Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained. The expectation of $X$ is ___________ (rounded off to two decimal places).

Consider the vectors

$$ a=\left[\begin{array}{l} 1 \\ 1 \end{array}\right], b=\left[\begin{array}{c} 0 \\ 3 \sqrt{2} \end{array}\right] $$

For real-valued scalar variable $x$, the value of

$$ \min _x\|a x-b\|_2 $$

is___________(rounded off to two decimal places).

$\|\cdot\|_2$ denotes the Euclidean norm, i.e., for $y=\left[\begin{array}{l}y_1 \\ y_2\end{array}\right],\|y\|_2=\sqrt{y_1^2+y_2^2}$.

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3 \Omega$ resistor are as indicated.

The voltage (in Volts) at node $X$ is __________ .

Let $i_C, i_L$, and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens(S). Which one of the following is true?