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

There are three events $\mathrm{A}, \mathrm{B}, \mathrm{C}$, one of which must and only one can happen. The odds are 8:3 against $\mathrm{A}, 5: 2$ against B and the odds against C is $43: 17 \mathrm{k}$, then value of k is

A
$\frac{1}{2}$
B
2
C
$\frac{1}{3}$
D
$\frac{1}{4}$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}=\frac{1}{3}|\overline{\mathrm{~b}}||\overline{\mathrm{c}}| \overline{\mathrm{a}}$. If $\theta$ is the angle between vectors $\bar{b}$ and $\bar{c}$, then the value of $\operatorname{cosec} \theta$ is

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

If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi$ and $x^2+y^2+z^2+k x y z=1$, then k is

A
$-1$
B
1
C
$-2$
D
2
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A radio-active substance has a half-life of h days, then its initial decay rate is given by (where radio-active substance has initial mass $\mathrm{m}_0$)

A
$\frac{\mathrm{m}_0}{\mathrm{~h}}(\log 2)$
B
$\left(\mathrm{m}_0 \mathrm{~h}\right)(\log 2)$
C
$-\frac{\mathrm{m}_0}{\mathrm{~h}}(\log 2)$
D
$-\left(m_0 h\right)(\log 2)$
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