CAT Exam Model Paper 3 with solutions for free online practice

(d) Since, so or
Similarly, as so, or
So, we can see that $5{\mathit{x}}^2$ varies between 0 and 5, while $\frac{1}{2}-3\frac{{\mathit{x}}^2}{4}$ varies between $\frac{1}{2}$ and $-\frac{1}{4}$. Hence there is a common zone of 0 to1/ 2 between the two. Let us check for some key values of x. If x = 0, then $\left(\frac{1}{2}-\frac{3{\mathit{x}}^2}{4}\right)>\frac{5{\mathit{x}}^2}{4}$ If x = 1, then . Hence between x = 0 andx = 1, there has to some value of x for which and this will be the maximum value of the given expression. Let us check for the same. If then $2{\mathit{x}}^2=\frac{1}{2}$ or ${\mathit{x}}^2=\frac{1}{4}$ For or ${\mathit{x}}^2=\frac{1}{2}$, the value of $\frac{5{\mathit{x}}^2}{4}=\frac{5}{16}=\left(\frac{1}{2}-\frac{3{\mathit{x}}^2}{4}\right)$