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
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 $x=2$
3
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2+x^5+x^6}}{x^4}=$
A
$\frac{1}{4 \sqrt{2}}$
B
$\frac{1}{2 \sqrt{2}}$
C
$\frac{1}{\sqrt{2}}$
D
$\frac{1}{3 \sqrt{2}}$
4
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{x \rightarrow 1} \frac{\sqrt{x}-1}{\left(\cos ^{-1} x\right)^2}=$
A
$-\frac{1}{4}$
B
$\frac{1}{2}$
C
$-\frac{1}{2}$
D
$\frac{1}{4}$
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