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1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then
A
$a=-1, b=2$
B
$a=-1, b=-2$
C
$a=1, b=-2$
D
$a=1, b=2$
2
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{d x}{x \sqrt{4 x^2-9}}=$
A
$\frac{2}{3} \log \left|\frac{x-3}{x+3}\right|+c$
B
$\frac{4}{3} \tan ^{-1}\left(\frac{\sqrt{4 x^2-9}}{3}\right)+c$
C
$\frac{2}{3} \log \left|\frac{x+3}{x-3}\right|+c$
D
$\frac{1}{3} \tan ^{-1}\left(\frac{\sqrt{4 x^2-9}}{3}\right)+c$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c$ then $\varphi(x)=$
A
$\frac{1}{5} \sin ^{-1}\left(\frac{x-4}{5}\right)$
B
$\sin ^{-1}\left(\frac{x-4}{5}\right)$
C
$\frac{1}{10} \log \left|\frac{4-x}{4+x}\right|$
D
$\log \left|\frac{4-x}{4+x}\right|$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \tan ^2\left(5-\frac{x}{2}\right) d x=$
A
$-\frac{1}{2} \tan \left(5-\frac{x}{2}\right)-x+c$
B
$-2 \tan \left(5-\frac{x}{2}\right)+c$
C
$\tan \left(5-\frac{x}{2}\right)+c$
D
$-2 \tan \left(5-\frac{x}{2}\right)-x+c$
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