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1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \sin ^{-1}\left(\sqrt{\frac{x-a}{x}}\right) d x$ is equal to
A
$x \cos ^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x-a^2}+c$
B
$x \sec ^{-1} \cdot \sqrt{\frac{a}{x}}+\sqrt{x^2-a x}+c$
C
$x \sin ^{-1} \sqrt{\frac{x}{a}}+\sqrt{x^2+a x}+c$
D
$\frac{x}{a} \sin ^{-1} \frac{x}{a}+\frac{x^2}{a} \sqrt{1+a^2}+c$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{\sin x \cos x}{\sqrt{\cos ^4 x-\sin ^4 x}} d x=-\frac{f(x)}{2}+c$, then domain of $f(x)$ is
A
$[2 n \pi,(2 n+1) \pi], n=0,1,2 \ldots$
B
$\left[(4 n-1) \frac{\pi}{2} \cdot(4 n+1) \frac{\pi}{2}\right], n=0,1,2 \ldots$
C
$\left[(4 n-1) \frac{\pi}{4} \cdot(4 n+1) \frac{\pi}{4}\right], n=0,1,2 \ldots$
D
$\left[\left(2 n \frac{\pi}{4} 1 .(2 n+1) \frac{\pi}{4}\right], n=0,1,2 \ldots\right.$
3
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6} \text {, then } A+B \text { is equal to } $$

A
8
B
18
C
3
D
5
4
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x$ is equal to
A
$\frac{e^{4 x^2+8 x-4}}{25}\left[3 \sin \left(3 x^2+6 x-4\right)-4 \cos \left(3 x^2+6 x-4\right)\right]+c$
B
$\frac{e^{4 x^2+8 x-4}}{50}\left[4 \cos \left(3 x^2+6 x-4\right)+3 \sin \left(3 x^2+6 x-4\right]+c\right.$
C
$\frac{e^{4 x^2+8 x-4}}{25}\left[3 \cos \left(3 x^2+6 x-4\right)+4 \sin \left(3 x^2+6 x-4\right]+c\right.$
D
$\frac{e^{4 x^2+8 x-4}}{50}\left[4 \sin \left(3 x^2+6 x-4\right)+3 \cos \left(3 x^2+6 x-4\right]+c\right.$
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IUPAC Nomenclatures General Organic Chemistry Isomerism Hydrocarbons Haloalkanes and Haloarenes Alcohol, Phenols and Ethers Aldehyde and Ketone Carboxylic Acids and Its Derivatives Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical Organic Chemistry
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Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integration Definite Integration Area Under The Curves Differential Equations
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Straight Lines and Pair of Straight Lines Circle Parabola Ellipse Hyperbola
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