CUET Mathematics 2026 21st May Shift 2 PYQs

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is $\tan^{-1}\left(\frac{2}{3}\right)$. Water is poured into it at a constant rate 6 cubic metre per hour. The rate at which the level of the water is rising at the instant when the depth of water in the tank is 5 meter is

Function $f(x) = x^x, x > 0$ decreases on the interval