GATE EE 2013: Electrical Engineering
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SESSION - 1
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2013 Question Booklet Code
A
EE : ELECTRICAL ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EE,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right half hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the
appropriate bubble under each digit of your registration number and (ii) write your registration number,
your name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EE
EE-A 1/20
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2013 ELECTRICAL ENGINEERING - EE
Q.1 to Q.25 carry one mark each.
Q.1 In the circuit shown below what is the output voltage (Vout) in Volts if a silicon transistor Q and an
ideal op-amp are used?
(A) 15 (B) 0.7 (C) 0.7 (D) 15
Q.2 V2 ( s )
The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.3 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
(D) e −t u (t )
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
Q.4 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1) (t − 1) 2 t2 −1
(A) t u (t ) (B) u (t − 1) (C) u (t − 1) (D) u (t − 1)
2 2 2 2
EE-A 2/20
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2013 ELECTRICAL ENGINEERING - EE
Q.5 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1.
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
Q.6 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
Q.7 A source vs (t ) = V cos100π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should
be
(A) 3 (B) 4 (C) 5 (D) 7
Q.8 A single-phase load is supplied by a single-phase voltage source. If the current flowing from the
load to the source is 10∠ − 1500 A and if the voltage at the load terminals is 100∠600 V, then the
(A) load absorbs real power and delivers reactive power.
(B) load absorbs real power and absorbs reactive power.
(C) load delivers real power and delivers reactive power.
(D) load delivers real power and absorbs reactive power.
Q.9 A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a
short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV
windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at
(A) 50.0% of the rated current.
(B) 64.0% of the rated current.
(C) 80.0% of the rated current.
(D) 88.8% of the rated current.
Q.10 The flux density at a point in space is given by B = 4 x a x + 2ky a y + 8 a z Wb/m2. The value of
constant k must be equal to
(A) –2 (B) –0.5 (C) +0.5 (D) +2
Q.11 A continuous random variable X has a probability density function f ( x) = e − x , 0 < x < ∞ . Then
P { X > 1} is
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
EE-A 3/20
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2013 ELECTRICAL ENGINEERING - EE
Q.12 The curl of the gradient of the scalar field defined by V = 2 x 2 y + 3 y 2 z + 4 z 2 x is
(A) 4 xy a x + 6 yz a y + 8 zx a z
(B) 4 a x + 6 a y + 8 a z
( ) ( ) (
(C) 4 xy + 4 z 2 a x + 2 x 2 + 6 yz a y + 3 y 2 + 8 zx a z )
(D) 0
Q.13 In the feedback network shown below, if the feedback factor k is increased, then the
+ v + + vout
in v1 A0 –
– –
vf = kvout+ k +
– –
(A) input impedance increases and output impedance decreases.
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
Q.14 The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite.
Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
EE-A 4/20
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2013 ELECTRICAL ENGINEERING - EE
Q.15 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s ) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s2 s s2
Q.16 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Q.17 For a periodic signal v(t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental
frequency in rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
Q.18 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency in kHz which is not valid is
(A) 5 (B) 12 (C) 15 (D) 20
Q.19 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
EE-A 5/20
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2013 ELECTRICAL ENGINEERING - EE
Q.20 The angle δ in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current.
(B) angular displacement of the rotor with respect to the stator.
(C) angular displacement of the stator mmf with respect to a synchronously rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.
Q.21 Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
Q.22 Three moving iron type voltmeters are connected as shown below. Voltmeter readings are
V , V1 and V2 , as indicated. The correct relation among the voltmeter readings is
V1 V2
(A) V = + (B) V = V1 + V2 (C) V = VV
1 2 (D) V = V2 − V1
2 2
Q.23 Square roots of −i , where i = −1 , are
(A) i, –i
π π 3π 3π
(B) cos( − ) + i sin( − ), cos( ) + i sin( )
4 4 4 4
π 3π 3π π
(C) cos( ) + i sin( ), cos( ) + i sin( )
4 4 4 4
3π 3π 3π 3π
(D) cos( ) + i sin( − ), cos( − ) + i sin( )
4 4 4 4
Given a vector field F = y x a x − yz a y − x a z , the line integral ∫ F ⋅ d l evaluated along a segment
2 2
Q.24
on the x-axis from x = 1 to x = 2 is
(A) –2.33 (B) 0 (C) 2.33 (D) 7
Q.25 2 − 2 x1 0
The equation = has
1 − 1 x2 0
(A) no solution
x 0
(B) only one solution 1 =
x2 0
(C) non-zero unique solution
(D) multiple solutions
EE-A 6/20
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Q.26 to Q.55 carry two marks each.
