Vegetative propagation in mint occurs by

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$,then a value of $\cos \left(\theta-\frac{\pi}{4}\right)$ among the following is

Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is $(\varepsilon_0 = \text{permittivity of air})$

If $A=\left[\begin{array}{rr}i & -i \\ -i & i\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ -1 & 1\end{array}\right]$,then find $A^8$. (in $B$)

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same total energy stored in it as the first combination. The value of $C_2$,in terms of $C_1$,is:

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is: