1
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int x^{49}\left[\tan ^{-1} x^{50}+\frac{x^{50}}{1+x^{100}}\right] d x=\frac{x^n}{k} f(x)+c$, then

$$ f(x)-f\left(\sqrt[k]{x^n}\right)= $$

A

$k+n$

B

$k-n$

C

$1 / k$

D

$1 / n$

2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x}{\sqrt{x^2-2 x+5}} d x= $$

A

$\sqrt{x^2-2 x+5}+\sinh ^{-1}\left(\frac{x-1}{2}\right)+C$

B

$\frac{1}{2} \sqrt{x^2-2 x+5}+\sin ^{-1}\left(\frac{x-1}{2}\right)+C$

C

$2 \sqrt{x^2-2 x+5}+\cosh ^{-1}\left(\frac{x-1}{2}\right)+C$

D

$\sqrt{x^2-2 x+5}-\cos ^{-1}\left(\frac{x-1}{2}\right)+C$

3
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

For $0 < x < 1, \int\left[\tan ^{-1}\left(1-x+x^2\right)+\tan ^{-1}(1-x)\right] d x=$

A

$x \cot ^{-1} x+\log \sqrt{1+x^2}+C$

B

$x \tan ^{-1} x-\log \left(1+x^2\right)+C$

C

$x \cot ^{-1} x+\frac{3}{4} \log \left(1+x^2\right)+C$

D

$x \tan ^{-1} x-\frac{3}{4} \log \sqrt{1+x^2}+C$

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{3 x+1}{(x-1)\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^2+2}$, then $5(A-B)=$

A

$A+C$

B

8 C

C

$C+8$

D

$\frac{C}{8}$

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