MHT CET 2025 5th May Evening Shift | Indefinite Integration Question 2 | Mathematics

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

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

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

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

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

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

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

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

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

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

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

MHT CET 2025 26th April Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x}= $$

$\tan x+\cot x+\mathrm{c}$, where c is the constant of integration.

$\tan x-\cot x+\mathrm{c}$, where c is the constant of integration.

$\tan x \cot x+\mathrm{c}$, where c is the constant of integration.

$\tan x-\cot 2 x+\mathrm{c}$, , where c is the constant of integration.

MHT CET 2025 26th April Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\mathrm{d} x}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}=\mathrm{A} x^{\frac{1}{2}}+\mathrm{B} x^{\frac{1}{3}}+\mathrm{C} x^{\frac{1}{6}}+\mathrm{D} \log \left(x^{\frac{1}{6}}+1\right)+\mathrm{k} $$

(where k is the integration constant) then values of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D are respectively,

$2,-3,6,-6$

$2,3,-6,6$

$2,-3,-6,6$

$-2,-3,6,6$

PREVIOUS NEXT

MHT CET Subjects