GATE EE 2021 Question Paper (07-Feb-2021) (Shift 1)

Suppose the probability that a coin toss shows "head" is p, where 0 < p < 1. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is

The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the RMS value of the full-wave rectified waveform to the RMS value of the clipped waveform is ______. (Round off to 2 decimal places.)

In the given circuit, for voltage V${}_y$ to be zero, the value of β should be ______. (Round off to 2 decimal places).

Two single-core power cables have total conductor resistance of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ______ × 10⁶.

A 16-bit synchronous binary up-counter is clocked with a frequency f${}_{CLK}$. The two most significant bits are OR-ed together to form an output Y. Measurements show that Y is periodic, and the duration for which Y remains high in each period is 24 ms. The clock frequency fCLK is ______ MHz. (Round off 2 decimal places.)