1
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
$f(x)=e^x,[-e, e]$
2
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
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{\sqrt[4]{x}}{\sqrt{x}+\sqrt[4]{x}} d x=$ $\frac{2}{3}\left[A \sqrt[4]{x^3}+B \sqrt[4]{x^2}+C \sqrt[4]{x}+D \log (1+\sqrt[4]{x})\right]+K$, then $\frac{2}{3}(A+B+C+D)$ is equal to
A
$2 / 3$
B
$-2 / 3$
C
$4 / 3$
D
$-4 / 3$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int(\log x)^m x^n d x$ is equal to
A
$\int t^m e^{n t} d t, \quad t=e^x$
B
$\int t^m e^{(n+1) t} d t, \quad t=e^x$
C
$\int t^m e^{(n+1) t} d t, \quad x=e^t$
D
$\int t^m e^{n t} d t, \quad x=e^t$
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