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

The curve $y=a x^3+b x^2+c x+5$ touches the $x$-axis at $(-2,0)$ and cuts the $y$-axis at a point Q where its gradient is 3 , then the value of $\mathrm{a}+\mathrm{b}+\mathrm{c}$ is

A
$\frac{7}{8}$
B
$\frac{7}{4}$
C
$\frac{7}{2}$
D
$\frac{7}{12}$
2
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
$\frac{3}{4}$
3
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
4
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
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