1
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
$\frac{\pi}{6},-\frac{\pi}{12}$
2
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
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{-1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then k is equal to

A
$\frac{-5}{6}$
B
$\frac{5}{6}$
C
$\frac{6}{5}$
D
$\frac{-6}{5}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A point moves along the arc of parabola $y=2 x^2$. Its abscissa increases uniformly at the rate of 2 units $/ \mathrm{sec}$. At the instant, the point is passing through ( 1,2 ), its distance from origin is increasing at the rate of

A
$\frac{36}{\sqrt{5}}$ units/sec.
B
$\frac{18}{\sqrt{5}}$ units $/ \mathrm{sec}$.
C
$\frac{36}{5}$ units/sec.
D
$\frac{18}{5}$ units $/ \mathrm{sec}$.
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