GATE-IN Previous Years Solved Paper
Basics of Circuits & Measurement Systems www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems year 2012 one mark Q. 1
Q. 2
The average power delivered to an impedance ^4 − j3h Ω by a current 5 cos ^100pt + 100h A is
(A) 44.2 W
(B) 50 W
(C) 62.5 W
(D) 125 W
In the circuit shown below, the current through the inductor is
(A) 2 A (B) − 1 A 1+j 1+j (C) 1 A (D) 0 A 1+j Q. 3
In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0 . The current i ^ t h for all t is
(A) zero (B) a step function (C) an exponentially decaying function (D) an impulse function
Q. 4
The impedance looking into nodes 1 and 2 in the given circuit is
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems
(A) 50 W (B) 100 W (C) 5 kW (D) 10.1 kW year 2012 two marks Q. 5
If VA − VB = 6 V , then VC - VD is
(A) - 5 V (C) 3 V Q. 6
(B) 2 V (D) 6 V
Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is
(A) 0.8 W (B) 1.4 W (C) 2 W (D) 2.8 W
Common
Data For
Question 7 and 8 :
With 10 V dc connected at port A in the linear nonreciprocal two-part network shown below, the following were observed : (A) 1 W connected at port B draws a current of 3 A. (B) 2.5 W connected at port B draws a current of 2 A.
Q. 7
For the same network with 6 V dc connected at part A, 1 W connected port B
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems draws 7/3 A. If 8 V dc is connected to port A, the pen circuit voltage at port B is (A) 6 V (B) 7 V (C) 8 V (D) 9 V
Q. 8
With 10 V dc connected at port A, the current drawn by 7 W connected at port B is (A) 3/7 A (B) 5/7 A (C) 1 A (D) 9/7 A
Statement For Linked
Answer
Q 9 and 10 :
In the circuit shown, the three voltmeter readings are V1 = 220 V , V2 = 122 V , V3 = 136 V .
Q. 9
Q. 10
The power factor of the load is (A) 0.45 (C) 0.55
(B) 0.50 (D) 0.60
If RL = 5 Ω , the approximate power consumption in the load is (A) 700 W (C) 800 W
(B) 750 W (D) 850 W
year 2011 one mark Q. 11
In the circuit shown below, the switch, initially at position 1 for a long time is changed to position 2 at t = 0 .
The current i through the inductor for t $ 0 is (A) 1 - e-20t A (B) 1 + e−20t A (C) 1 + 2e−20t A (D) 2 - e-20t A
Q. 12
The current I shown in the circuit given below is equal to
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems
(A) 3 A (C) 6 A
(B) 3.67 A (D) 9 A
year 2011 two marks Q. 13
Power in a three phase star connected balanced inductive load is measured by two wattmeter method. The phase voltage and phase current are 230 V and 5 A, respectively. The power factor of the load is 0.707. The readings P1 and P 2 of the two wattmeters are (A) P1 = 298 W and P 2 = 1111 W (B) P1 = 517 W and P 2 = 1924 W (C) P1 = 1220 W and P 2 = 1220 W (D) P1 = 1111 W and P 2 =− 516 W
Common
Data For
Question 14 and 15 :
Consider the circuit shown below.
