1
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x, & x>1\end{array}\right.$

is differentiable, $\forall x \in R$, then $f^{\prime}(2)=$

A
5
B
4
C
-4
D
-10
2
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=t^2+t^3$ and $x=t-t^4$, then $\frac{d^2 y}{d x^2}$ at $t=1$ is
A
$\frac{-2}{3}$
B
$\frac{-4}{3}$
C
$\frac{8}{3}$
D
4
3
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
In the interval $[0,3]$ The function $f(x)=|x-1|+|x-2|$ is
A
discontinuous
B
differentiable
C
continuous but not differentiable at $x=2$ only
D
continuous but not differentiable at $x=1$ and $x=2$
4
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$p_1$ and $p_2$ are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ respectively. If $k_1 p_1^2+k_2 p_2^2=a^2$, then $k_1+k_2=$
A
7
B
6
C
5
D
4
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