1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\frac{\pi}{3}$
B
$\cos ^{-1}\left(\frac{2}{3}\right)$
C
$\frac{2 \pi}{3}$
D
$\cos ^{-1}\left(\frac{1}{3}\right)$
2
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{\sec x \cdot \tan x}{9-16 \tan ^2 x} \mathrm{dx}$ is equal to

A
$\frac{1}{24} \log \left(\frac{5+4 \sec x}{5-4 \sec x}\right)+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{1}{40} \log \left(\frac{5+4 \sec x}{5-4 \sec x}\right)+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{1}{24} \log \left(\frac{5-4 \sec x}{5+4 \sec x}\right)+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{1}{40} \log \left(\frac{5-4 \sec x}{5+4 \sec x}\right)+\mathrm{c}$, (where c is a constant of integration)
3
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $n(A)=4, n(B)=2$. Then the number of subsets of the set $\mathrm{A} \times \mathrm{B}$ each having at least 3 elements are

A
275
B
510
C
219
D
256
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A radio active substance has half-life of $h$ days, then its initial decay rate is given by Note that at $\mathrm{t}=0, \mathrm{M}=\mathrm{m}_{\mathrm{o}}$

A
$\frac{\mathrm{m}_{\mathrm{o}}}{\mathrm{h}}(\log 2)$
B
$\left(\mathrm{m}_{\mathrm{o}} \mathrm{h}\right)(\log 2)$
C
$-\frac{\mathrm{m}_{\mathrm{o}}}{\mathrm{h}}(\log 2)$
D
$\left(-\mathrm{m}_{\mathrm{o}} \mathrm{h}\right)(\log 2)$
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