GATE Technical: Electrical Engineering Set 2 (2nd stage) questions with solutions

Q1. Consider a causal LTI system characterized by differential equation dy(t)/dt + (1/6)y(t) = 3x(t). The response of the system to the input x(t) = 3e^(-t/3)u(t), where u(t) denotes the unit step function, is

1. 9e^(-t/3)u(t).
2. 9e^(-t/6)u(t).
3. 9e^(-t/3)u(t) - 9e^(-t/6)u(t).
4. 54e^(-t/6)u(t) - 54e^(-t/3)u(t).

Answer: 54e^(-t/6)u(t) - 54e^(-t/3)u(t).

The correct option represents the system's response to the input by applying the principle of superposition and the system's impulse response, which results in a combination of exponential terms that reflect the system's dynamics and the input characteristics.

Q2. A parallel plate capacitor filled with two dielectrics is shown in the figure below. If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is ________.

1. 1
2. 2
3. 4
4. 16

Answer: 2

The electric field in a capacitor filled with different dielectrics is inversely proportional to the dielectric constants of the materials. Since the electric field in region A is 4 kV/cm and region B has a different dielectric constant, the electric field in region B is reduced to 2 kV/cm.

Q3. The Boolean expression (a + b̅ + c + d̅) + (b + c̅) simplifies to

1. 1
2. a̅.b̅
3. a.b
4. 0

Answer: 1

The expression simplifies to 1 because it covers all possible combinations of the variables a, b, c, and d, ensuring that at least one term will always evaluate to true regardless of the values of the individual variables.

Q4. The value of the integral 2∫ from −∞ to ∞ of (sin 2πt)/(πt) dt is equal to

1. 0
2. 0.5
3. 1
4. 2

Answer: 2

The integral evaluates to 1, and since it is multiplied by 2, the final result is 2. This is a known result from Fourier analysis, where the integral of the sinc function over its entire range yields a specific value.

Q5. The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function G(s) = K / ((s−1)(s−4)) is

1. 1
2. 2
3. 5
4. 9

Answer: 2

At the breakaway point of the root locus, the gain K can be determined by analyzing the characteristic equation and the conditions for stability. For this system, the calculations show that the gain at the breakaway point is 2, which corresponds to the specific configuration of the poles and the feedback system.