1
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
2
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)
3
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
$56^{\circ} \mathrm{C}$
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Derivative of $\sin ^2 x$ with respect to $e^{\cos x}$

A
$2 \sin x \cos ^2 x e^{\cos x}$
B
$\frac{2 \cos x}{\mathrm{e}^{\cos x}}$
C
$\frac{2 \sin x}{\mathrm{e}^{\cos x}}$
D
$\frac{-2 \cos x}{e^{\cos x}}$
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