$A$ stone is thrown vertically upwards and the height $x \text{ ft}$ reached by the stone in $t$ seconds is given by $x = 80t - 16t^2$. The stone reaches the maximum height in (in $\text{ s}$)

Two sides of a triangle are given. If the area of the triangle is maximum,then the angle between the given sides is (in $^{\circ}$)

The minimum value of the function $f(x) = 2x^2 - \ln|x|$ for $x \geq 1$ is:

If the function $y = a \log x + bx^2 + x$ has extreme values at $x = 1$ and $x = 2$,then $(a, b) = \dots$

$A$ tank with a rectangular base and rectangular sides, open at the top is made. The depth of the tank is $4 \text{ m}$ and its volume is $36 \text{ m}^3$. The cost of the base material is $\text{Rs. } 100 \text{ per m}^2$ and the cost of the side material is $\text{Rs. } 50 \text{ per m}^2$. Find the minimum cost of the tank.

Let $f(x) = x^{2025} - x^{2000}$, $x \in [0, 1]$ and the minimum value of the function $f(x)$ in the interval $[0, 1]$ be $(80)^{80}(n)^{-81}$. Then $n$ is equal to