GATE 2026 Question Paper Electrical Engineering (EE)

FOR GATE EXAM PREPARATION

GATE 2026
Question Paper ·
Electrical Engineering
(EE)
EXAM YEAR TYPE SUBJECT

GATE 2026 Question Paper Electrical Engineering (EE)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 ‘The shopkeeper sells lemons.’

In this sentence, the word ‘lemons’ is the ________.
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s e l a
(A)
g l a
object ag
a
(B) subject

(C) predicate

(D) verb
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Q.2 The figure below is supposed to show three non-overlapping shapes – one oval
and two triangles. Which one of the following figures P, Q, R, or S fits the
missing portion indicated by ‘?’ and completes the oval and the two triangles?

P Q

R S

(A) P

(B) Q

(C) R

(D) S

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Q.3 At how many points will the curves 𝑦 = 𝑥 2 and 𝑦 = −𝑥 2 − 2𝑥 − 1 intersect in
the real (𝑥, 𝑦) plane?

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(A) 0

e m
e m l as
(B)
l as 1
ag
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(C) a 2

(D) 3

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s e
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a

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a

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Q.4 ‘If Anish had scored hundred runs in today’s match, he would have been made the
captain of his team. He would have then become the youngest captain in his
team’s history. Unfortunately, he got out without scoring any runs. Hence, there
won’t be any change in the captaincy for now.’

Based on the paragraph above, which one of the following statements is true?

(A) Anish made hundred runs but was denied captaincy.

(B) Anish was the captain of his team before the game today.

(C) The current captain is older than Anish.

(D) Anish is the youngest player in his team.

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Q.5 Which one of the following figures P, Q, R, or S, correctly shows the 45°
clockwise-rotated version of figure (I)?

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(I)
s e l
g l a ag
a

P Q

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s e
g la
a
R S

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(A) P
m
c. o(B) s e m
e m Q
l a
las ag
ag (C) R

(D) S

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.co s e m
s em l a
la
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Q.6 – Q.10 Carry TWO marks Each

Q.6 Match the words in Column I with their synonyms in Column II.

Column I Column II
(i) Lonely (p) Verbatim
(ii) Literal (q) Solitary
(iii) Lousy (r) Deadly
(iv) Lethal (s) Terrible

(A) (i)-(q); (ii)-(p); (iii)-(s); (iv)-(r)

(B) (i)-(q); (ii)-(s); (iii)-(r); (iv)-(p)

(C) (i)-(s); (ii)-(p); (iii)-(q); (iv)-(r)

(D) (i)-(r); (ii)-(s); (iii)-(p); (iv)-(q)

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Q.7 ̅̅̅̅ is the diameter of a circle with center 𝑂. Two points 𝑅
In the given figure, 𝑃𝑄
and 𝑆 are chosen on the circle such that ∠𝑅𝑂𝑆 = 80°. When ̅̅̅̅ 𝑃𝑅 and ̅̅̅̅
𝑄𝑆 are
extended, they meet at 𝑇. The value of ∠𝑅𝑇𝑆 is _________________

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(A) 40°

(B) 50°

(C) 60°

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(D) 80°
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ag

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Q.8 Based on the relationship between each polygon and the number inside it, the
value of ‘X’ is ______

(A) 720

(B) 596

(C) 24

(D) 240

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Q.9 Consider a linear arrangement of seven bulbs, each of which can be in the ON or
OFF states. The initial configuration of the bulbs is shown in the figure. In every
Step, the states of the bulbs are changed based on the following rules:

 Any OFF bulb with exactly one ON neighbor at the end of the

m
previous Step is turned ON.

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
m
Any ON bulb with both neighbors ON at the end of the previous

 . c o Step is turned OFF.
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em
The state of any bulb not meeting the conditions above is left
l as
l as unchanged.
ag
agThe state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______

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s e
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a

(A) 5

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(B) 4

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s e (C) 3
g l a
g la a
a (D) 0

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Q.10 𝑃 and 𝑄 are two positive integers such that 𝑃2 = 𝑄 2 + 13.

