From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $$X$$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $$X$$ is $$\frac{m}{n}$$, where $$\operatorname{gcd}(m, n)=1$$, then $$n-m$$ is equal to _________.

A car of $$800 \mathrm{~kg}$$ is taking turn on a banked road of radius $$300 \mathrm{~m}$$ and angle of banking $$30^{\circ}$$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $$(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73)$$

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $$t_1$$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $$t_2$$. Time required to reach the ground, if it is dropped from the top of the tower, is :

Given below are two statements:

Statement (I) : Dimensions of specific heat is $$[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]$$.

Statement (II) : Dimensions of gas constant is $$[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}]$$.

In the light of the above statements, choose the most appropriate answer from the options given below.