Q.26 A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance
without any load as Rs = 300 Ω. Other bridge resistances are R1 = R2 = R3 = 300 Ω. The maximum
permissible current through the strain gauge is 20 mA. During certain measurement when the
bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by
1% over the nominal value, the output voltage V0 in mV is
Rs R1
V0
+ ‐ +
Vi ‐
R3 R2
(A) 56.02 (B) 40.83 (C) 29.85 (D) 10.02
Q.27 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW
respectively are
(A) 125 and 125 (B) 125 and 250 (C) 250 and 125 (D) 250 and 250
ω (s) 10
Q.28 The open-loop transfer function of a dc motor is given as = . When connected in
Va ( s) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
R(s) Va(s) 10 ω(s)
+_ Ka
1+10s
(A) 1 (B) 5 (C) 10 (D) 100
EE-A 7/20
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2013 ELECTRICAL ENGINEERING - EE
Q.29 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
Q.30 Three capacitors C1, C2, and C3, whose values are 10µF, 5µF, and 2µF respectively, have
breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum
safe voltage in Volts that can be applied across the combination and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
Q.31 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
EE-A 8/20
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2013 ELECTRICAL ENGINEERING - EE
Q.32 The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated
armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature
voltage. If La= 0.1 mH, Ra= 1 Ω, neglecting armature reaction, the duty ratio of the chopper to
obtain 50% of the rated torque at the rated speed and the rated field current is
200 V La ,Ra
(A) 0.4 (B) 0.5 (C) 0.6 (D) 0.7
Q.33 For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The
voltage at node 3 is 1.3 ∠–10° per unit. If a capacitor having reactance of –j3.5 per unit is now
added to the network between node 3 and the reference node, the current drawn by the capacitor per
unit is
(A) 0.325 ∠–100° (B) 0.325 ∠80° (C) 0.371 ∠–100° (D) 0.433 ∠80°
Q.34 A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform
electric field of E = 6 a x + 8 a y kV/mm. The relative permittivity of the dielectric material is equal to
2. The value of constant ε 0 is 8.85 × 10−12 F/m. The energy stored in the dielectric in Joules is
(A) 8.85 × 10–11 (B) 8.85 × 10–5 (C) 88.5 (D) 885
1 1
Q.35 A matrix has eigenvalues –1 and –2. The corresponding eigenvectors are and
−1 − 2
respectively. The matrix is
1 1 1 2 − 1 0 0 1
(A) (B) (C) (D)
− 1 − 2 − 2 − 4 0 − 2 − 2 − 3
z2 − 4
Q.36
∫ z 2 + 4 dz evaluated anticlockwise around the circle z − i = 2 , where i = −1 , is
(A) −4π (B) 0 (C) 2 + π (D) 2 + 2i
EE-A 9/20
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2013 ELECTRICAL ENGINEERING - EE
Q.37 The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial
state of the output Q of the flip-flop is ‘0’, then the frequency of the output waveform Q in kHz is
(A) 0.25 (B) 0.5 (C) 1 (D) 2
Q.38 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Q.39 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
EE-A 10/20
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2013 ELECTRICAL ENGINEERING - EE
Y (s)
Q.40 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s + 4s + 2
2
5s + 6s + 2
2
Q.41 The impulse response of a continuous time system is given by h(t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Q.42 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 R1 + q2 R2 (B) q1 / R1 + q2 / R2
(C) (q1R1 + q2 R2 ) / ( R1 + R2 ) (D) q1R2 + q2 R1
Q.43 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
EE-A 11/20
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2013 ELECTRICAL ENGINEERING - EE
Q.44 Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10 µs. It
is given that L = (100π
) µ H and C = (100π )µ F. Assuming latching and holding currents of the
thyristor are both zero and the initial charge on C is zero, T conducts for
+ L
T
15 V C
‐
(A) 10 µs (B) 50 µs (C) 100 µs (D) 200 µs
Q.45 A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50 Hz source, is rotating at
1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is
(A) 100 (B) 98 (C) 52 (D) 48
Q.46 A function y = 5 x 2 + 10 x is defined over an open interval x = (1, 2) . At least at one point in this
dy
interval, is exactly
dx
(A) 20 (B) 25 (C) 30 (D) 35
When the Newton-Raphson method is applied to solve the equation f ( x ) = x + 2 x − 1 = 0, the
3
Q.47
solution at the end of the first iteration with the initial guess value as x0 = 1.2 is
(A) –0.82 (B) 0.49 (C) 0.705 (D) 1.69
Common Data Questions
Common Data for Questions 48 and 49:
In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is
switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.
100 µH
12 V 470 µF
Q 20 Ω
Q.48 The average source current in Amps in steady-state is
(A) 3/2 (B) 5/3 (C) 5/2 (D) 15/4
Q.49 The PEAK-TO-PEAK source current ripple in Amps is
(A) 0.96 (B) 0.144 (C) 0.192 (D) 0.288
EE-A 12/20
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2013 ELECTRICAL ENGINEERING - EE
Common Data for Questions 50 and 51:
The state variable formulation of a system is given as
x&1 − 2 0 x1 1 x1
x& = 0 − 1 x + 1 u , x1 (0) = 0, x 2 (0) = 0 and y = [1 0] x
2 2 2
Q.50 The system is
(A) controllable but not observable
(B) not controllable but observable
(C) both controllable and observable
(D) both not controllable and not observable
Q.51 The response y (t ) to a unit step input is
1 1 −2 t 1 −2 t 1 − t
(A) − e (B) 1 − e − e
2 2 2 2
(C) e −2 t − e − t (D) 1 − e − t
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles
are very small, and the line resistances are negligible. All the line reactances are equal to j1 Ω.
Bus 1(slack) j1 Ω Bus 2
P2=0.1 pu
j1 Ω j1 Ω
Bus 3
P3=0.2 pu
Q.52 The voltage phase angles in rad at buses 2 and 3 are
(A) θ 2 = −0.1, θ3 = −0.2
(B) θ 2 = 0, θ3 = −0.1
(C) θ 2 = 0.1, θ3 = 0.1
(D) θ 2 = 0.1, θ3 = 0.2
Q.53 If the base impedance and the line-to-line base voltage are 100 Ω and 100 kV, respectively, then the
real power in MW delivered by the generator connected at the slack bus is
(A) −10 (B) 0 (C) 10 (D) 20
EE-A 13/20
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Statement for Linked Answer Questions 54 and 55:
The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave
ac output voltage (vo) across an R-L load. Reference polarity of vo and reference direction of the output
current io are indicated in the figure. It is given that R = 3 Ω , L = 9.55 mH .
Q1 Q3
D1 D3 L
V dc + vo io R
Q4 Q2 ‐
D4 D2
Q.54 In the interval when v 0 < 0 and i0 > 0 the pair of devices which conducts the load current is
(A) Q1, Q2 (B) Q3, Q4 (C) D1, D2 (D) D3, D4
Q.55 Appropriate transition i.e., Zero Voltage Switching (ZVS)/Zero Current Switching (ZCS) of the
IGBTs during turn-on/turn-off is
(A) ZVS during turn-off (B) ZVS during turn-on
(C) ZCS during turn-off (D) ZCS during turn-on
EE-A 14/20
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2013 ELECTRICAL ENGINEERING - EE
General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.57 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.58 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.59 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.60 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.61 to Q.65 carry two marks each.