The product of the numbers 𝑃 and 𝑄 is _________

(A) 13

(B) 26

(C) 39

(D) 42

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Q.11 – Q.35 Carry ONE mark Each

|𝑛|
Q.11 Consider the infinite-length, discrete-time sequence 𝑥 [𝑛] = 0.9 , where
𝑛 is an integer. The region of convergence of its Z-transform 𝑋(𝑧) is given by:
(Note: 𝑧 is a complex variable)
m
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.co s e m
s em l a
g la > 0.9 ag
(A)
a |𝑧|

(B) |𝑧| < 0.9

(C) 0.9 < |𝑧| < 1/0.9

(D) m |𝑧| > 1/0.9 }
{𝑧 such that |𝑧| < 0.9 } ∪ { 𝑧 such othat
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Q.12 Let 𝑥𝑐 (𝑡) be any continuous-time periodic signal with period 𝑇 . It is sampled
uniformly with a sampling period 𝑇𝑠 where 𝑇𝑠 ≠ 𝑇 , resulting in the discrete
sequence

𝑥 [𝑛] = 𝑥𝑐 (𝑛𝑇𝑠 ), where 𝑛 is an integer.
Which one of the following statements is correct about 𝑥 [𝑛]?

(A) 𝑥 [𝑛] will always be periodic with period 𝑇/𝑇𝑠 for all values of 𝑇/𝑇𝑠

(B) 𝑥 [𝑛] will always be periodic with period 1 for all values of 𝑇/𝑇𝑠

(C) 𝑥 [𝑛] will never be periodic

(D) 𝑥 [𝑛] will be periodic if and only if 𝑇/𝑇𝑠 is a rational number

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Q.13 The Laplace transform of the step response of a system is given by

100
𝑌(𝑠) =
𝑠(𝑠 + 100)
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The rise time is defined as the time taken for the response to go from 0.1 to 0.9
m
of its final value. The settling time is defined as the time taken for the response
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to reach 0.98 of its final value.
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For s emsystem, the rise time (Tr), settling time (Ts), and time constant (Tc), glas
laexpressed in seconds, are a
this

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(A) Tr = 0.022, Ts = 0.04, Tc = 0.01

(B) Tr = 0.22, Ts = 0.404, Tc = 0.01
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(C)
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Tr = 2.2, Ts = 4.04, Tc = 1.01
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(D) Tr = 22, Ts = 40.4, Tc = 10.1

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Q.14 Consider the following differential equation:

d2 y dy
t2 2
+ 7t + 8ty = 10 sin(t)
dt dt
Which one of the following options is correct?

(A) It is a linear differential equation

(B) It is a nonlinear differential equation

(C) It is a time-invariant differential equation

(D) It is a second-order partial differential equation

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Q.15 A uniform ring charge of radius R carries a total charge 𝑄. Which one of the
following options correctly quantifies the magnitude of the force on a point
charge of strength 𝑞 kept at the center of the ring?

(𝜖 is the permittivity of the medium)

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𝑄𝑞
(A)
g l a
4𝜋𝜖𝑅
a
(B) 𝑄𝑞
4𝜋𝜖𝑅 2

(C) 0

𝑞 𝑄
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(D)
×
4𝜋𝜖𝑅 2𝜋𝑅
e m
las
ag

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Q.16 A positive point charge with velocity 𝑣⃗ = 5 𝑥̂ enters a region having electric
field 𝐸⃗⃗ = 4 𝑦̂ and magnetic field 𝐵⃗⃗ = − 6 𝑧̂ . Which one of the following
statements is correct for the force on the charge as it enters the region?

(A) The force will be along the magnetic field but perpendicular to the electric field

(B) The force will be along the electric field but perpendicular to the magnetic field

(C) The force will be perpendicular to both electric and magnetic field

(D) The magnetic field does not exert any force on the charge

Q.17 A 15 kVA, 1100 V/220 V, single-phase two-winding transformer is configured as
a 1.32 kV/1.1 kV autotransformer.

What will be the rating of the autotransformer?

