1
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int\left(\frac{x}{x \cos x-\sin x}\right)^2 d x= $$
A
$\frac{x \operatorname{cosec} x}{x \cos x-\sin x}+\cot x+c$
B
$\frac{x \operatorname{cosec} x}{x \cos x-\sin x}-\cot x+c$
C
$\frac{x \operatorname{cosec} x}{x \cos +\sin x}+\cot x+c$
D
$\frac{x}{x \cos x-\sin x}-\cot x+c$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=a e^b$, then $$ a+b= $$
A
$\pi-2$
B
$\pi$
C
$\pi+2$
D
$\frac{\pi}{2}$
3
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int_0^\pi x \sin ^4 x \cos ^6 x d x= $$
A
$\frac{3 \pi^2}{512}$
B
$\frac{3 \pi^2}{256}$
C
$\frac{\pi^2}{256}$
D
$\frac{\pi^2}{512}$
4
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x$, then $I_{13}+I_{11}=$
A
$\frac{1}{13}$
B
$\frac{1}{12}$
C
$\frac{1}{10}$
D
$\frac{1}{11}$
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