1
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$ where $a=7^x, b=7^{7^x}, c=7^{7^{7^x}}$ then $\int|A| d x$, (Where $|A|$ is the determinant of the matrix $A$ ) is equal to

A

$\frac{7^{7^x}}{(\log 7)^3}+\mathrm{k}$, where k is constant of integration

B

$\frac{7^{7^{7^x}}}{\log 7}+\mathrm{k}$, where k is constant of integration

C

$\frac{7^{7^{7^x}}}{(\log 7)^3}+\mathrm{k}$, where k is constant of integration

D

$7^{7^{7^x}}(\log 7)^3+\mathrm{k}$, where k is constant of integration

2
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{\sin 7 x}{\cos 9 x \cos 2 x} \mathrm{~d} x$ is equal to

A

$\log \sec (9 x)-\log \sec (2 x)+\mathrm{c}$, where c is the constant of integration

B

$\log \sec (9 x)+\log \sec (2 x)+\mathrm{c}$, where c is the constant of integration

C

$\frac{1}{9} \log \sec (9 x)-\frac{1}{2} \log \sec (2 x)+\mathrm{c}$, where c is the constant of integration

D

$\frac{1}{9} \log \sec (9 x)+\frac{1}{2} \log \sec (2 x)+\mathrm{c}$, where c is the constant of integration

3
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The solution of the equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1}{x+y+1}$ is

A

$x=\log (x+y+2)+\mathrm{c}$, where c is the constant of integration

B

$x=\log (x+y-2)+\mathrm{c}$, where c is the constant of integration

C

$y=\log (x+y+2)+c$, where $c$ is the constant of integration

D

$y=\log (x+y-2)+\mathrm{c}$, where c is the constant of integration

4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage has begun, is

A
$\frac{9}{7}$
B
$-\frac{2}{9}$
C
$\frac{9}{2}$
D
$\frac{2}{9}$

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