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

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0

A
$y=\cos x+3 x^2+\mathrm{c}$, where c is a constant of integration.
B
$y+\cos x=3 x^2+\mathrm{c}$, where c is a constant of integration.
C
$y=3 x^2 \cos x+\cos x$, where c is a constant of integration.
D
$y \cdot \cos x=3 x^2+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Equation of the plane, through the points $(-1,2,-2)$ and $(-1,3,2)$ and perpendicular to $y \mathrm{z}$ - plane, is

A
$4 y+z=10$
B
$4 y-z+10=0$
C
$4 y-z=10$
D
$4 y+z+10=0$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The values of $a$ and $b$, so that the function

$$f(x)= \begin{cases}x+\mathrm{a} \sqrt{2} \sin x & , 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+b & , \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ \mathrm{a} \cos 2 x-\mathrm{b} \sin x & , \frac{\pi}{2}< x \leq \pi\end{cases}$$

is continuous for $0 \leq x \leq \pi$, are respectively given by

A
$+\frac{\pi}{12},-\frac{\pi}{6}$
B
  $-\frac{\pi}{6},-\frac{\pi}{12}$
C
$\frac{\pi}{6}, \frac{\pi}{12}$
D
$\frac{\pi}{6},-\frac{\pi}{12}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ are unit vectors inclined at $\frac{\pi}{3}$ with each other and $(\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})) \cdot(\overline{\mathrm{a}} \times \overline{\mathrm{c}})=5$, then the value of $5[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]=$

A
$-$10
B
10
C
50
D
$-$50
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