Firstranker's choice
GATE 2015
--- Content provided by FirstRanker.com ---
Q. 1 – Q. 25 carry one mark each.
Q.1 Given f(z) = g(z) + h(z), where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE?
(A) If f(z) is differentiable at zo, then g(z) and h(z) are also differentiable at zo.
(B) If g(z) and h(z) are differentiable at zo, then f(z) is also differentiable at zo.
(C) If f (z) is continuous at zo, then it is differentiable at zo.
--- Content provided by FirstRanker.com ---
(D) If f(z) is differentiable at zo, then so are its real and imaginary parts.
Q.2 We have a set of 3 linear equations in 3 unknowns. ‘X = Y' means X and Y are equivalent statements and ‘X ? Y' means X and Y are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
--- Content provided by FirstRanker.com ---
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
(A) P = Q = R = S
(B) P = R ? Q = S
(C) P = Q ? R = S
--- Content provided by FirstRanker.com ---
(D) P? Q?R?S
Q.3 Match the following.
P. Stokes's Theorem 1. ff D. ds = Q
Q. Gauss's Theorem 2. § f(z)dz = 0
R. Divergence Theorem 3. fff (?.A)dv = ff A. ds
--- Content provided by FirstRanker.com ---
S. Cauchy's Integral Theorem 4. ff (? × A). ds = § A.dl
(A) P-2 Q-1 R-4 S-3
(B) P-4 Q-1 R-3 S-2
(C) P-4 Q-3 R-1 S-2
(D) P-3 Q-4 R-2 S-1
--- Content provided by FirstRanker.com ---
Q.4 The Laplace transform of f(t) = vt/p is s-3/2. The Laplace transform of g(t) = v1/pt is
(A) 3s-5/2/2
(B)
(C) s1/2
(D) $3/2
--- Content provided by FirstRanker.com ---
Q.5 Match the following.
Instrument Type Used for
P. Permanent magnet moving coil 1. DC Only
Q. Moving iron connected through current transformer 2. AC Only
R. Rectifier 3. AC and DC
--- Content provided by FirstRanker.com ---
S. Electrodynamometer
(A) P-1 Q-2 R-1 S-3
(B) P-1 Q-3 R-1 S-2
(C) P-1 Q-2 R-3 S-3
(D) P-3 Q-1 R-2 S-1
--- Content provided by FirstRanker.com ---
Q.6 A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The readings of the two wattmeters are
(A) 3.94 kW and 1.06 kW
(B) 2.50 kW and 2.50 kW
(C) 5.00 kW and 0.00 kW
--- Content provided by FirstRanker.com ---
(D) 2.96 kW and 2.04 kW
Q.7 A capacitive voltage divider is used to measure the bus voltage Vbus in a high-voltage 50 Hz AC system as shown in the figure. The measurement capacitors C1 and C2 have tolerances of ±10% on their nominal capacitance values. If the bus voltage Vbus is 100 kV rms, the maximum rms output voltage Vout (in kV), considering the capacitor tolerances, is
C1 1µF ± 10% Vbus
C2 9µF ± 10% Vout
Q.8 In the following circuit, the input voltage Vin is 100 sin(100pt). For 100pRC = 50, the average voltage across R (in Volts) under steady-state is nearest to
--- Content provided by FirstRanker.com ---
(A) 100
(B) 31.8
Vin + C
(C) 200
(D) 63.6
--- Content provided by FirstRanker.com ---
Q.9 Two semi-infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y < 0) and region 2 (y > 0) are 2 and 5, respectively. Region 1 has uniform electric field E = 3âx + 4ây + 2âz, where âx, ây, and â2 are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is
(A) 3âx + 1.6ây + 2âz
(B) 1.2âx + 4ây + 2âz
(C) 1.2âx + 4ây + 0.8âz
(D) 3âx + 10ây + 0.8âz
--- Content provided by FirstRanker.com ---
Q.10 A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of µo is 4p × 10-7in SI unit. If a uniform magnetic field intensity H = 1072 A/m is applied, then the peak value of the induced voltage, Vturn ( in Volts), is
Z
X Vturn
Q.11 The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is V1 = 2 sin(2p × 2000t). The amplitude of the output voltage V (in Volt) is
--- Content provided by FirstRanker.com ---
0.1 µF
1 ?O
1 ?O
Vo
Q.12 In the following circuit, the transistor is in active mode and Vc = 2 V. To get Vc = 4 V, we replace Rc with R. Then the ratio R/Rc is
--- Content provided by FirstRanker.com ---
+10 V
Rc
RB
Vc
Q.13 Consider the following Sum of Products expression, F.
