1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

In a triangle ABC , with usual notations, if $\mathrm{m} \angle \mathrm{A}=45^{\circ}, \mathrm{m} \angle B=75^{\circ}$, then $\mathrm{a}+\mathrm{c} \sqrt{2}$ has the

A
$b$
B
$\frac{b}{2}$
C
$2b$
D
$3b$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is

A
1
B
$-$1
C
2
D
0
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are mutually perpendicular vectors having magnitudes $1,2,3$ respectively, then the value of $\left[\begin{array}{lll}\bar{a}+\bar{b}+\bar{c} & \bar{b}-\bar{a} & \bar{c}\end{array}\right]$ is

A
0
B
6
C
12
D
18
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The volume of a ball is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$. The rate of increase of the radius, when the volume is $288 \pi \mathrm{cc}$, is

A
$\frac{1}{6} \mathrm{~cm} / \mathrm{sec}$
B
$\frac{1}{36} \mathrm{~cm} / \mathrm{sec}$
C
$6 \mathrm{~cm} / \mathrm{sec}$
D
$36 \mathrm{~cm} / \mathrm{sec}$
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