1
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{e^{\cot x}}{\sin ^2 x}(2 \log \operatorname{cosec} x+\sin 2 x) d x=$$

A
$$-2 e^{\cot x} \log \left(\operatorname{cosec}^2 x\right)+C$$
B
$$-2 e^{\cot x} \log (\operatorname{cosec} x)+C$$
C
$$-2 e^{\cot x} \log (\operatorname{cosec} x+\sin x)+C$$
D
$$-2 e^{\cot x} \log (\operatorname{cosec} x-\cot x)+C$$
2
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The parametric form of a curve is $$x=\frac{t^3}{t^2-1} y=\frac{t}{t^2-1}$$, then $$\int \frac{d x}{x-3 y}=$$

A
$$\frac{1}{2} \log \left(t^2-1\right)+C$$
B
$$2 \log \left(t\left(t^2-1\right)\right)+C$$
C
$$\frac{1}{4} \log \left(\frac{t}{t^2-3}\right)+C$$
D
$$\frac{5}{2} \log \left(t+\frac{1}{t^2}\right)+C$$
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int_0^1 a^k x^k d x=$$

A
$$\lim _\limits{n \rightarrow \infty} \frac{a^k\left(1+2^k+3^k \ldots+n^k\right)}{n^{k+1}}$$
B
$$\lim _\limits{n \rightarrow \infty} \frac{a^k+a^k+\ldots+a^k}{n^{k+1}}$$
C
$$\lim _\limits{n \rightarrow \infty} \frac{1}{n} \Sigma\left(\frac{r}{n}\right)^k$$
D
$$\lim _\limits{n \rightarrow \infty} \frac{1}{n} \Sigma\left(\frac{2 r}{n}\right)^k$$
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $$\alpha$$ and $$\beta(\alpha<\beta)$$ are roots of $$18 x^2-9 \pi x+\pi^2=0, f(x)=x^2, g(x)=\cos x$$. Then, $$\int_\alpha^\beta x(g \circ f(x)) d x=$$

A
$$\frac{\sqrt{3}-1}{4}$$
B
$$\frac{\sqrt{3}}{4}$$
C
$$\frac{2+\sqrt{3}}{2}$$
D
$$\frac{1}{2}\left(\sin \frac{\pi^2}{9}-\sin \frac{\pi^2}{36}\right)$$
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