Q.61 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.62 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
Q.63 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
EE-A 15/20
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2013 ELECTRICAL ENGINEERING - EE
Q.64 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
Q.65 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1)+1
8
(C)
(
9 9n −1 )+n
8
(D)
(
9 9n − 1 )
+ n2
8
END OF THE QUESTION PAPER
EE-A 16/20
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SESSION - 2
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2013 Question Booklet Code
B
EE : ELECTRICAL ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EE,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right half hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the
appropriate bubble under each digit of your registration number and (ii) write your registration number,
your name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EE
EE-B 1/20
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2013 ELECTRICAL ENGINEERING - EE
Q.1 to Q.25 carry one mark each.
Q.1 The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite.
Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
Q.2 In the feedback network shown below, if the feedback factor k is increased, then the
+ v + + vout
in v1 A0 –
– –
vf = kvout+ k +
– –
(A) input impedance increases and output impedance decreases.
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
EE-B 2/20
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Q.3 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s ) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s2 s s2
Q.4 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Q.5 For a periodic signal v(t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental
frequency in rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
Q.6 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency in kHz which is not valid is
(A) 5 (B) 12 (C) 15 (D) 20
Q.7 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
EE-B 3/20
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2013 ELECTRICAL ENGINEERING - EE
Q.8 The angle δ in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current.
(B) angular displacement of the rotor with respect to the stator.
(C) angular displacement of the stator mmf with respect to a synchronously rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.
Q.9 Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
Q.10 Three moving iron type voltmeters are connected as shown below. Voltmeter readings are
V , V1 and V2 , as indicated. The correct relation among the voltmeter readings is
V1 V2
(A) V = + (B) V = V1 + V2 (C) V = VV
1 2 (D) V = V2 − V1
2 2
Q.11 Square roots of −i , where i = −1 , are
(A) i, –i
π π 3π 3π
(B) cos( − ) + i sin( − ), cos( ) + i sin( )
4 4 4 4
π 3π 3π π
(C) cos( ) + i sin( ), cos( ) + i sin( )
4 4 4 4
3π 3π 3π 3π
(D) cos( ) + i sin( − ), cos( − ) + i sin( )
4 4 4 4
Q.12 2 − 2 x1 0
The equation = has
1 − 1 x2 0
(A) no solution
x 0
(B) only one solution 1 =
x2 0
(C) non-zero unique solution
(D) multiple solutions
Given a vector field F = y x a x − yz a y − x a z , the line integral ∫ F ⋅ d l evaluated along a segment
2 2
Q.13
on the x-axis from x = 1 to x = 2 is
(A) –2.33 (B) 0 (C) 2.33 (D) 7
EE-B 4/20
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2013 ELECTRICAL ENGINEERING - EE
Q.14 In the circuit shown below what is the output voltage (Vout) in Volts if a silicon transistor Q and an
ideal op-amp are used?
(A) 15 (B) 0.7 (C) 0.7 (D) 15
Q.15 V2 ( s )
The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.16 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
(D) e −t u (t )
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
Q.17 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1) (t − 1) 2 t2 −1
(A) t u (t ) (B) u (t − 1) (C) u (t − 1) (D) u (t − 1)
2 2 2 2
EE-B 5/20
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2013 ELECTRICAL ENGINEERING - EE
Q.18 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1.
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
Q.19 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
Q.20 A source vs (t ) = V cos100π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should
be
(A) 3 (B) 4 (C) 5 (D) 7
Q.21 A single-phase load is supplied by a single-phase voltage source. If the current flowing from the
load to the source is 10∠ − 1500 A and if the voltage at the load terminals is 100∠600 V, then the
(A) load absorbs real power and delivers reactive power.
(B) load absorbs real power and absorbs reactive power.
(C) load delivers real power and delivers reactive power.
(D) load delivers real power and absorbs reactive power.
Q.22 A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a
short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV
windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at
(A) 50.0% of the rated current.
(B) 64.0% of the rated current.
(C) 80.0% of the rated current.
(D) 88.8% of the rated current.
Q.23 The flux density at a point in space is given by B = 4 x a x + 2ky a y + 8 a z Wb/m2. The value of
constant k must be equal to
(A) –2 (B) –0.5 (C) +0.5 (D) +2
Q.24 A continuous random variable X has a probability density function f ( x) = e − x , 0 < x < ∞ . Then
P { X > 1} is
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
Q.25 The curl of the gradient of the scalar field defined by V = 2 x y + 3 y z + 4 z 2 x is
2 2
(A) 4 xy a x + 6 yz a y + 8 zx a z
(B) 4 a x + 6 a y + 8 a z
( ) ( ) ( )
(C) 4 xy + 4 z 2 a x + 2 x 2 + 6 yz a y + 3 y 2 + 8 zx a z
(D) 0
EE-B 6/20
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2013 ELECTRICAL ENGINEERING - EE
Q.26 to Q.55 carry two marks each.
