$ of $\triangle A B C$ with position vectors of points $A, B, C$ as $\bar{a}, \bar{b}, \bar{c}$ respectively is

$$ \frac{|\overline{\mathrm{b}} \times \overline{\mathrm{c}}|}{|\overline{\mathrm{c}}-\overline{\mathrm{b}}|} $$

$$ \frac{|\overline{\mathrm{a}} \times \overline{\mathrm{b}}+\overline{\mathrm{b}} \times \overline{\mathrm{c}}+\overline{\mathrm{c}} \times \overline{\mathrm{a}}|}{|\overline{\mathrm{c}}-\overline{\mathrm{b}}|} $$

$$ \frac{|\overline{\mathrm{b}} \times \overline{\mathrm{c}}|}{|\overline{\mathrm{a}}|} $$

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\mathrm{d} x}{(x+\mathrm{a})^{\frac{9}{7}}(x-\mathrm{b})^{\frac{5}{7}}}= $$

$\frac{7}{\mathrm{a}+\mathrm{b}}\left(\frac{x-\mathrm{b}}{x+\mathrm{a}}\right)^{\frac{9}{7}}+\mathrm{c}$, where c is the constant of integration.

$\frac{7}{a+b}\left(\frac{x-b}{x+a}\right)^{\frac{5}{7}}+c$, where $c$ is the constant of integration.

$\frac{7}{2(a+b)}\left(\frac{x-b}{x+a}\right)^{\frac{2}{7}}+c$, where $c$ is the constant of integration.

$\frac{7}{a+b}\left(\frac{x-b}{x+a}\right)^{\frac{1}{7}}+c$, where $c$ is the constant of integration.

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