The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns . The propagation delay of all the flip-flops is assumed to be Zero. The clock (Clk) frequency provided to the circuit is 500 MHz .

Starting from the initial value of the flip-flop outputs $Q_2 Q_1 Q_0=111$ with $D_2=1$, the minimum number of triggering clock edges after which the flip-flop outputs $Q_2 Q_1 Q_0$ becomes 100 (in integer) is $\_\_\_\_$

Consider a rectangular coordinate system $(x, y, z)$ with unit vectors $a_x, a_y$ and $a_z$. A plane wave traveling in the region $z \geq 0$ with electric field vector $E=10 \cos \left(2 \times 10^8 t+\beta z\right) a_y$ is incident normally on the plane at $z=0$, where $\beta$ is the phase constant. The region $z \geq 0$ is in free space and the region $z<0$ is filled with a lossless medium (permittivity $\varepsilon=\varepsilon_0$ permeability $\mu=4 \mu_0$, where $\varepsilon_0=8.85 \times 10^{-12} \mathrm{F} / \mathrm{m}$ and $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ ). The value of the reflection coefficient is

The impedance matching Network shown in figure is to match a lossless line having characteristic impedance $Z_o= 50 \Omega$ with a load impedance $Z_L$. A quarter - Wave line having a characteristic impedance $Z_1=75 \Omega$ is connected to $Z_L$. Two stubs having characteristic impedance of $75 \Omega$ each are connected to this quarter - wave line. One is a short - circuited (S.C) stub of length $0.25 \lambda$ connected across PQ and the other one in an open - Circuted (O.C) stub of length 0.5 $\lambda$ connected across RS.

The impedance matching is achieved when the real part of $Z_L$ is

The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48 respectively. The critical propagation angle. Which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is $\_\_\_\_$ degree.