Q. 14
The current i (t) through the capacitor is (A) sin (5t) A (B) cos (5t) A (C) sin (5t - 45c) A (D) 1 A
Q. 15
The average total power delivered by the two sources is (A) 0 W (B) 0.5 W (C) 2 W (D) 4 W year 2010 one mark
Q. 16
A measurement system with input x (t) and output y (t) is described by the dy differential equation 3 + 5y = 8x . The static sensitivity of the system is dt (A) 0.60 (B) 1.60 (C) 1.67 (D) 2.67
Q. 17
In the dc circuit shown in the adjoining figure, the node voltage V2 at steady state
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems is
(A) 0 V (C) 2 V Q. 18
(B) 1 V (D) 3 V
A 100 W, 1 W resistor and a 800 W, 2 W resistor are connected in series. The maximum dc voltage that can be applied continuously to the series circuit without exceeding the power limit of any of the resistors is (A) 90 V (B) 50 V (C) 45 V (D) 40 V year 2010 two marks
Q. 19
The volume of a cylinder is computed from measurements of its height (h) and diameter (d). A set of several measurements of height has an average value of 0.2 m and a standard deviation of 1%. The average value obtained for the diameter is 0.1 m and the standard deviation is 1%. Assuming the errors in the measurements of height and diameter are un-correlated, the standard deviation of the computed volume is (A) 1.00 % (B) 1.73 % (C) 2.23 % (D) 2.41 %
Statement For Linked
Answer
Q 20 and 21 :
A coil having an inductance (L) of 10 mH and resistance R is connected in series with an ideal 100 µF capacitor (C). When excited by a voltage source of value 10 2 cos (100t) V, the series RLC circuit draws 20 W power. Q. 20
Q. 21
The value of the coil resistance R is (A) 1 W (C) 4 W
(B) 2 W (D) 5 W
The Q factor of the coil at an angular frequency of 1000 rad/s is (A) 1 (B) 2 (C) 4 (D) 5 year 2009 two marks
Q. 22
A quantity x is calculated by using the formula x = (p − q)/r , The measured values are p = 9, q = 6, r = 0.5 . Assume that the measurement errors in p, q and r are independent. The absolute maximum error in the measurement of each of the three quantities is e. The absolute maximum error in the calculated value of x is (A) e (B) 2e
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems (C) 3e (D) 16e Q. 23
The response of a first order measurement system to a unit step input is 1 - e- 0.5t , where t is in seconds. A ramp of 0.1 units per second is given as the input to this system. The error in the measured value after transients have died down is (A) 0.02 units (B) 0.1 units (C) 0.2 units (D) 1 unit
Q. 24
The source network S is connected to the load network L as shown by dashed lines. The power transferred form S to L would be maximum when RL is
(A) 0 W (C) 0.8 W Q. 25
(B) 0.6 W (D) 2 W
The root mean squared value of x (t) = 3 + 2 sin (t) cos (2t) (A)
3 (B)
8
(C)
10 (D)
11
year 2008 one mark Q. 26
The power supplied by the dc voltage source in the circuit shown below is
(A) 0 W (C) 2.5 W Q. 27
(B) 1.0 W (D) 3.0 W
The current I supplied by the dc voltage source in the circuit shown below is
(A) 0 A (C) 1 A
www.gatescore.in
(B) 0.5 A (D) 2 A
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems year 2008 two marks Q. 28
In the circuit shown below the maximum power that can be transferred to the load ZL is
(A) 250 W (C) 1000 W Q. 29
For the circuit shown below the input resistance R11 = V1 I1
(A) - 3 W (C) 3 W Q. 30
is I2 = 0
(B) 2 W (D) 13 W
In the circuit shown below the average power consumed by the 1 W resistor is
(A) 50 W (C) 5000 W
Q. 31
(B) 500 W (D) 2000 W
(B) 1050 W (D) 10100 W
Which one of the following equations is valid for the circuit shown below ?
(A) I 3 + I5 − I6 + I7 = 0 (B) I 3 − I5 + I6 + I7 = 0 (C) I 3 + I5 + I6 + I7 = 0 (D) I 3 + I5 + I6 − I7 = 0
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems Q. 32
Q. 33
For the circuit shown below the steady-state current I is
(A) 0 A
(B) 5 2 cos (1000t) A
(C) 5 2 cos a1000t − π k A 4
(D) 5 2 A
(A) (10 + j0) V (C) (0 + j100) V
(B) (100 + j0) V (D) (0 - j100) V
For the circuit shown below the voltage across the capacitor is
Statement For Linked
Answer
Q 34 and 35 :
In the circuit shown below the steady-state is reached with the switch K open. Subsequently the switch is closed at time t = 0
Q. 34
Q. 35
At time t = 0+ , current I is (A) - 5 A 3 5 (C) A 3 At time t = 0+ , dI2 is dt (A) - 5 A/s (C) 0 A/s
(B) 0 A (D) 3
(B) (D)
- 10 A/s 3 5 A/s
year 2007 one mark Q. 36
In full sunlight, a solar cell has a short circuit current of 75 mA and a current of 70 mA for a terminal voltage of 0.6 with a given load. The Thevenin resistance of the solar cell is (A) 8W (B) 8.6 W (C) 120 W (D) 240 W
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems
Q. 37
The DC voltage gain V0 in the following circuit is given by Vi
R1 R2 (B) A v R1 + R 2 R1 + R 2 (C) Av R2 + R 0 (D) Av R1 + R 2
(A) Av
year 2007 two marks Q. 38
In the circuit shown in the following figure, the current through the 1W resistor is
(A) (1 + 5 cos 2t) A (B) (5 + cos 2t) A (C) (1 - 5 cos 2t) A (D) 6A Q. 39
In the circuit shown in the following figure, the switch is kept closed for a long time and then opened at t = 0 .
