match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists:

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ List $$I$$
(P.)$$\,\,\,\,$$ Volume of parallelopiped determined by vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is $$2.$$ Then the volume of the parallelepiped determined by vectors $$2\left( {\overrightarrow a \times \overrightarrow b } \right),3\left( {\overrightarrow b \times \overrightarrow c } \right)$$ and $$\left( {\overrightarrow c \times \overrightarrow a } \right)$$ is
(Q.)$$\,\,\,\,$$ Volume of parallelopiped determined by vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is $$5.$$ Then the volume of the parallelepiped determined by vectors $$3\left( {\overrightarrow a + \overrightarrow b } \right),\left( {\overrightarrow b + \overrightarrow c } \right)$$ and $$2\left( {\overrightarrow c + \overrightarrow a } \right)$$ is
(R.)$$\,\,\,\,$$ Area of a triangle with adjacent sides determined by vectors $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$20.$$ Then the area of the triangle with adjacent sides determined by vectors $$\left( {2\overrightarrow a + 3\overrightarrow b } \right)$$ and $$\left( {\overrightarrow a - \overrightarrow b } \right)$$ is
(S.)$$\,\,\,\,$$ Area of a parallelogram with adjacent sides determined by vectors $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$30.$$ Then the area of the parallelogram with adjacent sides determined by vectors $$\left( {\overrightarrow a + \overrightarrow b } \right)$$ and $${\overrightarrow a }$$ is

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ List $$II$$
(1.)$$\,\,\,\,$$ $$100$$
(2.)$$\,\,\,\,$$ $$30$$
(3.)$$\,\,\,\,$$ $$24$$
(4.)$$\,\,\,\,$$ $$60$$

A box $${B_1}$$ contains $$1$$ white ball, $$3$$ red balls and $$2$$ black balls. Another box $${B_2}$$ contains $$2$$ white balls, $$3$$ red balls and $$4$$ black balls. A third box $${B_3}$$ contains $$3$$ white balls, $$4$$ red balls and $$5$$ black balls.

If $$1$$ ball is drawn from each of the boxex $${B_1},$$ $${B_2}$$ and $${B_3},$$ the probability that all $$3$$ drawn balls are of the same colour is

A box $${B_1}$$ contains $$1$$ white ball, $$3$$ red balls and $$2$$ black balls. Another box $${B_2}$$ contains $$2$$ white balls, $$3$$ red balls and $$4$$ black balls. A third box $${B_3}$$ contains $$3$$ white balls, $$4$$ red balls and $$5$$ black balls.

If $$2$$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these $$2$$ balls are drawn from box $${B_2}$$ is

Let $$f:\left[ {0,1} \right] \to R$$ (the set of all real numbers) be a function. Suppose the function $$f$$ is twice differentiable,
$$f(0) = f(1)=0$$ and satisfies $$f''\left( x \right) - 2f'\left( x \right) + f\left( x \right) \ge .{e^x},x \in \left[ {0,1} \right]$$.

If the function $${e^{ - x}}f\left( x \right)$$ assumes its minimum in the interval $$\left[ {0,1} \right]$$ at $$x = {1 \over 4}$$, which of the following is true?