1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $H(x)=3 x^4+6 x^3-2 x^2+1$ and $g(x)$ be a linear polynomial. If $\frac{H(x)}{(x-1)(x+1)(x-2)}=f(x) +\frac{g(x)}{(x-1)(x+1)(x-2)}$, then

$H(-1)+2 H(2)-3 H(1)=$

A

$f(-1)+2 f(2)-3 f(1)$

B

$H(-1)+f(2)+g(3)$

C

$g(-1)+2 g(2)-3 g(1)$

D

$H(1)+2 f(2)-g(1)$

2
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_{\pi / 4}^{\pi / 3} \frac{\cos x-\sin x}{\sin 2 x} d x= $$

A

$\frac{1}{2} \log \left[\frac{(3+2 \sqrt{2})(2-\sqrt{3})}{\sqrt{3}}\right]$

B

$\frac{1}{2} \log \left[\frac{(3-2 \sqrt{2})(2+\sqrt{3})}{\sqrt{3}}\right]$

C

$\log \left[\frac{(3-2 \sqrt{2})(2-\sqrt{3})}{\sqrt{3}}\right]$

D

$\log \left[\frac{(3+2 \sqrt{2})(2-\sqrt{3})}{\sqrt{3}}\right]$

3
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\pi / 2} \frac{\sin x}{1+\cos x+\sin x} d x= $$

A

$\frac{\pi}{2}+\frac{1}{2} \log 2$

B

$\frac{\pi}{4}-\frac{1}{2} \log 2$

C

$\frac{\pi}{4}$

D

$\frac{3 \pi}{4}+\log 2$

4
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x= $$

A

$\frac{\pi^2}{4}$

B

$\frac{\pi}{2}$

C

$\frac{\pi^2}{2}$

D

$\frac{\pi}{4}$

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