The values of the current i just before opening the switch (t = 0−) and just after the opening the switch (t = 0+) are, respectively (A) 3 A and 1A (B) 3 A and 5 A 4 4 4 7 (C) 1A and A (D) 1A and 1A 6 Q. 40
Consider the coupled circuit shown below.
At angular frequency w, this circuit can be represented by the equivalent T-network, shown below.
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems
Indicate the correct set of expressions for the impedances of the T-network. (A) Z1 = jω (L1 − M12) (B) Z1 = jω (L1 + M12) Z2 = jω (L2 − M12) Z2 = j ω (L2 + M12) Z 3 = jωM12 Z 3 = jωM12 (C) Z1 = jωL1 (D) Z1 = jω (L1 − M12) Z2 = jωL2 Z2 = jω (L2 − M12) Z 3 =− jωM12 Z 3 = jω (L1 + L2 + M12) Q. 41
In the circuit shown in the figure, the input signal is vi (t) = 5 + 3 cos ωt
The steady state output is expressed as v 0 (t) = P + Q cos (ωt − φ) . If ωCR = 2 , the values of P and Q are (A) P = 0 and Q = 6/ 5 (B) P = 0 and Q = 3/ 5 (C) P = 5 and Q = 6/ 5 (D) P = 5 and Q = 3 year 2006 one mark Q. 42
The root-mean-square value of a voltage waveform consisting of a superimposition of 2 V dc and a 4V peak-to-peak square wave is (A) 2 V (B) 6 V (C)
8 V
(D)
14 V
year 2006 two marks Q. 43
In the circuit shown in the following figure, the input voltage vi (t) is constant at 2V for time >> 1s and then it changes to 1 V. The output voltage, v 0 (t), 2s after the change will be
(A) - exp (- 2) V (B) − 1 + exp (− 2) V (C) exp (- 2) V (D) 1 - exp (- 2) V
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems Q. 44
A metal wire has a uniform cross-section A, length l , and resistance R between its two end points. It is uniformly stretched so that its length becomes a l . The new resistance is (A) aR (B) a2 R (C)
a R (D) ea R
year 2005 one mark Q. 45
A mass of 10 kg is measured with an instrument and the readings are normally distributed with respect to the mean of 10 kg. Given that 2 # exp (− η2 /2) dη = 0.6 and that 60 per cent of the readings 2π are found to be within 0.05 kg from the mean, the standard deviation of the data is (A) 0.02 (B) 0.04 (C) 0.06 (D) 0.08
Q. 46
The measurements of a source voltage are 5.9 V, 5.7 V and 6.1 V. The sample standard deviation of the readings is (A) 0.013 (B) 0.04 (C) 0.115 (D) 0.2 year 2005 two marks
Q. 47
Q. 48
Q. 49
Position sensor units having a constant sensitivity of 1V/ mm are used for feedback in number of position controlled system units, each having an overall forward path dc gain of 50. If the random dc bias errors in the outputs of various sensor units are characterized as normal with mean 0 and standard deviation (s) 0.01 V, for a constant set point of 5V, the true position outputs of the various controlled system units can be characterized as normal with. (A) mean of 5.0 s of 0.01 (B) mean of 0.0, s of 0.01 (C) mean of 5.0, s of 0.0098 (D) mean of 4.902, s of 0.0098 A surface height profile is given by, y = a + b sin 2πx (0 # x # 1) where a, b, l are l constants and x is the horizontal coordinate. The roughness of the surface, based an absolute deviation, is (A) 2b (B) 4b p p (C) 6b (D) 8b p p In the circuit shown in the figure, the switch S is closed at time t = 0 .The supply current at t = 0+ and the capacitor voltage at t " 3 are, respectively
