1
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=a \log x+b x^2+x$ has its extreme value at $x=-1$ and $x=2$, then the value of $a+b$ is

A
$\frac{3}{2}$
B
$\frac{1}{2}$
C
$\frac{5}{2}$
D
$\frac{3}{4}$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=x^3+b x^2+c x+d$ and $0< b^2< c$, then in $(-\infty, \infty)$

A
$f(x)$ is strictly increasing function
B
$\mathrm{f}(x)$ is bounded
C
$\mathrm{f}(x)$ has a local maxima
D
$\mathrm{f}(x)$ is a strictly decreasing function
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The minimum value of the function $\mathrm{f}(x)=2 x^3-15 x^2+36 x-48$ on the set $\mathrm{A}=\left\{x \mid x^2+20 \leqslant 9 x\right\}$ is

A
$-$16
B
$-$7
C
16
D
7
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of c for which Rolle's theorem for the function $\mathrm{f}(x)=x^3-3 x^2+2 x$ in the interval $[0,2]$ are

A
$\pm 1$
B
$\pm 2$
C
$1 \pm \frac{1}{\sqrt{3}}$
D
$\sqrt{3}(1 \pm \sqrt{3})$
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