In the interval $(-4, 4)$,the function $f(x) = \int_{-10}^x (t^4 - 4)e^{-4t} dt$ has:

The minimum value of $\frac{\log x}{x}$ in the interval $(2, \infty)$ is

Let $f$ be a function defined on $R$ (the set of all real numbers) such that $f^{\prime}(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4$ for all $x \in R$. If $g$ is a function defined on $R$ with values in the interval $(0, \infty)$ such that $f(x)=\ln(g(x))$ for all $x \in R$,then the number of points in $R$ at which $g$ has a local maximum is

The equation of motion of a stone,thrown vertically upwards is $s = ut - 6.3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$. If the stone reaches its maximum height in $3$ $sec$,then $u =$ ......... $cm/sec$.

If the point of minima of the function $f(x) = 1 + a^2x - x^3$ satisfies the inequality $\frac{x^2 + x + 2}{x^2 + 5x + 6} < 0$,then $a$ must lie in the interval:

$A$ wire of length $28 \, m$ is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?