1
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $P(x)=x^4+a x^3+b x^2+c x+d$ be such that $x=0$ is the only real root of $P^1(x)=0$. If $P(-1)
A

$P(-1)$ is not minimum of $P(x)$, but $P(1)$ is the maximum of $P(x)$

B

$P(-1)$ is minimum of $P(x)$, but $P(1)$ is not the maximum of $P(x)$

C

Neither $P(-1)$ is the minimum nor $P(1)$ is the maximum of $P(x)$

D

$P(-1)$ is the minimum and $P(1)$ is the maximum of $P(x)$

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

If the volume of a sphere is increasing at the rate of 12 c.c. $/ \mathrm{sec}$, then the rate (in $\mathrm{sq} . \mathrm{cm} / \mathrm{sec}$ ) at which its surface area is increasing, when the diameter of the sphere is 12 cm is

A

2

B

3

C

4

D

6

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

If the lengths of the tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at the point $(1,1)$ are $a, b, c$ and $d$ respectively, then their increasing order is

A

$b, d, a, c$

B

b, a, c, d

C

$a, b, c, d$

D

$b, a, d, c$

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

$$ \int \frac{x+1}{x^3-1} d x= $$

A

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

B

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

C

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

D

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