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems (B) V and VR 2 R1 R1 + R 2 V and VR 2 (D) V andV (C) R1 R1 + R 2 R1 + R 2 (A) 0 and V
year 2004 two marks Q. 50
The calibration data for a pressure compensator of a pump is given below Input x
0
1
2
3
4
5
6
7
8
9
10
Output y 9.5 8.4 7.8 7.4 6.1 5.4 5.2 4.6 3.2 1.9 1.1 For the given data, the slope of the best-fit line applying least square method is (A) 0.921 (B) - 0.803 (C) 0.819 (D) - 0.945 year 2003 one mark Q. 51
A large number of 230 W resistors are obtained by combining 120 W resistors with a standard deviation of 4.0 W and 110 W resistors with a standard deviation of 3.0 W. The standard deviation of the 230 W resistors thus formed will be (A) 3.5 W (B) 5.0 W (C) 7.0 W (D) 12.0 W year 2003 two marks
Q. 52
The primary of a 200/1 A, 5 VA, 0.8 PF current transformer (CT) carries 100 A. The ratio error of the CT is (A) - 1.0% (B) - 0.5% (C) + 0.5% (D) + 1.0% Year 2001
Q. 53
One Mark
In the circuit shown in figure, current through the 5 Ω resistor is
(A) zero (B) 2 A (C) 3 A (D) 7 A Q. 54
Two identical 2-port networks with Y -parameters Y11 =− Y12 =− Y21 = Y22 1 S are connected in cascade. The overall Y -parameters will satisfy the condition (A) Y11 = 1 S (B) Y12 =− 1 S 2 (C) Y21 =− 2 S (D) Y22 = 1 S
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - IN BasicsofCircuits&Measurementsystems Year 2000 Q. 55
One Mark
For the circuit shown in figure VR = 20 V when R = 10 Ω and VR = 30 V when R = 20 Ω . For R = 80 Ω , VR will read as
(A) 48 V (B) 60 V (C) 120 V (D) 160 V Q. 56
For the circuit shown in figure R is adjusted to have maximum power transferred to it. The maximum power transferred is
(A) 16 W (b) 32 W (C) 64 W (D) 100 W Q. 57
The value of the impedance Zd ^S h between 1.1 of the circuit shown in figure as s " 3 is
(A) zero (C) 5/4
(B) 1 (D) 5
Year 2000 Q. 58
Two Marks
Superposition theorem does not hold for (A) RLC networks (B) networks containing diodes and RC elements (C) linear op-amp circuits (D) LC networks
**********
www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - in BasicsofCircuits&Measurementsystems ANSWER KEY Basics of Circuits & Measurement systems 1
2
3
4
5
6
7
8
9
10
(B)
(C)
(D)
(A)
(A)
(A)
(B)
(C)
(A)
(B)
11
12
13
14
15
16
17
18
19
20
(D)
(A)
(B)
(A)
(C)
(B)
(B)
(C)
(C)
(D)
21
22
23
24
25
26
27
28
29
30
(B)
(C)
(C)
(D)
(D)
(D)
(A)
(B)
(D)
(B)
31
32
33
34
35
36
37
38
39
40
(D)
(A)
(D)
(A)
(B)
(A)
(A)
(A)
(C)
(A)
41
42
43
44
45
46
47
48
49
50
(A)
(C)
(B)
(B)
(C)
(D)
(C)
(A)
(B)
(B)
51
52
53
54
55
56
57
58
(B)
(A)
(B)
(B)
(A)
(C)
(B)
(B)
www.gatescore.in
