The cosine of the angle $A$ of the triangle with vertices $A(1, -1, 2)$, $B(6, 11, 2)$, and $C(1, 2, 6)$ is:

$A$ diode having a potential difference of $0.5\,V$ across its junction,which does not depend on the current,is connected in series with a resistance of $20\,\Omega$ across a source. If $0.1\,A$ current passes through the resistance,what is the voltage of the source (in $,V$)?

Assertion $(A):$ Above Curie temperature, a ferromagnetic material becomes paramagnetic.

Reason $(R):$ When a magnetic material is heated to very high temperature, it loses its magnetic properties.

In a $YDSE$,bichromatic light of wavelengths $\lambda_1 = 400\, nm$ and $\lambda_2 = 560\, nm$ are used. The distance between the slits is $d = 0.1\, mm$ and the distance between the plane of the slits and the screen is $D = 1\, m$. The minimum distance between two successive regions of complete darkness is.......$mm$.

If $\frac{x-4}{x^2-5x-2k} = \frac{2}{x-2} - \frac{1}{x+k}$,then $k$ is equal to