Match the statements of Column I with the values of Column II

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Match the statements of Column I with the values of Column II.

Column I	Column II
(a) The dimensions of the rectangle of perimeter $36\text{ cm}$ that sweeps out the largest volume when revolved about one of its sides are	(p) $6$
(b) Let $A(-1,2)$ and $B(2,3)$ be two fixed points. If a point $P$ lies on $y=x$ such that the perimeter of $\triangle PAB$ is minimum, then the sum of the abscissa and ordinate of $P$ is	(q) $12$
(c) If $x_1$ and $x_2$ are abscissae of two points on the curve $f(x)=x-x^2$ in the interval $[0,1]$ , then the maximum value of $(x_1+x_2)-(x_1^2+x_2^2)$ is	(r) $4$
(d) The number of non-zero integral values of $a$ for which $f(x)=x^4+ax^3+\frac{3x^2}{2}+1$ is concave upward along the entire real line is	(s) $\frac12$