1
KCET 2025
MCQ (Single Correct Answer)
+1
-0

$\int_0^1 \log \left(\frac{1}{x}-1\right) d x$ is

A
1
B
0
C
$\log _{\mathrm{e}} 2$
D
$\log _{\mathrm{e}}\left(\frac{1}{2}\right)$
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

The area bounded by the curve $y=\sin \left(\frac{x}{3}\right)$, $x$ axis, the lines $x=0$ and $x=3 \pi$ is

A
9 sq. units
B
$\frac{1}{3}$ sq. units
C
6 sq. units
D
3 sq. units
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0
The area of the region bounded by the curve $y=x^2$ and the line $y=16$ is
A
$\frac{32}{3}$ sq. units
B
$\frac{256}{3}$ sq. units
C
$\frac{64}{3}$ sq. units
D
$\frac{128}{3}$ sq. units
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0
General solution of the differential equation $\frac{d y}{d x}+y \tan x=\sec x$ is
A
$y \sec x=\tan x+c$
B
$y \tan x=\sec x+c$
C
$\operatorname{cosec} x=y \tan x+c$
D
$x \sec x=\tan y+c$
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