List of top Statistics Questions on Maxima and Minima asked in CUET (PG)

The function $f(x)=\int_{e^{x}}^{e^{2x}} t \log_{e}t \, dt$ has an absolute minima at $x=0$ and a local maxima at $x=$

Match List I with List - II. List - I & List - II
A. $x$ where $f(x)=9x(x-1)^{2}$ attains maximum & I. $e$

B. $x$ where $f(x)=\frac{1}{x}e^{-\frac{1}{2}(\log_{e}x-2)^{2}}$ attains maximum & II. $\frac{2}{3}$

C. $x$ where $f(x)=x^{2}(1-x)^{6}$ attains maximum & III. $\frac{1}{3}$

D. $x$ where $f(x)=x^{2}e^{-3x}$ attains maximum & IV. $\frac{1}{4}$

The maximum values of the function
\(\sin(x)+\cos(2x)\), are

Function, \(f(x) = -|x-1|+5, \forall x \in R\) attains maximum value at x =

It is given that at x = 1, the function \(f(x) = x^4 - 62x^2 + ax + 9\), attains its maximum value in the interval \([0, 2]\). Then, the value of 'a' is