Q.26 The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial
state of the output Q of the flip-flop is ‘0’, then the frequency of the output waveform Q in kHz is
(A) 0.25 (B) 0.5 (C) 1 (D) 2
Q.27 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Q.28 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
EE-B 7/20
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2013 ELECTRICAL ENGINEERING - EE
Y (s)
Q.29 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s + 4s + 2
2
5s + 6s + 2
2
Q.30 The impulse response of a continuous time system is given by h(t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 R1 + q2 R2 (B) q1 / R1 + q2 / R2
(C) (q1R1 + q2 R2 ) / ( R1 + R2 ) (D) q1R2 + q2 R1
Q.32 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
EE-B 8/20
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2013 ELECTRICAL ENGINEERING - EE
Q.33 Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10 µs. It
is given that L = (100π
) µ H and C = (100π )µ F. Assuming latching and holding currents of the
thyristor are both zero and the initial charge on C is zero, T conducts for
+ L
T
15 V C
‐
(A) 10 µs (B) 50 µs (C) 100 µs (D) 200 µs
Q.34 A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50 Hz source, is rotating at
1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is
(A) 100 (B) 98 (C) 52 (D) 48
Q.35 A function y = 5 x 2 + 10 x is defined over an open interval x = (1, 2) . At least at one point in this
dy
interval, is exactly
dx
(A) 20 (B) 25 (C) 30 (D) 35
When the Newton-Raphson method is applied to solve the equation f ( x ) = x + 2 x − 1 = 0, the
3
Q.36
solution at the end of the first iteration with the initial guess value as x0 = 1.2 is
(A) –0.82 (B) 0.49 (C) 0.705 (D) 1.69
Q.37 A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance
without any load as Rs = 300 Ω. Other bridge resistances are R1 = R2 = R3 = 300 Ω. The maximum
permissible current through the strain gauge is 20 mA. During certain measurement when the
bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by
1% over the nominal value, the output voltage V0 in mV is
Rs R1
V0
+ ‐ +
Vi ‐
R3 R2
(A) 56.02 (B) 40.83 (C) 29.85 (D) 10.02
EE-B 9/20
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2013 ELECTRICAL ENGINEERING - EE
Q.38 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW
respectively are
(A) 125 and 125 (B) 125 and 250 (C) 250 and 125 (D) 250 and 250
ω (s) 10
Q.39 The open-loop transfer function of a dc motor is given as = . When connected in
V a ( s ) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
R(s) Va(s) 10 ω(s)
+_ Ka
1+10s
(A) 1 (B) 5 (C) 10 (D) 100
Q.40 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
EE-B 10/20
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2013 ELECTRICAL ENGINEERING - EE
Q.41 Three capacitors C1, C2, and C3, whose values are 10µF, 5µF, and 2µF respectively, have
breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum
safe voltage in Volts that can be applied across the combination and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
Q.42 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.43 The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated
armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature
voltage. If La= 0.1 mH, Ra= 1 Ω, neglecting armature reaction, the duty ratio of the chopper to
obtain 50% of the rated torque at the rated speed and the rated field current is
200 V La ,Ra
(A) 0.4 (B) 0.5 (C) 0.6 (D) 0.7
Q.44 For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The
voltage at node 3 is 1.3 ∠–10° per unit. If a capacitor having reactance of –j3.5 per unit is now
added to the network between node 3 and the reference node, the current drawn by the capacitor per
unit is
(A) 0.325 ∠–100° (B) 0.325 ∠80° (C) 0.371 ∠–100° (D) 0.433 ∠80°
EE-B 11/20
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2013 ELECTRICAL ENGINEERING - EE
Q.45 A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform
electric field of E = 6 a x + 8 a y kV/mm. The relative permittivity of the dielectric material is equal to
2. The value of constant ε 0 is 8.85 × 10 −12 F/m. The energy stored in the dielectric in Joules is
(A) 8.85 × 10–11 (B) 8.85 × 10–5 (C) 88.5 (D) 885
1 1
Q.46 A matrix has eigenvalues –1 and –2. The corresponding eigenvectors are and
−1
− 2
respectively. The matrix is
1 1 1 2 − 1 0 0 1
(A) (B) (C) (D)
− 1 − 2 − 2 − 4 0 − 2 − 2 − 3
z2 − 4
Q.47
∫ z 2 + 4 dz evaluated anticlockwise around the circle z − i = 2 , where i = −1 , is
(A) −4π (B) 0 (C) 2 + π (D) 2 + 2i
Common Data Questions
Common Data for Questions 48 and 49:
The state variable formulation of a system is given as
x&1 − 2 0 x1 1 x1
x& = 0 − 1 x + 1 u , x1 (0) = 0, x 2 (0) = 0 and y = [1 0] x
2 2 2
Q.48 The system is
(A) controllable but not observable
(B) not controllable but observable
(C) both controllable and observable
(D) both not controllable and not observable
Q.49 The response y (t ) to a unit step input is
1 1 −2 t 1 −2 t 1 − t
(A) − e (B) 1 − e − e
2 2 2 2
(C) e −2 t − e − t (D) 1 − e − t
EE-B 12/20
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Common Data for Questions 50 and 51:
In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is
switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.
100 µH
12 V 470 µF
Q 20 Ω
Q.50 The average source current in Amps in steady-state is
(A) 3/2 (B) 5/3 (C) 5/2 (D) 15/4
Q.51 The PEAK-TO-PEAK source current ripple in Amps is
(A) 0.96 (B) 0.144 (C) 0.192 (D) 0.288
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave
ac output voltage (vo) across an R-L load. Reference polarity of vo and reference direction of the output
current io are indicated in the figure. It is given that R = 3 Ω , L = 9.55 mH .
Q1 Q3
D1 D3 L
Vdc + vo io R
Q4 Q2 ‐
D4 D2
Q.52 In the interval when v 0 < 0 and i0 > 0 the pair of devices which conducts the load current is
(A) Q1, Q2 (B) Q3, Q4 (C) D1, D2 (D) D3, D4
Q.53 Appropriate transition i.e., Zero Voltage Switching (ZVS)/Zero Current Switching (ZCS) of the
IGBTs during turn-on/turn-off is
(A) ZVS during turn-off (B) ZVS during turn-on
(C) ZCS during turn-off (D) ZCS during turn-on
EE-B 13/20
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Statement for Linked Answer Questions 54 and 55:
In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles
are very small, and the line resistances are negligible. All the line reactances are equal to j1 Ω.
