The associated figure shows the two types of rotate right instruction $${R_1},\,{R_2}$$ available in a microprocessor where Register is a $$8$$-bit register and $$C$$ is the carry bit. The rotate left instructions $$L1$$ and $$L2$$ are similar except that $$C$$ now links the most significant bit of Register instead of the least significant one.

Such a division can be correctly performed by the following set of operations

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2$$ $$\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {{\rm I}^2}{}_{NL}$$. The power dissipated in the non-linear resistance is

The matrix $$A$$ given below is the node incidence matrix of a network. The columns correspond to braches of the network while the rows correspond to nodes. Let
$$V = {\left[ {{v_1}\,\,{v_2}....{v_6}} \right]^T}$$ denote the vector of branches voltages while
$${\rm I} = {\left[ {{i_1}\,{i_2}....{i_6}} \right]^T}$$ that of branch currents. The vector $$E = {\left[ {{e_1}\,{e_2}\,\,{e_3}\,{e_4}} \right]^T}$$ denotes the vector of node voltages relative to a common ground. $$$A = \left[ {\matrix{ 1 & 1 & 1 & 0 & 0 & 0 \cr 0 & { - 1} & 0 & { - 1} & 1 & 0 \cr { - 1} & 0 & 0 & 0 & { - 1} & { - 1} \cr 0 & 0 & { - 1} & 1 & 0 & 1 \cr } } \right]$$$

Which of the following statements is true?

In the figure, transformer $${T_1}$$ has two secondaries, all three windings having the same number of turns and with polarities having the same number of turns and with polarities as indicated. One secondary is shorted by a $$10\,\Omega $$ resistor $$R,$$ and the other by a $$15\mu F$$ capacitor. The switch $$SW$$ is opened $$(t=0)$$ when the capacitor is charged to $$5$$ $$V$$ with the left plate as positive. At $$t=0+$$ the voltage $${V_P}$$ and current $${I_R}$$ are