1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left\{\begin{array}{cl}\frac{\sqrt{a^2-a x+x^2}-\sqrt{x^2+a x+a^2}}{\sqrt{a+x}-\sqrt{a-x}}, & x \neq 0 \text { is } \\ K & x=0\end{array}\right.$ continuous at $x=0$, then $K$ is equal to
A
$-\sqrt{a}$
B
$\sqrt{a}$
C
-1
D
$a+\sqrt{a}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left\{\begin{array}{cc}a x^2+b x-\frac{13}{8}, & x \leq 1 \\ 3 x-3, & 1 < x \leq 2 \text { is differentiable } \\ b x^3+1, & x > 2\end{array}\right.$ $\forall x \in R$, then $a-b$ is equal to
A
$\frac{9}{8}$
B
$\frac{5}{4}$
C
$\frac{11}{8}$
D
$\frac{1}{4}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange's mean value theorem is not applicable
A
$f(x)=|x|, 1 \leq x \leq 5$
B
$f(x)=[x],[\sqrt{2}, \sqrt{3}]$
C
$f(x)=\log \left(x^2-1\right),\left[\frac{1}{e}, e-2\right]$
D
$f(x)=e^x,[-e, e]$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The function $f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & x \neq 0 \\ 2, & x=0\end{array}\right.$
A
is continuous, $\forall x \in R$
B
has maximum value 2
C
has neither minimum nor maximum
D
has minimum value 2
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