The acceleration $f \text{ ft/sec}^2$ of a particle after a time $t \text{ sec}$ starting from rest is given by $f = 6 - \sqrt{1.2t}$. Then the maximum velocity $v$ and time $T$ to attain this velocity are:

The number of solution$(s)$ satisfying the equation $3x^2 - 2x^3 = \log_2 (x^2 + 1) - \log_2 x$ is

The adjacent sides of a rectangle with a given perimeter of $100 \, cm$ and enclosing the maximum area are:

Find the local maximum and local minimum values of $f(x) = \sin 2x - x$ on the interval $[0, \pi]$.

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

Suppose that $f$ is a polynomial of degree $3$ and that $f''(x) \neq 0$ at any of the stationary points. Then