(A) 60 kVA

(B) 75 kVA

(C) 90 kVA

(D) 100 kVA

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Q.18 Consider a power system with N buses, of which P are generator buses and the
remaining Q are load buses (where there is no generation).

Assume that there are no reactive power-limit violations at the generator buses.

What is the size of the Jacobian matrix in the Newton-Raphson load flow
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method?
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s em l a
g la ag
(A)
a 2𝑁 × 2𝑁

(B) (2𝑁 − 1 − 𝑃) × (2𝑁 − 1 − 𝑃)

(C) (2𝑁 − 𝑄) × (2𝑁 − 𝑄)

(D) (𝑃 + 𝑄) × (𝑃 + 𝑄)
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Q.19 The initial three-phase voltage phasors (𝑉̅𝐴 , 𝑉̅𝐵 , and 𝑉̅𝐶 ) at a bus of a power
network are as shown in Case-1. Due to a disturbance, the bus voltage phasors
changed in phase by a small angle 𝛥𝜃, and the magnitudes remained the same as
depicted in Case-2.

Which one of the following statements is correct about the zero sequence
components?

(A) The zero sequence components in Case-1 and Case-2 have the same phase angle
and magnitude

(B) The magnitude of the zero sequence component in Case-1 is greater than that in
Case-2

(C) The magnitude of the zero sequence component in Case-2 is greater than that in
Case-1

(D) The zero sequence components in Case-1 and Case-2 have the same magnitude
but different phase angles

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Q.20 A certain application requires power at a frequency of 16.67 Hz, while the
available grid frequency is 50 Hz. A 3-phase synchronous motor connected to the
50 Hz, 3-phase grid, driving a synchronous generator, is used for this application.

Which one of the following combinations is a suitable choice for the number of
poles in the motor and generator, respectively?
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m .co s e m
se l a
2,la ag
ag
(A) 6

(B) 6, 2

(C) 4, 6

(D) 6, 4
m
.co
s em
g la is correct regarding the typical
Q.21
a used in induction motors?
Which one of the following options
double-squirrel-cage structure

(A) At starting, a larger portion of the rotor current flows in the outer cage
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.co em
(B) At starting, a larger portion of the rotor current flows in the inner cage

e m la s
las (C) At rated speed, most of the rotor current flows in the outergcage
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ag
(D) The purpose of the double-squirrel-cage structure is to lower the effective rotor
resistance at starting

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s em l a
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Q.22 The figure shows the single-line diagram of a synchronous generator delivering P
= 50 MW of power at unity power factor to an infinite bus.

𝐼𝑠 denotes the stator current phasor. If the field excitation is increased, which one
of the following options correctly describes its effect on the stator current, power
factor, and load angle of the machine?

(A) Stator current increases, power factor becomes lagging,
load angle remains the same

(B) Stator current decreases, power factor becomes leading,
load angle remains the same

(C) Stator current increases, power factor becomes lagging,
load angle decreases

(D) Stator current increases, power factor becomes leading,
load angle increases

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Q.23 A circuit with ideal elements is shown.

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.co s e m
s emone of the following options correctly identifies all the linear elements in la
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a
Which
l a
ag
the circuit?

(A) R only

(B) R, L, and C only
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(C) D only
s e
g la
(D) L, C, and D only a

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g la a
a

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Q.24 For the circuit shown, which one of the following options correctly identifies the
Thevenin’s equivalent parameters between nodes Y and Z?

(A) VTH = 100 V, RTH = 10 kΩ

(B) VTH = 140 V, RTH = 0 Ω

(C) VTH = 100 V, RTH = 0 Ω

(D) VTH = 140 V, RTH = 10 kΩ

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Q.25 Refer to the four circuits shown.

