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1
MHT CET 2026 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int \sin 4x \cos 3x\, dx$ is
A
$-\dfrac{1}{14}\cos 7x - \dfrac{1}{2}\cos x + c$
B
$-\dfrac{1}{14}\cos 7x + \dfrac{1}{2}\cos x + c$
C
$\dfrac{1}{14}\cos 7x - \dfrac{1}{2}\cos x + c$
D
$\dfrac{1}{14}\cos 7x + \dfrac{1}{2}\cos x + c$
2
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{d x}{\cos x(1+\cos x)}= $$

A

$\quad \log (\sec x+\tan x)+2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

B

$\quad \log (\sec x+\tan x)-2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

C

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

D

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

3
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

4
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

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