Bus 1(slack) j1 Ω Bus 2
P2=0.1 pu
j1 Ω j1 Ω
Bus 3
P3=0.2 pu
Q.54 The voltage phase angles in rad at buses 2 and 3 are
(A) θ 2 = −0.1, θ3 = −0.2
(B) θ 2 = 0, θ3 = −0.1
(C) θ 2 = 0.1, θ3 = 0.1
(D) θ 2 = 0.1, θ3 = 0.2
Q.55 If the base impedance and the line-to-line base voltage are 100 Ω and 100 kV, respectively, then the
real power in MW delivered by the generator connected at the slack bus is
(A) −10 (B) 0 (C) 10 (D) 20
EE-B 14/20
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.57 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.58 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.59 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.60 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.61 to Q.65 carry two marks each.
Q.61 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.62 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.63 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
EE-B 15/20
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Q.64 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
Q.65 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
END OF THE QUESTION PAPER
EE-B 16/20
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SESSION - 3
Text of page 36
2013 Question Booklet Code
C
EE : ELECTRICAL ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EE,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right half hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the
appropriate bubble under each digit of your registration number and (ii) write your registration number,
your name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EE
EE-C 1/20
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2013 ELECTRICAL ENGINEERING - EE
Q.1 to Q.25 carry one mark each.
Q.1 The curl of the gradient of the scalar field defined by V = 2 x 2 y + 3 y 2 z + 4 z 2 x is
(A) 4 xy a x + 6 yz a y + 8 zx a z
(B) 4 a x + 6 a y + 8 a z
( ) ( ) ( )
(C) 4 xy + 4 z 2 a x + 2 x 2 + 6 yz a y + 3 y 2 + 8 zx a z
(D) 0
Q.2 A continuous random variable X has a probability density function f ( x) = e − x , 0 < x < ∞ . Then
P { X > 1} is
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
Q.3 The flux density at a point in space is given by B = 4 x a x + 2ky a y + 8 a z Wb/m2. The value of
constant k must be equal to
(A) –2 (B) –0.5 (C) +0.5 (D) +2
Q.4 A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a
short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV
windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at
(A) 50.0% of the rated current.
(B) 64.0% of the rated current.
(C) 80.0% of the rated current.
(D) 88.8% of the rated current.
Q.5 A single-phase load is supplied by a single-phase voltage source. If the current flowing from the
load to the source is 10∠ − 1500 A and if the voltage at the load terminals is 100∠600 V, then the
(A) load absorbs real power and delivers reactive power.
(B) load absorbs real power and absorbs reactive power.
(C) load delivers real power and delivers reactive power.
(D) load delivers real power and absorbs reactive power.
Q.6 A source vs (t ) = V cos100π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should
be
(A) 3 (B) 4 (C) 5 (D) 7
Q.7 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
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Q.8 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1.
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
Q.9 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1) (t − 1) 2 t2 −1
(A) t u (t ) (B) u (t − 1) (C) u (t − 1) (D) u (t − 1)
2 2 2 2
Q.10 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
(D) e −t u (t )
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
Q.11 V2 ( s )
The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
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Q.12 In the circuit shown below what is the output voltage (Vout) in Volts if a silicon transistor Q and an
ideal op-amp are used?
(A) 15 (B) 0.7 (C) 0.7 (D) 15
Q.13 2 − 2 x1 0
The equation = has
1 − 1 x2 0
(A) no solution
x 0
(B) only one solution 1 =
x2 0
(C) non-zero unique solution
(D) multiple solutions
Given a vector field F = y x a x − yz a y − x a z , the line integral ∫ F ⋅ d l evaluated along a segment
2 2
Q.14
on the x-axis from x = 1 to x = 2 is
(A) –2.33 (B) 0 (C) 2.33 (D) 7
Q.15 Square roots of −i , where i = −1 , are
(A) i, –i
π π 3π 3π
(B) cos( − ) + i sin( − ), cos( ) + i sin( )
4 4 4 4
π 3π 3π π
(C) cos( ) + i sin( ), cos( ) + i sin( )
4 4 4 4
3π 3π 3π 3π
(D) cos( ) + i sin( − ), cos( − ) + i sin( )
4 4 4 4
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Q.16 Three moving iron type voltmeters are connected as shown below. Voltmeter readings are
V , V1 and V2 , as indicated. The correct relation among the voltmeter readings is
V1 V2
(A) V = + (B) V = V1 + V2 (C) V = 1
VV2 (D) V = V2 − V1
2 2
Q.17 Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
Q.18 The angle δ in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current.
(B) angular displacement of the rotor with respect to the stator.
(C) angular displacement of the stator mmf with respect to a synchronously rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.
Q.19 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.20 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency in kHz which is not valid is
(A) 5 (B) 12 (C) 15 (D) 20
Q.21 For a periodic signal v(t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental
frequency in rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
Q.22 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
EE-C 5/20
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Q.23 The Bode plot of a transfer function G (s ) is shown in the figure below.
40
32
20
0
1 10 100
‐8 ω (rad/s)
The gain (20 log G ( s ) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s2 s s2
Q.24 The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite.
Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
Q.25 In the feedback network shown below, if the feedback factor k is increased, then the
(A) input impedance increases and output impedance decreases.
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
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Q.26 to Q.55 carry two marks each.
