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

$$ \int_{\frac{5}{6}}^\pi \cos ^{-4} x d x= $$

A

$\frac{64}{9 \sqrt{3}}$

B

$\frac{52 \sqrt{3}}{9}$

C

$\frac{62 \sqrt{3}}{9}$

D

$\frac{44}{9 \sqrt{3}}$

2
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int\limits_0^{\frac{3 \pi}{2}} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x= $$

A

0

B

1

C

$\frac{\pi}{4}$

D

$\frac{3 \pi}{4}$

3
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\sec (x-y+1) d y=d x$ is

A

$x+\cot \left(\frac{x-y+1}{2}\right)=C$

B

$x+\cot (x-y+1)=C$

C

$x-\cot \left(\frac{x-y+1}{2}\right)=C$

D

$x-\cot (x-y+1)=C$

4
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The differential equation for which $y^2=4 a(x+a)$ ( $a$ is the parameter) is the general solution is
A

$y=2 x \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2$

B

$y=y \frac{d y}{d x}-x\left(\frac{d y}{d x}\right)^2$

C

$x=3 \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2$

D

$y=3 x^2 \frac{d y}{d x}+y^2\left(\frac{d y}{d x}\right)^2$