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

If the normal drawn at the point $P$ on the curve $y=x \log x$ is parallel to the line $2 x-2 y=3$, then $P=$

A

$(e, e)$

B

$\left(\frac{1}{e}, \frac{-1}{e}\right)$

C

$\left(\frac{1}{e^2}, \frac{-2}{e^2}\right)$

D

$\left(e^3, 3 e^3\right)$

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

If the curves $y^2=16 x$ and $9 x^2+\alpha y^2=25$ intersect at right angles, then $\alpha=$

A

6

B

9

C

$\frac{9}{2}$

D

3

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

If the function $y=\sin x(1+\cos x)$ is defined in the interval $[-\pi, \pi]$, then $y$ is strictly increasing in the interval

A

$\left(-\pi,-\frac{\pi}{3}\right) \cup\left(\frac{\pi}{3}, \pi\right)$

B

$\left(\frac{\pi}{6}, \frac{\pi}{2}\right)$

C

$\left(-\frac{\pi}{3}, \frac{\pi}{3}\right)$

D

$\left(-\pi,-\frac{\pi}{6}\right) \cup\left(\frac{\pi}{6}, \pi\right)$

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

If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is

A

constant

B

inversely proportional to its velocity

C

proportional to its velocity

D

proportional to its displacement