1
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \cos (\log x) \mathrm{d} x=$$

A
$\frac{x}{2}(\sin (\log x)-\cos (\log x))+c$, (where c is a constant of integration)
B
$x(\cos (\log x)-\sin (\log x))+c$, (where c is a constant of integration)
C
$\frac{x}{2}(\cos (\log x)+\sin (\log x))+\mathrm{c}$, (where c is a constant of integration)
D
$x(\cos (\log x)+\sin (\log x))+c$, (where c is a constant of integration)
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{2 x+5}{\sqrt{7-6 x-x^2}} d x=A \sqrt{7-6 x-x^2}+B \sin ^{-1}\left(\frac{x+3}{4}\right)+\mathrm{c} $$ (where c is a constant of integration) then the value of $A+B$ is

A
$-$3
B
1
C
$-$1
D
3
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{x \mathrm{~d} x}{(x-1)^2(x+2)}=$$

A
$\frac{2}{9} \log (x-1)+\frac{1}{3} \times \frac{1}{x-1}+\frac{2}{9} \log (x+2)+\mathrm{c}$, where c is a constant of integration
B
$\frac{2}{9} \log (x-1)-\frac{1}{3} \times \frac{1}{(x-1)}+\frac{2}{9} \log (x+2)+\mathrm{c}$, where c is a constant of integration
C
$\frac{2}{9} \log (x-1)+\frac{1}{3} \times \frac{1}{x-1}-\frac{2}{9} \log (x+2)+\mathrm{c}$, where c is a constant of integration
D
$\frac{2}{9} \log (x-1)-\frac{1}{3} \times \frac{1}{x-1}-\frac{2}{9} \log (x+2)+\mathrm{c}$, where c is a constant of integration
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\begin{aligned} & \text { If } \\ & \int(7 x-2) \sqrt{3 x+2} \mathrm{~d} x=\mathrm{A}(3 x+2)^{\frac{5}{2}}+\mathrm{B}(3 x+2)^{\frac{3}{2}}+\mathrm{c} \end{aligned}$$

(where c is a constant of integration), then the values of $A$ and $B$ are respectively

A
$\frac{14}{45}, \frac{40}{27}$
B
$\frac{14}{15}, \frac{-40}{9}$
C
$\frac{14}{15}, \frac{40}{9}$
D
$\frac{14}{45}, \frac{-40}{27}$
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