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1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_{\log 4}^{\log 4} \frac{e^{2 x}+e^x}{e^{2 r}-5 e^x+6} d x=$
A
$\log \left(\frac{64}{9}\right)$
B
$\log \left(\frac{256}{81}\right)$
C
$\log \left(\frac{32}{3}\right)$
D
$\log \left(\frac{128}{27}\right)$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_1^2 \frac{x^4-1}{x^6-1} d x=$
A
$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
B
$\frac{121}{6}$
C
$\sqrt{2}-1$
D
$\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
3
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
4
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
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