1
MHT CET 2024 11th 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 values of $a, b, c$ respectively, are

A
$3,-\frac{1}{2},-\frac{3}{4}$
B
$-\frac{3}{4},-\frac{1}{2}, 3$
C
$-\frac{1}{2},-\frac{3}{4}, 3$
D
$-\frac{1}{2}, 3,-\frac{3}{4}$
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$-$16
B
$-$7
C
16
D
7
3
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the normal to the curve $y=\mathrm{f}(x)$ at the point $(3,4)$ makes an angle of $\left(\frac{3 \pi}{4}\right)$ with the positive $X$-axis, then the value of $f^{\prime}(3)$ is

A
$-1$
B
$-\frac{3}{4}$
C
$\frac{4}{3}$
D
1
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=x^3-6 x^2+9 x+3$ is monotonically decreasing function, then $x$ lies in

A
$(3, \infty)$
B
$(1,3)$
C
$[3, \infty)$
D
$[0,3]$
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