gate questions

Q. During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction (Q1-2 = W1-2) when the process is             (A) Isentropic                           (B) Polytropic             (C) Isothermal                           (D) Adiabatic Ans: Isothermal                          

Q. A spur gear with 20° full depth teeth is transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is             (A) 0.36 kN          (B) 0.73 kN               (C) 1.39 kN               (D) 2.78 kN Ans: 0.73

Q. The natural frequencies corresponding to the spring-mass systems I and II are 𝜔𝐼 and 𝜔𝐼𝐼, respectively. The ratio 𝜔𝐼/𝜔𝐼I is Ans: 1/2 Sol:

Q. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity 𝜔. At time 𝑡 = 0, the vertical position of the follower is 𝑦(0) = 0, and the system is in the configuration shown below. The vertical position of the follower face, 𝑦(𝑡) is given by            (A) 𝑒

Q. The lengths of a large stock of titanium rods follow a normal distribution with a mean (𝜇) of 440 mm and a standard deviation (𝜎) of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?             (A) 81.85%           (B) 68.4%                  (C) 99.75%                  (D) 86.64% Ans: 81.85%

Q. A parabola x = y2 with 0 £ x £ 1 is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360° around the x-axis is Ans: π/2 Sol:

Q. M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily FALSE? (A) M is the grandmother of Y  (B) R is the

Q. A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown. There were a total of 600 employees in 2010 and the total employment increased by 15% from 2010 to

Q. Consider a Michelson interferometer as shown in the figure below. When the wavelength of the laser light source is switched from 400 nanometer to 500 nanometer, it is observed that the intensity measured at the output port P goes from a minimum to a maximum. This observation is possible when the smallest path difference

Q. A signal 𝑥(𝑡) has a bandwidth 2𝐵 about a carrier frequency of 𝑓𝑐 = 2 GHz as shown in Figure (a) below. In order to demodulate this signal, it is first mixed (multiplied) with a local oscillator of frequency 𝑓𝐿𝑂 = 1.5 GHz, and then passed through an ideal low-pass filter (LPF) with a