1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the function defined by $$f(x)=K(x-x^2)$$ if $$0 < x < 1=0$$, otherwise is the p.d.f. of a r.v.X, then the value of $$P\left(X<\frac{1}{2}\right)$$ is

A
$$ \frac{1}{2} $$
B
$$ \frac{1}{3} $$
C
$$ \frac{1}{4} $$
D
$$ \frac{2}{3} $$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+1
-0

The moment of inertia of a body about the given axis, rotating with angular velocity 1 rad/s is numerically equal to 'P' times its rotational kinetic energy. The value of 'P' is

A
$$\frac{1}{4}$$
B
$$\frac{1}{2}$$
C
2
D
1
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+1
-0

An electron in a circular orbit of radius $$0.05 \mathrm{~nm}$$ performs $$10^{14}$$ revolutions/second. What is the magnetic moment due to the rotation of electron? $$(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C})$$

A
$$3.21 \times 10^{-23}$$
B
$$2.16 \times 10^{-23}$$
C
$$3.21 \times 10^{-22}$$
D
$$1.26 \times 10^{-28}$$
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+1
-0

A glass rod of radius '$$r_1$$' is inserted symmetrically into a vertical capillary tube of radius '$$r_2$$' ($$r_1 < \mathrm{r}_2$$) such that their lower ends are at same level. The arrangement is dipped in water. The height to which water will rise into the tube will be ($$\rho=$$ density of water, T = surface tension in water, g = acceleration due to gravity)

A
$$\frac{2 T}{\left(r_2-r_1\right) \rho g}$$
B
$$\frac{T}{\left(r_2^2-r_1^2\right) \rho g}$$
C
$$\frac{T}{\left(r_2-r_1\right) \rho g}$$
D
$$\frac{2 \mathrm{~T}}{\left(\mathrm{r}_2^2-\mathrm{r}_1^2\right) \rho g}$$
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