If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

$A$ $U$-tube has a left limb with a cross-sectional area that is one-quarter of the right limb. The tube contains mercury (density $13.6 \ g/cm^3$). The level of mercury in the narrow left limb is at a distance of $36 \ cm$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water (in $cm$)? (Density of water = $1 \ g/cm^3$)

Let $h(x)$ be differentiable for all $x$ and let $f(x) = (kx + e^x) h(x)$. Where $k$ is some constant. If $h(0) = 5$,$h'(0) = -2$,and $f'(0) = 18$,then the value of $k$ is equal to:

Which one of the following pairs is incorrectly matched?

Cerium $(Z = 58)$ is an important member of the lanthanoids. Which of the following statements is $NOT$ correct for Cerium?

How many types of sporophylls are found in Pteridophytes?