GATE Technical: GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage) questions with solutions

Q1. Consider a continuous-time system with input x(t) and output y(t) given by y(t) = x(t) cos(t). This system is

1. linear and time-invariant
2. non-linear and time-invariant
3. linear and time-varying
4. non-linear and time-varying

Answer: linear and time-varying

The system is linear because it satisfies the principles of superposition, meaning that the output for a sum of inputs is the sum of the outputs for each input. However, it is time-varying because the output depends on the time-varying function cos(t), which alters the system's behavior over time.

Q2. A temperature in the range of −40°C to 55°C is to be measured with a resolution of 0.1°C. The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is

1. 8
2. 10
3. 12
4. 14

Answer: 10

Range = 55-(-40) = 95 C; at 0.1 C resolution that is 950 levels. 2^9=512 is too few, 2^10=1024 suffices, so 10 bits are required. Stored answer 12 is more than needed.

Q3. Loop transfer function of a feedback system is G(s)H(s)=(s+3)/(s²(s-3)). Take the N nyquist contour in the clockwise direction. Then, the N nyquist plot of G(s)H(s) encircles -1+j0

1. once in clockwise direction
2. twice in clockwise direction
3. once in anticlockwise direction
4. twice in anticlockwise direction

Answer: once in clockwise direction

The Nyquist plot encircles the point -1+j0 once in the clockwise direction, indicating that the system has one pole in the right half-plane, which corresponds to a single unstable pole affecting the stability of the closed-loop system.