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m .co s e m
s e l a
g l a ag
a

Which one of the following options for k1, k2, k3, and k4 makes all of them
realizable?

m
.co
(A)
s em
k1 = 1, k4 = –1/3, for all values of k2 and k3

g la
(B) 2 3 a of k and k
k = –2, k = +1/3, for all values 1 4

(C) k1 = 2, k2 = 0.5, k3 = –2/3, k4 = –3

(D) k1 = 2, k2 = –0.5, k3 = –2/3, k4 = +3

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Q.26 A single-phase voltage source vs = 325 sin(2𝜋50𝑡) V delivers a current,
𝑖 = 12 sin(2𝜋50𝑡) + 9 sin(2𝜋150𝑡) A to a load.

The load power factor, correct up to two decimal places, is:

(A) 1.00

(B) 0.80

(C) 0.65

(D) 0.57

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Q.27 The figure shows a straight-line approximation for the forward characteristics of
a power diode. A continuous on-state current of 15 A is flowing through the
diode.

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m .co s e m
s e l a
g l a ag
a
What is the power loss in the diode?

m
.co
(A) 32.8 W

e m
(B) 21.2 W
las
ag
(C) 18.6 W

(D) 23.1 W

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Q.28 Consider the circuit shown in Figure (a). A gate pulse vg is applied between time
instants t0 and t1. After t1, during the MOSFET turn OFF process, it experiences a
voltage overshoot.

(a) (b)

Based on the vds waveforms shown in Figure (b), which one of the following
options is correct?

(A) 𝑅1 > 𝑅2 > 𝑅3

(B) 𝑅1 > 𝑅3 > 𝑅2

(C) 𝑅3 > 𝑅2 > 𝑅1

(D) 𝑅2 > 𝑅3 > 𝑅1

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Q.29 The asymptotic Bode magnitude plot of a system is shown.

m
m .co
m .co s e m
s e l a
g l a ag
a
Which one of the following options best represents the transfer function of the
system?

m
.co
(A) 𝑠
1+
𝜔0
𝐺(𝑠) = 𝑠
e m
𝜔0
las
(B) 𝑠 ag
𝜔0
𝐺(𝑠) = 𝑠
1+ 𝜔
0

(C) 𝑠
1+ 𝜔
0
𝐺(𝑠) = 𝑠
1−𝜔
0
m
m
c. o(D) m.co
m
1−𝜔
𝑠
s e
s e 𝐺(𝑠) = 𝑠
0

g l a
la
1+ 𝜔

g
0
a
a

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.co s e m
s em l a
la
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Q.30 Two n × n matrices A and B have a common eigenvalue 2, and the same
corresponding nonzero eigenvector.

Which of the following options is/are correct?

(Note: I is the n × n identity matrix.)

(A) Determinant ( A − 2I ) = 0

(B) Determinant ( B − 2I ) = 0

(C) Determinant ( A + B − 2I ) = 0

(D) Determinant ( A + B − 4I ) = 0

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Q.31 A 220V/12V single-phase transformer is designed for use in India and rated
100 VA at 50 Hz. Later, this unit is shipped to the USA where it is used as a
110V/6V transformer at 60 Hz.

Which of the following statements is/are correct?

m
m .co
.co e m
(A)
s
No-loademcurrent drawn would be smaller for operation in the USA compared to glas
g la in India
that a
a
(B) For the same load current, the losses would be higher in the USA compared to
that in India

(C) The peak magnetic flux density in the core would be higher while operating in the
USA compared to that in India

m
(D)
.co
The eddy current losses in the core would be approximately 44% higher while
m
e
operating in the USA compared to that in India

las
ag

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Q.32 ⃗ (𝑥, 𝑦, 𝑧) = sin(𝑦) 𝑥̂ + cos(𝑥 ) 𝑦̂ + 5 𝑧̂ , the integral
Given that 𝐹
∯𝑆 𝐹⃗ (𝑥, 𝑦, 𝑧) ∙ ⃗⃗⃗⃗⃗
𝑑𝑠 over the unit sphere S centered at the origin evaluates
to ________

(Round off to one decimal place)

Q.33 In the linear regulator circuit shown, the base to emitter voltage VBE of the BJT
is 0.6 V. The Zener diode clamps the base voltage to 5.4 V. Ignore the biasing
current of the Zener diode and BJT.

