If the function $f(x)=2 x^3-9 a x^2+12 a^2 x+1$,where $a > 0$,attains its local maximum and local minimum values at $p$ and $q$ respectively,such that $p^2=q$,then $f(3)$ is equal to:

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

The equations of motion of two stones thrown vertically upwards simultaneously are $s_1 = 19.6t - 4.9t^2$ and $s_2 = 9.8t - 4.9t^2$ respectively. If the maximum height attained by the first stone is $h$,then when the first stone is at its maximum height,the height of the second stone will be:

The abscissa of the points,where the tangent to the curve $y=x^3-3x^2-9x+5$ is parallel to the $X$-axis,are

If $m$ is the minimum value of $k$ for which the function $f(x) = x\sqrt{kx - x^2}$ is increasing in the interval $[0, 3]$ and $M$ is the maximum value of $f$ in $[0, 3]$ when $k = m$,then the ordered pair $(m, M)$ is equal to

Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity $u$ and the second starts from rest with constant acceleration $f$. Then,