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1
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{2-\sin x}{2 \cos x+3} d x=$
A
$\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)-\log \sqrt{2 \cos x+3}+c$
B
$\frac{4}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x+3}+c$
C
$\frac{3}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x-3}+c$
D
$\frac{1}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{3}\right)-\log \sqrt{2 \cos x-3}+c$
2
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=$
A
$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+c$
B
$\frac{1}{a+x} \tan ^{-1}\left(\frac{x}{a}\right)-\sqrt{a x}+c$
C
$(a+x) \tan ^{-1}\left(\frac{a}{x}\right)+\sqrt{a x}+c$
D
$\sqrt{a+x} \tan ^{-1}\left(\frac{x}{a}\right)+a x+c$
3
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{A}{x-a}+\frac{B x+C}{x^2+b^2}=\frac{1}{(x-a)\left(x^2+b^2\right)}$, then $\mathrm{C}=$
A
$\frac{-1}{a^2+b^2}$
B
$\frac{1}{a^2+b^2}$
C
$\frac{-a}{a^2+b^2}$
D
$\frac{a}{a^2+b^2}$
4
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{2 x^2-3}{\left(x^2-4\right)\left(x^2+1\right)} d x=A \tan ^{-1} x+B \log (x-2)+C \log (x+2)$, then $6 A+7 B-5 C=$
A
9
B
10
C
6
D
8
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