The maximum possible efficiency of the regulator circuit is ___________ %

(Round off to one decimal place)

Q.34 Consider the circuit shown. Assume that the diode D is ideal. The supply voltage
vs = 325 sin(2𝜋50𝑡) V, 𝐿 = 500 µH, and 𝑅 = 10 Ω. The peak diode current (in
amperes) is ______________

(Round off to one decimal place)

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a
Q.35 A is an m×m skew-symmetric matrix with real-valued entries, and x is an
m-dimensional column vector with real-valued entries such that xTx = 1.
The quantity xTAx evaluates to _________

(Answer in integer)

m
m .co
m .co s e m
s e l a
g l a ag
a

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.36 – Q.65 Carry TWO marks Each

Q.36 A time-limited waveform g(𝑥) is specified as follows:

−𝑘, −𝜋 < 𝑥 ≤0
g(𝑥) = { +𝑘, 0 < 𝑥 ≤𝜋
0, otherwise

A new waveform f(𝑥) is constructed from g(𝑥) as follows:
∞

f(𝑥) = ∑ g(𝑥 + 2𝜋𝑚), for all 𝑥 ∈ 𝑅
𝑚=−∞

The sum of the coefficients of the third harmonics of the sine and cosine
2
terms in the trigonometric Fourier series expansion of f(𝑥) is .
3𝜋

What is the value of 𝑘 ?

(A) 1

(B) 1
2

(C) 1
3

(D) 1
4

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m
m .co

m .co s e m

se g l a
a
Q.37 In the circuit shown, the open loop gain of the operational amplifier is A0 = 105.

m
m .co
.co s e m
s em l a
g la ag
aWhat is the voltage gain of the circuit?
(Round off to two decimal places)

–16.67 m
.co
(A)

e m
(B) –20.00
las
ag
(C) –21.00

(D) –12.67

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.38 Three single-phase 11kV/3.3kV transformers are connected to form a
three-phase transformer bank with connections as shown.

Considering ABC phase sequence, the vector group of the transformer is:

(A) Dd0

(B) Dd4

(C) Dd6

(D) Dd10

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m .co

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Q.39 In the circuit shown, the phase currents are

I A  572.812  j50.115 A

I B  254.525  j 459.175 A
m
m
IC  207.083  j 444.091 A
.co
m .co s e m
s e l a
g l a ag
a

m
.co
Given that the CTs are ideal with no saturation, and the turns ratio of the Main CT
is 300:5 and that of the Auxiliary Transformer (ΥnΔ) is 2:1 on every phase, the

e m
value of I AR , rounded off to three decimal places, is:

las
ag
(A) 0A

(B) 0.653 17.556o A

m
m 537.240  4.105o A
.co
(C)

m .co s e m
s e (D) 8.954  4.105o A
g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.40 The operating characteristic of a reactance relay is given by X  1  ,
where X is the reactance calculated by the relay. Its operating characteristic
in the admittance plane (G-B plane, where G and B denote conductance and
susceptance, respectively, expressed in Ʊ) is given by:

(A) 1
G 2  ( B  0.5)2 
4

(B) B 1

(C) 1
(G  1)2  B 2 
2

(D) 1
G 2  ( B  1)2 
2

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m .co

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Q.41 A three-phase two-winding transformer has a voltage transformation ratio
VP
 0.866  j 0.5 , where VP is the primary side voltage in p.u., and VS is the
VS
secondary side voltage in p.u. I P and I S represent the currents injected into the
primary and secondary sides of the transformer, respectively. The admittance
m
.co
corresponding to the leakage impedance of the transformer referred to the
m
.co
secondary is yt p.u. Neglect the magnetizing branch.
e m
e m l as
l as ag
ag

The Y bus representation of this transformer is:

m
(A)  yt

yt 
m .co
IP   0.866  j 0.5
s e
0.866  j 0.5  VP 
la
     
 I S    VS 

yt yt
ag
 0.866  j 0.5 0.866  j 0.5 


(B)  I P   yt  yt  VP 
 I    y yt  VS 
 S  t

 
m
(C) yt

.co
 yt
IP  0.866  j 0.5  VP 
m   
.co
I  
 S   y  VS 
e m
m s
t
 0.866  j 0.5 yt 
s e  
g l a
g la a
a (D) 
yt 
yt 
IP   0.866  j 0.5  VP 
I     
 S   yt
yt
 VS 
 0.866  j 0.5 
 

m .
.co s e m
s em l a
la
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Q.42 An electrical component has voltage drop v  Vm sin ( t ) , when the current
through it is i  I m sin ( t   ) .