--- Content provided by FirstRanker.com ---
F = ABC + ABC + AB C + ABC + ABC
The equivalent Product of Sums expression is
(A) F = (A + B + C)(A + B + C) (A + B + C)
(B) F = (A + B + C)(A + B + C)(A + B + C)
(C) F = (A + B + C)(A + B + C) (A + B + C)
--- Content provided by FirstRanker.com ---
(D) F = (A + B + C)(A + B + C) (A + B + C)
Q.14 The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown in Figure (c).
Vo/Vi F1 F2 Vo/Vi
Vi Vo Vi
--- Content provided by FirstRanker.com ---
f1 f f2 f
(a) (b)
R/2 +Vsat R
F1 Vi R F2 + Vo
-Vsat
--- Content provided by FirstRanker.com ---
(c)
The cut-off frequencies of F1 and F2 are f1 and f2 respectively. If f1 <f2, the resultant circuit exhibits the characteristic of a
(A) Band-pass filter
(B) Band-stop filter
(C) All pass filter
--- Content provided by FirstRanker.com ---
(D) High-Q filter
Q.15 When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?
(A) The CB junction is forward biased and the BE junction is reverse biased.
(B) The CB junction is reverse biased and the BE junction is forward biased.
(C) Both the CB and BE junctions are forward biased.
--- Content provided by FirstRanker.com ---
(D) Both the CB and BE junctions are reverse biased.
Q.16 The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t1 by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle 8 shows the transient correctly?
(A) Synchronous generator Line 1 Infinite Bus
Xs Line 2
--- Content provided by FirstRanker.com ---
d
8=0- time
t1
(B)
d
--- Content provided by FirstRanker.com ---
8=0-
t1
(C)
d? ?d time
t1
--- Content provided by FirstRanker.com ---
(D)
d
-0=9
t1 time
--- Content provided by FirstRanker.com ---
Q.17 A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is
[-j6 j3 j4
j3 -j7 j5 pu.
j4 j5 -j8]
If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3rd row 3rd column element (in pu) of the bus admittance matrix after compensation is
--- Content provided by FirstRanker.com ---
(A) -j7.0
(B) -j8.5
(C) -j7.5
(D) -j9.0
Q.18 A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of d2i/dt2 at t = 0+ is
--- Content provided by FirstRanker.com ---
R
V
(A) V/L
(B) -V/R
(C) 0
--- Content provided by FirstRanker.com ---
(D) -RV/L2
Q.19 The current i (in Ampere) in the 2 O resistor of the given network is
1 O
5V 1O 2 S i
Q.20 Find the transformer ratios a and b such that the impedance (Zin) is resistive and equals 2.5 O when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.
--- Content provided by FirstRanker.com ---
20O
uF
L=1 mH
R=2.5O
1:b 1:a
--- Content provided by FirstRanker.com ---
(A) a = 0.5, b = 2.0
(B) a = 2.0, b = 0.5
(C) a = 1.0, b = 1.0
(D) a = 4.0, b = 0.5
Q.21 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 T1 depends on its rotational speed ?r (in radian/second), such that T1 = 2.78 × ?r. Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is
--- Content provided by FirstRanker.com ---
Q.22 The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The “air-gap” voltage, Vg across the magnetizing inductance, is 210 V rms, and the slip, s, is 0.05. The torque (in Nm) produced by the motor is
V
0.04 O j0.22 O
j6.28 O
--- Content provided by FirstRanker.com ---
Vo
g
j0.22 O
0.05 O/S
Q.23 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?
--- Content provided by FirstRanker.com ---
(A) 230 and 5
(B) 115 and 5
(C) 115 and 2.5
230 and 2.5
Q.24 An open loop control system results in a response of e-2t (sin 5t + cos 5t) for a unit impulse input. The DC gain of the control system is
--- Content provided by FirstRanker.com ---
Q.25 Nyquist plots of two functions G1(s) and G2(s) are shown in figure.
G1(s)
Im? ?=8
00
G2(s)
--- Content provided by FirstRanker.com ---
Im?
? Re ?= 0 Re
?
0
Nyquist plot of the product of G1(s) and G2(s) is
--- Content provided by FirstRanker.com ---
(A)
(C)
818
Im? Im?
?= 0
--- Content provided by FirstRanker.com ---
Re Im?
(D)
00
Im?
? Re ?
--- Content provided by FirstRanker.com ---
30
Q. 26 – Q. 55 carry two mark each.
Q.26 The volume enclosed by the surface f (x,y) = ex over the triangle bounded by the lines x = y; x = 0; y = 1 in the xy plane is
Q.27 Two coins R and S are tossed. The 4 joint events HRHS, TRTs, HRTS, TRHS have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?
