1
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
$\sqrt{3}(1 \pm \sqrt{3})$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $A(-4,5, P), B(3,1,4)$ and $C(-2,0, q)$ are the vertices of a triangle $A B C$ and $G(r, q, 1)$ is its centroid, then the value of $2 p+q-r$ is equal to

A
$-$3
B
$-$6
C
9
D
4
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \mathrm{e}^x\left(\frac{1-\sin x}{1-\cos x}\right) \mathrm{dx}$ is equal to

A
$-\mathrm{e}^x \cot \frac{x}{2}+\mathrm{c}$,(where c is a constant of integration)
B
$\mathrm{e}^x \cot \frac{x}{2}+\mathrm{c}$, (where c is a constant of integration)
C
$\mathrm{e}^x \operatorname{cosec} \frac{x}{2}+\mathrm{c}$,(where c is a constant of integration)
D
$-\mathrm{e}^x \operatorname{cosec} \frac{x}{2}+\mathrm{c}$, (where c is a constant of integration)
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If a body cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in the room temperature of $30^{\circ} \mathrm{C}$ in 30 min , then the temperature of a body after one hour is

A
$42^{\circ} \mathrm{C}$
B
$24^{\circ} \mathrm{C}$
C
$48^{\circ} \mathrm{C}$
D
$56^{\circ} \mathrm{C}$
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