1 1
Q.26 A matrix has eigenvalues –1 and –2. The corresponding eigenvectors are and
−1 − 2
respectively. The matrix is
1 1 1 2 − 1 0 0 1
(A) (B) (C) (D)
− 1 − 2 − 2 − 4 0 − 2 − 2 − 3
z2 − 4
Q.27
∫ z 2 + 4 dz evaluated anticlockwise around the circle z − i = 2 , where i = −1 , is
(A) −4π (B) 0 (C) 2 + π (D) 2 + 2i
Q.28 A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform
electric field of E = 6 a x + 8 a y kV/mm. The relative permittivity of the dielectric material is equal to
2. The value of constant ε 0 is 8.85 × 10−12 F/m. The energy stored in the dielectric in Joules is
(A) 8.85 × 10–11 (B) 8.85 × 10–5 (C) 88.5 (D) 885
Q.29 For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The
voltage at node 3 is 1.3 ∠–10° per unit. If a capacitor having reactance of –j3.5 per unit is now
added to the network between node 3 and the reference node, the current drawn by the capacitor per
unit is
(A) 0.325 ∠–100° (B) 0.325 ∠80° (C) 0.371 ∠–100° (D) 0.433 ∠80°
Q.30 The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated
armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature
voltage. If La= 0.1 mH, Ra= 1 Ω, neglecting armature reaction, the duty ratio of the chopper to
obtain 50% of the rated torque at the rated speed and the rated field current is
200 V La ,Ra
(A) 0.4 (B) 0.5 (C) 0.6 (D) 0.7
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Q.31 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.32 Three capacitors C1, C2, and C3, whose values are 10µF, 5µF, and 2µF respectively, have
breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum
safe voltage in Volts that can be applied across the combination and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
Q.33 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
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ω (s) 10
Q.34 The open-loop transfer function of a dc motor is given as = . When connected in
V a ( s ) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
R(s) Va(s) 10 ω(s)
+_ Ka
1+10s
(A) 1 (B) 5 (C) 10 (D) 100
Q.35 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW
respectively are
(A) 125 and 125 (B) 125 and 250 (C) 250 and 125 (D) 250 and 250
Q.36 A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance
without any load as Rs = 300 Ω. Other bridge resistances are R1 = R2 = R3 = 300 Ω. The maximum
permissible current through the strain gauge is 20 mA. During certain measurement when the
bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by
1% over the nominal value, the output voltage V0 in mV is
Rs R1
V0
+ ‐ +
Vi ‐
R3 R2
(A) 56.02 (B) 40.83 (C) 29.85 (D) 10.02
EE-C 9/20
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When the Newton-Raphson method is applied to solve the equation f ( x ) = x + 2 x − 1 = 0, the
3
Q.37
solution at the end of the first iteration with the initial guess value as x0 = 1.2 is
(A) –0.82 (B) 0.49 (C) 0.705 (D) 1.69
Q.38 A function y = 5 x 2 + 10 x is defined over an open interval x = (1, 2) . At least at one point in this
dy
interval, is exactly
dx
(A) 20 (B) 25 (C) 30 (D) 35
Q.39 A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50 Hz source, is rotating at
1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is
(A) 100 (B) 98 (C) 52 (D) 48
Q.40 Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10 µs. It
is given that L = (100π
) µ H and C = (100π )µ F. Assuming latching and holding currents of the
thyristor are both zero and the initial charge on C is zero, T conducts for
+ L
T
15 V C
‐
(A) 10 µs (B) 50 µs (C) 100 µs (D) 200 µs
Q.41 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
Q.42 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 R1 + q2 R2 (B) q1 / R1 + q2 / R2
(C) (q1R1 + q2 R2 ) / ( R1 + R2 ) (D) q1R2 + q2 R1
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Q.43 The impulse response of a continuous time system is given by h(t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Y (s)
Q.44 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
s +1 s +1
(A) (B)
5s2 + 6s + 2 s2 + 6 s + 2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
Q.45 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
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Q.46 The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial
state of the output Q of the flip-flop is ‘0’, then the frequency of the output waveform Q in kHz is
(A) 0.25 (B) 0.5 (C) 1 (D) 2
Q.47 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Common Data Questions
Common Data for Questions 48 and 49:
In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is
switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.
100 µH
12 V 470 µF
Q 20 Ω
Q.48 The PEAK-TO-PEAK source current ripple in Amps is
(A) 0.96 (B) 0.144 (C) 0.192 (D) 0.288
Q.49 The average source current in Amps in steady-state is
(A) 3/2 (B) 5/3 (C) 5/2 (D) 15/4
EE-C 12/20
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Common Data for Questions 50 and 51:
The state variable formulation of a system is given as
x&1 − 2 0 x1 1 x1
x& = 0 − 1 x + 1 u , x1 (0) = 0, x 2 (0) = 0 and y = [1 0] x
2 2 2
Q.50 The response y (t ) to a unit step input is
1 1 −2 t 1 −2 t 1 − t
(A) − e (B) 1 − e − e
2 2 2 2
(C) e −2 t − e − t (D) 1 − e − t
Q.51 The system is
(A) controllable but not observable
(B) not controllable but observable
(C) both controllable and observable
(D) both not controllable and not observable
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave
ac output voltage (vo) across an R-L load. Reference polarity of vo and reference direction of the output
current io are indicated in the figure. It is given that R = 3 Ω , L = 9.55 mH .
Q1 Q3
D1 D3 L
V dc + vo io R
Q4 Q2 ‐
D4 D2
Q.52 In the interval when v 0 < 0 and i0 > 0 the pair of devices which conducts the load current is
(A) Q1, Q2 (B) Q3, Q4 (C) D1, D2 (D) D3, D4
Q.53 Appropriate transition i.e., Zero Voltage Switching (ZVS)/Zero Current Switching (ZCS) of the
IGBTs during turn-on/turn-off is
(A) ZVS during turn-off (B) ZVS during turn-on
(C) ZCS during turn-off (D) ZCS during turn-on
EE-C 13/20
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Statement for Linked Answer Questions 54 and 55:
In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles
are very small, and the line resistances are negligible. All the line reactances are equal to j1 Ω.
Bus 1(slack) j1 Ω Bus 2
P2=0.1 pu
j1 Ω j1 Ω
Bus 3
P3=0.2 pu
Q.54 The voltage phase angles in rad at buses 2 and 3 are
(A) θ 2 = −0.1, θ3 = −0.2
(B) θ 2 = 0, θ3 = −0.1
(C) θ 2 = 0.1, θ3 = 0.1
(D) θ 2 = 0.1, θ3 = 0.2
Q.55 If the base impedance and the line-to-line base voltage are 100 Ω and 100 kV, respectively, then the
real power in MW delivered by the generator connected at the slack bus is
(A) −10 (B) 0 (C) 10 (D) 20
EE-C 14/20
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.57 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.58 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.59 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.60 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.61 to Q.65 carry two marks each.
