GATE

Q. A function 𝐹(𝐴, 𝐵, 𝐶) defined by three Boolean variables A, B and C when expressed as sum of products is given by 𝐹 = 𝐴̅ ⋅ 𝐵̅ ⋅ 𝐶̅ + 𝐴̅ ⋅ 𝐵 ⋅ 𝐶̅ + 𝐴 ⋅ 𝐵̅ ⋅ 𝐶̅ where, 𝐴̅, 𝐵̅, and 𝐶̅ are the complements of the respective variables. […]

Q. The logic function f (X , Y) realized by the given circuit is (A) NOR                      (B) AND                     (C) NAND                   (D) XOR Ans: XOR

Q. In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE? A. The hole and electron diffusion current components are in the same direction. B. The hole and electron drift current components are in the same direction. C. On an average, holes and electrons drift in opposite direction. D.

Q. Consider 𝑝(𝑠) = 𝑠3 + 𝑎2𝑠2 + 𝑎1𝑠 + 𝑎0 with all real coefficients. It is known that its derivative 𝑝′(𝑠) has no real roots. The number of real roots of 𝑝(𝑠) is (A) 0                          (B) 1                          (C) 2                          (D) 3 Ans: 1 Sol: Given p(s) = s3 + a2 s2 + a1s + a0

Q. The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE: A. Both the criteria provide information relative to the stable gain range of the system. B. The general shape of the Nyquist plot is readily obtained

Q. A good transimpedance amplifier has A. low input impedance and high output impedance. B. high input impedance and high output impedance. C. high input impedance and low output impedance. D. low input impedance and low output impedance. Ans: low input impedance and low output impedance.

Q. In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e. 𝑣𝐼𝑁(𝑡) = 𝑢(𝑡) volts. . Also, at 𝑡 = 0, the voltage across each of the capacitors is zero. The time 𝑡, in milliseconds, at which the

Q. A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter

Q. A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. i. 85% of cabs in the city are green and the remaining cabs are blue. ii. A witness identified the cab involved in the accident as blue.

Q. The Cricket Board has long recognized John’s potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that