Electrical Engineering Gate 2015 Set-2 Questions with Answer

Ques 14 GATE 2015 SET-2

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables x and y. The integration time step is h.
(x_k+1 - x_k)/h = y_k
(y_k+1 - y_k)/h = -x_k
For this discrete-time system, which one of the following statements is TRUE?

Ques 15 GATE 2015 SET-2

The unit step response of a system with the transfer function G(s) = (1-2s)/(1+s) is given by which one of the following waveforms?

Ques 16 GATE 2015 SET-2

An open loop transfer function G(s) of a system is G(s) = K/(s(s+1)(s+2)). For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

Ques 17 GATE 2015 SET-2

For the system governed by the set of equations:
dx₁/dt = 2x₁ + x₂ + u
dx₂/dt = -2x₁ + u
y = 3x₁
the transfer function Y(s)/U(s) is given by

Ques 18 GATE 2015 SET-2

In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is Q₁Q₀=00. The state (Q₁Q₀), immediately after the 333^rd clock pulse is

Ques 19 GATE 2015 SET-2

A Boolean function f(A,B,C,D)=Π(1,5,12,15) is to be implemented using an 8x1 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S₂S₁S₀ of the multiplexer respectively. Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?

Ques 20 GATE 2015 SET-2

Consider the following Sum of Products expression, F.
F = ABC + A̅B̅C + AB̅C + A̅BC + A̅B̅C̅
The equivalent Product of Sums expression is

Ques 21 GATE 2015 SET-2

A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to directly drive a load whose load torque T_L depends on its rotational speed ω_r (in radian/second), such that T_L = 2.78 x ω_r. Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is ________.

Ques 22 GATE 2015 SET-2

The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The "air-gap" voltage, V_g across the magnetizing inductance, is 210 V rms, and the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.

Ques 23 GATE 2015 SET-2

A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the reconnected machine if the field circuit is left unchanged?

Ques 24 GATE 2015 SET-2

A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected and I_s = 100∠0°A, then what is the value of I_p in Ampere?

Ques 25 GATE 2015 SET-2

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of aL is obtained by interconnecting these two coils, the minimum value of a is ________.

Ques 26 GATE 2015 SET-2

A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: N₁=100, N₂=50, N₃=50. If the magnetizing current is neglected, and the currents in two windings are I₂ = 2∠30° A and I₃ = 2∠150° A, then what is the value of the current I₁ in Ampere?