Q.61 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
Q.62 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
EE-C 15/20
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Q.63 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
Q.64 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.65 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
END OF THE QUESTION PAPER
EE-C 16/20
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SESSION - 4
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2013 Question Booklet Code
D
EE : ELECTRICAL ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EE,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right half hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the
appropriate bubble under each digit of your registration number and (ii) write your registration number,
your name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EE
EE-D 1/20
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Q.1 to Q.25 carry one mark each.
Given a vector field F = y x a x − yz a y − x a z , the line integral ∫ F ⋅ d l evaluated along a segment
2 2
Q.1
on the x-axis from x = 1 to x = 2 is
(A) –2.33 (B) 0 (C) 2.33 (D) 7
Q.2 2 − 2 x1 0
The equation = has
1 − 1 x2 0
(A) no solution
x 0
(B) only one solution 1 =
x2 0
(C) non-zero unique solution
(D) multiple solutions
Q.3 Square roots of −i , where i = −1 , are
(A) i, –i
π π 3π 3π
(B) cos( − ) + i sin( − ), cos( ) + i sin( )
4 4 4 4
π 3π 3π π
(C) cos( ) + i sin( ), cos( ) + i sin( )
4 4 4 4
3π 3π 3π 3π
(D) cos( ) + i sin( − ), cos( − ) + i sin( )
4 4 4 4
Q.4 Three moving iron type voltmeters are connected as shown below. Voltmeter readings are
V , V1 and V2 , as indicated. The correct relation among the voltmeter readings is
V1 V2
(A) V = + (B) V = V1 + V2 (C) V = VV
1 2 (D) V = V2 − V1
2 2
Q.5 Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
Q.6 The angle δ in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current.
(B) angular displacement of the rotor with respect to the stator.
(C) angular displacement of the stator mmf with respect to a synchronously rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.
EE-D 2/20
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Q.7 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.8 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency in kHz which is not valid is
(A) 5 (B) 12 (C) 15 (D) 20
Q.9 For a periodic signal v(t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental
frequency in rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
Q.10 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Q.11 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s ) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s 2 s s2
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Q.12 In the feedback network shown below, if the feedback factor k is increased, then the
+ v + + vout
in v1 A0 –
– –
vf = kvout+ k +
– –
(A) input impedance increases and output impedance decreases.
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
Q.13 The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite.
Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
Q.14 The curl of the gradient of the scalar field defined by V = 2 x 2 y + 3 y 2 z + 4 z 2 x is
(A) 4 xy a x + 6 yz a y + 8 zx a z
(B) 4 a x + 6 a y + 8 a z
( ) ( ) (
(C) 4 xy + 4 z 2 a x + 2 x 2 + 6 yz a y + 3 y 2 + 8 zx a z )
(D) 0
Q.15 A continuous random variable X has a probability density function f ( x) = e − x , 0 < x < ∞ . Then
P { X > 1} is
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
Q.16 The flux density at a point in space is given by B = 4 x a x + 2ky a y + 8 a z Wb/m2. The value of
constant k must be equal to
(A) –2 (B) –0.5 (C) +0.5 (D) +2
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Q.17 A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a
short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV
windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at
(A) 50.0% of the rated current.
(B) 64.0% of the rated current.
(C) 80.0% of the rated current.
(D) 88.8% of the rated current.
Q.18 A single-phase load is supplied by a single-phase voltage source. If the current flowing from the
load to the source is 10∠ − 1500 A and if the voltage at the load terminals is 100∠600 V, then the
(A) load absorbs real power and delivers reactive power.
(B) load absorbs real power and absorbs reactive power.
(C) load delivers real power and delivers reactive power.
(D) load delivers real power and absorbs reactive power.
Q.19 A source vs (t ) = V cos100π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should
be
(A) 3 (B) 4 (C) 5 (D) 7
Q.20 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
Q.21 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1.
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
Q.22 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1) (t − 1) 2 t2 −1
(A) t u (t ) (B) u (t − 1) (C) u (t − 1) (D) u (t − 1)
2 2 2 2
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Q.23 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
(D) e −t u (t )
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
Q.24 V2 ( s )
The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.25 In the circuit shown below what is the output voltage (Vout) in Volts if a silicon transistor Q and an
ideal op-amp are used?
(A) 15 (B) 0.7 (C) 0.7 (D) 15
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Q.26 to Q.55 carry two marks each.
