GATE

Q. The signal energy of the continuous-time signal x(t) = [(t -1) u(t -1)]-[(t – 2)u(t – 2)]-[(t – 3)u(t – 3)]+[(t – 4)u(t – 4)] is (A) 11/3                      (B) 7/3                        (C) 1/3                       (D) 5/3 Ans: 5/3

Q.Digital input signals 𝐴, 𝐵, 𝐶 with 𝐴 as the MSB and 𝐶 as the LSB are used to realize the Boolean function 𝐹 = 𝑚0 + 𝑚2 + 𝑚3 + 𝑚5 + 𝑚7, where 𝑚𝑖 denotes the 𝑖𝑡ℎ minterm. In addition, 𝐹 has a don’t care for 𝑚1. The simplified expression for 𝐹 is

Q. Which one of the following statements is true about the digital circuit shown in the figure A. It can be used for dividing the input frequency by 3. B. It can be used for dividing the input frequency by 5. C. It can be used for dividing the input frequency by 7. D. It

Q. The number of roots of the polynomial, 𝑠7 + 𝑠6 + 7𝑠5 + 14𝑠4 + 31𝑠3 + 73𝑠2 + 25𝑠 + 200, in the open left half of the complex plane is (A) 3 (B) 4 (C) 5 (D) 6 Ans: 3

Q. The equivalent impedance Zeq for the infinite ladder circuit shown in the figure is (A) j12 Ω                    (B) –j12 Ω                  (C) j13 Ω                   (D) 13 Ω Ans: j12Ω Sol:

Q. A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the figure. Assume i(0) = 0, v(0) = 0 . Which one of the following circular loci represents the plot of i(t) versus v(t) ? Ans: Option B

Q. The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, 𝑃 = 1.4 sin 𝛿 + 0.15 sin 2𝛿, where 𝛿 is the load angle. Newton- Raphson method is used to calculate the value of 𝛿 for 𝑃 = 0.8 pu. If the initial

Q. Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G1 and G2 are QG1 and QG2 respectively. The per unit values of QG1, QG2, and line reactive power loss (Qloss) respectively

Q. The positive, negative and zero sequence impedances of a three phase generator are 𝑍1, 𝑍2 and 𝑍0 respectively. For a line-to-line fault with fault impedance 𝑍𝑓, the fault current is 𝐼𝑓1 = 𝑘𝐼𝑓, where 𝐼𝑓 is the fault current with zero fault impedance. The relation between 𝑍𝑓 and 𝑘 is Ans: Option A Sol:

Q. A 0-1 Ampere moving iron ammeter has an internal resistance of 50 mΩ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in mΩ of the shunt coil respectively are (A) 2, 5.55                  (B) 2,