1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $$T>0$$ be a fixed number. $$f: R \rightarrow R$$ is a continuous function such that $$f(x+T)=f(x), x \in R$$ If $$I=\int_\limits0^T f(x) d x$$, then $$\int_\limits0^{5 T} f(2 x) d x=$$

A
10 I
B
$$\frac{5}{2} I$$
C
5 I
D
2 I
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int_\limits1^3 x^n \sqrt{x^2-1} d x=6 \text {, then } n=$$

A
2
B
3
C
4
D
5
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

[ . ] represents greatest integer function, then $$\int_{-1}^1(x[1+\sin \pi x]+1) d x=$$

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

$$\begin{aligned} & \lim _{n \rightarrow \infty}\left[\frac{n}{(n+1) \sqrt{2 n+1}}+\frac{n}{(n+2) \sqrt{2(2 n+2)}}\right. \\ & \left.+\frac{n}{(n+3) \sqrt{3(2 n+3)}}+\ldots n \text { terms }\right]=\int_\limits0^1 f(x) d x \end{aligned}$$

then $$f(x)=$$

A
$$\frac{1}{(1+x) \sqrt{x^2+2 x}}$$
B
$$\frac{1}{(1+x) \sqrt{x+2}}$$
C
$$\frac{1}{(1+x) \sqrt{x^2+x+1}}$$
D
$$\frac{1}{(1+x) \sqrt{x^2-2 x}}$$
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