When the Newton-Raphson method is applied to solve the equation f ( x ) = x + 2 x − 1 = 0, the
3
Q.26
solution at the end of the first iteration with the initial guess value as x0 = 1.2 is
(A) –0.82 (B) 0.49 (C) 0.705 (D) 1.69
Q.27 A function y = 5 x 2 + 10 x is defined over an open interval x = (1, 2) . At least at one point in this
dy
interval, is exactly
dx
(A) 20 (B) 25 (C) 30 (D) 35
Q.28 A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50 Hz source, is rotating at
1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is
(A) 100 (B) 98 (C) 52 (D) 48
Q.29 Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10 µs. It
is given that L = (100π
) µ H and C = (100π )µ F. Assuming latching and holding currents of the
thyristor are both zero and the initial charge on C is zero, T conducts for
+ L
T
15 V C
-
(A) 10 µs (B) 50 µs (C) 100 µs (D) 200 µs
Q.30 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
Q.31 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 R1 + q2 R2 (B) q1 / R1 + q2 / R2
(C) (q1R1 + q2 R2 ) / ( R1 + R2 ) (D) q1R2 + q2 R1
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Q.32 The impulse response of a continuous time system is given by h(t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Y (s)
Q.33 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
s +1 s +1
(A) (B)
5s2 + 6s + 2 s2 + 6 s + 2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
Q.34 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
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Q.35 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Q.36 The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial
state of the output Q of the flip-flop is ‘0’, then the frequency of the output waveform Q in kHz is
(A) 0.25 (B) 0.5 (C) 1 (D) 2
z2 − 4
Q.37
∫ z 2 + 4 dz evaluated anticlockwise around the circle z − i = 2 , where i = −1 , is
(A) −4π (B) 0 (C) 2 + π (D) 2 + 2i
1 1
Q.38 A matrix has eigenvalues –1 and –2. The corresponding eigenvectors are and
−1
− 2
respectively. The matrix is
1 1 1 2 − 1 0 0 1
(A) (B) (C) (D)
− 1 − 2 − 2 − 4 0 − 2 − 2 − 3
Q.39 A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform
electric field of E = 6 a x + 8 a y kV/mm. The relative permittivity of the dielectric material is equal to
2. The value of constant ε 0 is 8.85 × 10−12 F/m. The energy stored in the dielectric in Joules is
(A) 8.85 × 10–11 (B) 8.85 × 10–5 (C) 88.5 (D) 885
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Q.40 For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The
voltage at node 3 is 1.3 ∠–10° per unit. If a capacitor having reactance of –j3.5 per unit is now
added to the network between node 3 and the reference node, the current drawn by the capacitor per
unit is
(A) 0.325 ∠–100° (B) 0.325 ∠80° (C) 0.371 ∠–100° (D) 0.433 ∠80°
Q.41 The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated
armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature
voltage. If La= 0.1 mH, Ra= 1 Ω, neglecting armature reaction, the duty ratio of the chopper to
obtain 50% of the rated torque at the rated speed and the rated field current is
200 V La ,Ra
(A) 0.4 (B) 0.5 (C) 0.6 (D) 0.7
Q.42 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.43 Three capacitors C1, C2, and C3, whose values are 10µF, 5µF, and 2µF respectively, have
breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum
safe voltage in Volts that can be applied across the combination and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
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Q.44 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
ω (s)
10
Q.45 The open-loop transfer function of a dc motor is given as = . When connected in
V a ( s ) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
R(s) Va(s) 10 ω(s)
+_ Ka
1+10s
(A) 1 (B) 5 (C) 10 (D) 100
Q.46 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW
respectively are
(A) 125 and 125 (B) 125 and 250 (C) 250 and 125 (D) 250 and 250
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Q.47 A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance
without any load as Rs = 300 Ω. Other bridge resistances are R1 = R2 = R3 = 300 Ω. The maximum
permissible current through the strain gauge is 20 mA. During certain measurement when the
bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by
1% over the nominal value, the output voltage V0 in mV is
Rs R1
V0
+ - +
Vi -
R3 R2
(A) 56.02 (B) 40.83 (C) 29.85 (D) 10.02
Common Data Questions
Common Data for Questions 48 and 49:
The state variable formulation of a system is given as
x&1 − 2 0 x1 1 x1
x& = 0 − 1 x + 1 u , x1 (0) = 0, x 2 (0) = 0 and y = [1 0] x
2 2 2
Q.48 The response y (t ) to a unit step input is
1 1 −2 t 1 −2 t 1 − t
(A) − e (B) 1 − e − e
2 2 2 2
(C) e −2 t − e − t (D) 1 − e − t
Q.49 The system is
(A) controllable but not observable
(B) not controllable but observable
(C) both controllable and observable
(D) both not controllable and not observable
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Common Data for Questions 50 and 51:
In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is
switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.
100 µH
12 V 470 µF
Q 20 Ω
Q.50 The PEAK-TO-PEAK source current ripple in Amps is
(A) 0.96 (B) 0.144 (C) 0.192 (D) 0.288
Q.51 The average source current in Amps in steady-state is
(A) 3/2 (B) 5/3 (C) 5/2 (D) 15/4
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles
are very small, and the line resistances are negligible. All the line reactances are equal to j1 Ω.
Bus 1(slack) j1 Ω Bus 2
P2=0.1 pu
j1 Ω j1 Ω
Bus 3
P3=0.2 pu
Q.52 The voltage phase angles in rad at buses 2 and 3 are
(A) θ 2 = −0.1, θ3 = −0.2
(B) θ 2 = 0, θ3 = −0.1
(C) θ 2 = 0.1, θ3 = 0.1
(D) θ 2 = 0.1, θ3 = 0.2
Q.53 If the base impedance and the line-to-line base voltage are 100 Ω and 100 kV, respectively, then the
real power in MW delivered by the generator connected at the slack bus is
(A) −10 (B) 0 (C) 10 (D) 20
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Statement for Linked Answer Questions 54 and 55:
The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave
ac output voltage (vo) across an R-L load. Reference polarity of vo and reference direction of the output
current io are indicated in the figure. It is given that R = 3 Ω , L = 9.55 mH .
Q1 Q3
D1 D3 L
V dc + vo io R
Q4 Q2 -
D4 D2
Q.54 In the interval when v 0 < 0 and i0 > 0 the pair of devices which conducts the load current is
(A) Q1, Q2 (B) Q3, Q4 (C) D1, D2 (D) D3, D4
Q.55 Appropriate transition i.e., Zero Voltage Switching (ZVS)/Zero Current Switching (ZCS) of the
IGBTs during turn-on/turn-off is
(A) ZVS during turn-off (B) ZVS during turn-on
(C) ZCS during turn-off (D) ZCS during turn-on
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.57 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.58 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.59 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.60 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.61 to Q.65 carry two marks each.
Q.61 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
Q.62 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
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Q.63 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
Q.64 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.65 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
END OF THE QUESTION PAPER
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Source: GATE. Question paper published by GATE.