--- Content provided by FirstRanker.com ---
(A) The coin tosses are independent.
(B) R is fair, S is not.
(C) S is fair, R is not.
(D) The coin tosses are dependent.
Q.28 A differential equation di/dt + 0.2i = 0 is applicable over -10 < t < 10. If i(4) = 10, then i(-5) is
--- Content provided by FirstRanker.com ---
Q.29 Consider a signal defined by
x(t) = { ej10t for |t| = 1
{0 for |t| > 1
Its Fourier Transform is
(A) 2 sin (?-10)/(?-10)
--- Content provided by FirstRanker.com ---
(B) 2 ej 10 sin (?-10)/(?-10)
(C) 2 sin ?/(?-10)
(D) ej 10? 2 sin ?
Q.30 The coils of a wattmeter have resistances 0.01 O and 1000 O; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The percentage error on the wattmeter reading is
M Load
--- Content provided by FirstRanker.com ---
Q.31 A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage Vo is 36 V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that will make the inductor current (i1) just continuous is
60 V + 5 mH S IL + 36 V Vo R
Q.32 For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is Ts. If the voltage V1 is as shown, the duty cycle of the switch S is
Vin + VL Vo
--- Content provided by FirstRanker.com ---
15 V
+ VL S R C
Ts
-45 V
Q.33 In the given rectifier, the delay angle of the thyristor T1 measured from the positive going zero crossing of V, is 30°. If the input voltage Vs is 100 sin(100pt) V, the average voltage across R (in Volt) under steady-state is
--- Content provided by FirstRanker.com ---
+ RVO
0
T1 ? S
D2
Q.34 For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE?
--- Content provided by FirstRanker.com ---
(A) The impulse response will be integrable, but may not be absolutely integrable.
(B) The unit impulse response will have finite support.
(C) The unit step response will be absolutely integrable.
(D) The unit step response will be bounded.
Q.35 The z-Transform of a sequence x[n] is given as_X(z) = 2z + 4 – 4/z + 3/z². If y[n] is the first difference of x[n], then Y(z) is given by
--- Content provided by FirstRanker.com ---
(A) 2z+2 -8/z + 7/z2 – 3/z3
(B) -2z + 2 - 6/z + 1/z2 – 3/z3
(C) -2z - 2 + 8/z – 7/z² + 3/z3
(D) 4z-2-8/z – 1/z² + 3/z3
--- Content provided by FirstRanker.com ---
Q.36 Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is Q2 K/4pe0 d2, where K is given by
y
d +Q
d
(A) 0 (B)--
--- Content provided by FirstRanker.com ---
(C)--
X
(D) 1-2v2
1-2v2/8v2 î+ 1-2v2/8v2
Q.37 In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is Q1Q? = 00. The state (Q1Q?), immediately after the 333rd clock pulse is
--- Content provided by FirstRanker.com ---
Qo
Q1
Jo Qo
J1 Q1
Ko Qo
--- Content provided by FirstRanker.com ---
K1 Q1
CLK
(A) 00
(B) 01
(C) 10
--- Content provided by FirstRanker.com ---
(D) 11
Q.38 A Boolean function f (A, B, C, D) = S(1,5,12,15) is to be implemented using an 8 × 1 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S2 S1 So of the multiplexer respectively.
MM
01234567
S2 S1 So
--- Content provided by FirstRanker.com ---
ABC
f(A,B,C,D)
Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?
(A) D, 0, D, 0, 0, 0, D, D
(B) D, 1, D, 1, 1, 1, D, D
--- Content provided by FirstRanker.com ---
(C) D, 1, D, 1, 1, 1, D, D
(D) D, 0, D, 0, 0, 0, D, D
Q.39 The saturation voltage of the ideal op-amp shown below is ±10 V. The output voltage vo of the following circuit in the steady-state is
1 ?O + 10 V
--- Content provided by FirstRanker.com ---
0.25 µF + VO
2 ?O
- 10 V
2 ?O
(A) square wave of period 0.55 ms.
--- Content provided by FirstRanker.com ---
(B) triangular wave of period 0.55 ms.
(C) square wave of period 0.25 ms.
(D) triangular wave of period 0.25 ms.
