1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The set of all real values of a such that the real valued function $f(x)=x^3+2 a x^2+3(a+1) x+5$ is strictly increasing in its entire domain is
A
$\left(-\infty-\frac{3}{4}\right) \cup(3, \infty)$
B
$\left(-\frac{3}{4}, 3\right)$
C
( 13
D
$(-\infty, 1) \cup(3-=)$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{x^5 \sqrt[3]{x^3+1}} d x=$
A
$\frac{4}{\sqrt{x^5+1}}+c$
B
$4 x^4\left(x^5+1\right)^{4 / 3}+0$
C
$=\frac{\left(x^3+1\right)^{4 / 3}}{4 x^4}+c$
D
$-\frac{\left(x^5+1\right)^{45}}{4 x^5}+c$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{x+1}{\sqrt{x^2+x+1}} d x=$
A
$\frac{1}{2} \sqrt{x^2+x+1}+\frac{1}{2} \cosh ^{-1}\left(\frac{x+2}{\sqrt{3}}\right)+c$
B
$\frac{1}{2} \sqrt{x^2+x+1}+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$
C
$\sqrt{x^2+x+1}+\frac{2}{\sqrt{3}} \log \left|x^2+x+1\right|+c$
D
$\sqrt{x^2+x+1}+\frac{1}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int\left(\tan ^9 x+\tan x\right) d x=0$
A
$\frac{\tan ^2 x}{12}\left(2 \tan ^3 x-3 \tan ^2 x+6\right)+c$
B
$\frac{\tan ^2 x}{6}-\frac{\tan ^5 x}{4}+\frac{\tan ^2 x}{2}+c$
C
$\left.\frac{\tan ^2 x^2}{6} \tan ^4 x+3 \tan ^2 x+4\right)+c$
D
$\frac{\tan x}{12} \tan ^4 x-3 \tan ^2 x+6+c$
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