1
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=(2 x-1)(3 x+2)(4 x-3)$ is a real valued function defined on $\left[\frac{1}{2}, \frac{3}{4}\right]$, then the value(s) of $c$ as defined in the statement of Rolle's theorem
A
does not exist
B
$\frac{7 \pm \sqrt{247}}{36}$
C
$\frac{7-\sqrt{247}}{36}$
D
$\frac{7+\sqrt{247}}{36}$
2
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the interval in which the real valued function $f(x)=\log \left(\frac{1+x}{1-x}\right)-2 x-\frac{x^3}{1-x^2}$ is decreasing in $(a, b)$, where $|b-a|$ is maximum, then $\frac{a}{b}=$
A
-1
B
1
C
$\frac{2}{3}$
D
$\frac{3}{2}$
3
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the slope of the tangent drawn at any point $(x, y)$ on the curve $y=f(x)$ is $\left(6 x^2+10 x-9\right)$ and $f(2)=0$, then $f(-2)=$
A
0
B
4
C
-6
D
-13
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

For all real values of $x$, the minimum value of $\frac{1-x+\lambda^2}{1+x+x^2}$ is

A
0
B
$\frac{1}{3}$
C
1
D
3
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