Q.40 The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers P1 and P2 in MW, and are given by
dC1/dP1 = 0.2P1 + 50
--- Content provided by FirstRanker.com ---
dC2/dP2 = 0.24P2 + 40
where
20 MW = P1 = 150 MW
20 MW = P2 = 150 MW.
For a certain load demand, P1 and P2 have been chosen such that dC1/dP1 = 76 Rs/MWh and dC2/dP2 = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then P2 is
--- Content provided by FirstRanker.com ---
Q.41 A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is
3R
R
60° \60°
--- Content provided by FirstRanker.com ---
Q.42 A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents i1 and i2, if the fault current is 300 A as shown in figure.
a
b i1
C i2 300 A
(A) i1 = 1/v3 A, i2 = 0 A
--- Content provided by FirstRanker.com ---
(B) i1 = 0 A, i2 = 0 A
(C) i1 = 0 A, i2 = 1/v3 A
(D) i1 = 1/v3 A, i2 = 1/v3 A
Q.43 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 = 10?0° A, then what is the value of Ip in Ampere?
Ip
--- Content provided by FirstRanker.com ---
Is
a • A
b
C B
R
--- Content provided by FirstRanker.com ---
R
R
(A) 50 230°
(B) 50 ? 30°
(C) 50 v3 230°
--- Content provided by FirstRanker.com ---
(D) 200 ?30°
Q.44 In the given network V1 = 100?0° V, V2 = 100?-120° V, V3 = 100?+120° V. The phasor current i (in Ampere) is
V1 -j1 V2 j1 V3 i
(A) 173.2/-60° (B) 173.2/120°
(C) 100.0/- 60° (D) 100.0/120°
--- Content provided by FirstRanker.com ---
Q.45 A symmetrical square wave of 50% duty cycle has amplitude of ±15 V and time period of 0.4p ms. This square wave is applied across a series RLC circuit with R = 5 O, L = 10 mH, and C = 4 µF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is
L
C
R
--- Content provided by FirstRanker.com ---
Q.46 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
Q.47 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?
11
N2
12 13
--- Content provided by FirstRanker.com ---
N1
(A) 1 290°
(B) 1 ?270°
(C) 4 <90°
(D) 4 2270°
--- Content provided by FirstRanker.com ---
Q.48 With an armature voltage of 100 V and rated field winding voltage, the speed of a separately excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature resistance is 1 O. The load torque of the fan load is proportional to the square of the rotor speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to 500 rpm is
Q.49 A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 O per phase, and its stator resistance is negligible. The motor has a constant field excitation. AtAt a particular load torque, its stator current is 100 A at unity power factor. If the load torque is increased so that the stator current is 120 A, then the load angle (in degrees) at this load is
Q.50 A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03 O/phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is
Q.51 Two three-phase transformers are realized using single-phase transformers as shown in the figure.
--- Content provided by FirstRanker.com ---
A2
a2
A1
a1
V1
--- Content provided by FirstRanker.com ---
B2
MB1
b2
b1
C2
--- Content provided by FirstRanker.com ---
C2
MM
C1
C1 m
A2
--- Content provided by FirstRanker.com ---
A1
a1
MM
a2
V2
--- Content provided by FirstRanker.com ---
B2
MB1
b1M
b2
C2
--- Content provided by FirstRanker.com ---
C2
C1
C1
MM
The phase difference (in degree) between voltages V1 and V2 is
--- Content provided by FirstRanker.com ---
Q.52 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.
Xk+1-Xk/h = ?
Yk+1 - ?/h = -Xk
For this discrete-time system, which one of the following statements is TRUE?
(A) The system is not stable for h > 0
--- Content provided by FirstRanker.com ---
(B) The system is stable for h > p
(C) The system is stable for 0 <h<p
(D) The system is stable for 0 <h<2p
Q.53 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?
--- Content provided by FirstRanker.com ---
(A) y (B) y
1 1
-2 -2
2 2
0 5 t 0 5 t
--- Content provided by FirstRanker.com ---
(C) y (D) y
1 1
2 2
1 1
0 5 t 0 5 t
--- Content provided by FirstRanker.com ---
-0.75
Q.54 An open loop transfer function G(s) of a system is K/s(s + 1)(s + 2). For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,
(A) -0.42 (B) -1.58
(D) none of the above
Q.55 For the system governed by the set of equations:
--- Content provided by FirstRanker.com ---
dx1/dt = 2 x1 + x2 + u
dx2/dt = 2 x1 + u
y = 3 x1
the transfer function Y(s)/U(s) is given by
(A) 3(s+1)/(s² - 2s + 2) (B) 3(2s+1)/(s² – 2s + 1)
--- Content provided by FirstRanker.com ---
(C) (s+1)/(s² - 2s + 1) (D) 3(2s+1)/(s² – 2s + 2)
END OF THE QUESTION PAPER
--- Content provided by FirstRanker.com ---
This download link is referred from the post: GATE Previous Last 10 Years 2010-2020 Question Papers With Solutions And Answer Keys