Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell length $a$. The distance between nearest neighbors is

Given $\lambda \in [0, 20]$,find the number of integral values of $\lambda$ for which the function $f(x) = x^3 - 12x + \lambda$ has a point of local maxima.

The amount of copper metal deposited at the cathode on passing an electric current of $500 \, mA$ for $20 \, minutes$ in a cupric chloride solution is ............ $g$.

In a stratified cambium,the fusiform initials are

The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k, \vec B = 4\hat i + 5\hat j + 6\hat k, \vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$. Then the displacement vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are:

$A$ light ray of wavelength $\lambda$ is passing through a pinhole of diameter $D$ and the effect is observed on a screen placed at a distance $L$ from the pinhole. The approximations of geometrical optics are applicable,if