What is the average power dissipated over a half cycle corresponding to  ?

(A) 0

(B) Vm I m cos 

(C) Vm I m
cos 
2

(D) Vm I m
cos 
4

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m
m .co

m .co s e m

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a
Q.43 The electrical network shown has an independent voltage source (10 V) and
a current source (1 u(t) mA).

m
m .co
m .co s e m
s e l a
Theavoltage across the capacitor at time instants (in seconds)
g l0+, t = 0.50, and t = ∞, respectively, is: ag
at =

(A) 8.00 V, 28.00 V, 26.36 V

m
.co
(B) 8.00 V, 26.36 V, 28.00 V

e m
(C) 10.00 V, 26.36 V, 28.00 V
las
ag
(D) 10.00 V, 28.00 V, 26.36 V

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.44 The terminal voltage and current of a linear electrical network shown in
Figure (a) are given in the table.

Terminal voltage (vt) Terminal current (it)
18 V – 0.5 A
30 V 0.5 A
36 V 1.0 A

The correct choice for the parameters (IN, RN) of the Norton equivalent circuit
shown in Figure (b) is:

(A) IN = 3.0 A, RN = 24.0 Ω

(B) IN = 12.0 A, RN = 2.0 Ω

(C) IN = 2.0 A, RN = 12.0 Ω

(D) IN = 2.0 A, RN = 24.0 Ω

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m
m .co

m .co s e m

se g l a
a

Q.45 The digital circuit shown has 3 inputs (x, y, and z).

m
m .co
m .co s e m
s e l a
g l a ag
a

The simplified logical expression for the output (OUT) is:

m
(A) 𝑥̅ 𝑦𝑧
̅̅̅
m .co
s e
g la
(B) 0 a
(C) 𝑥̅ ( 𝑦 + 𝑧 )

(D) 1

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.46 The MOSFET switches shown in the circuit are ideal.

Which of the following is the correct option for Boolean logical expression of the
output (OUT), and the maximum possible power (P) consumed by the circuit?

(A) OUT = ̅̅̅̅̅̅̅̅̅̅
AB + C̅ , P = 5 mW

(B) OUT = ̅̅̅̅̅̅̅̅̅̅̅̅
(A + B)C̅ , P = 5 mW

(C) OUT = ̅̅̅̅̅̅
ABC̅ + C̅ , P = 7.5 mW

(D) OUT = ̅̅̅̅
ABC , P = 7.5 mW

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m .co

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a
Q.47 Consider the single-phase voltage source inverter circuit feeding an inductive
load (L). Assume that the power MOSFET switches are ideal. S1 and S2 are
switched on during the first 10 µs, and S3 and S4 are switched on during the next
10 µs in a switching cycle. The switches in the same leg are thus switched in a
complementary fashion. Neglect the dead time. The waveform of the inductor

m
current (iL) in the steady state is triangular with a peak value of 5 A as shown.

m .co
m .co s e m
s e l a
g l a ag
a
The rms value of the current through the switch S1 is:

m
(A) 2.88 A
m .co
s e
(B) 2.04 A
g la
a
(C) 3.54 A

(D) 2.50 A

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.48 Consider the boost converter circuit shown. Assume that the semiconductor
devices are ideal. In steady state, the inductor current rises linearly from 0 A
to 6 A in the first 10 µs and then falls linearly from 6 A to 0 A in the next
10 µs of every switching cycle as shown. The load resistance R is 10 Ω and
the capacitance C is 500 µF.

Neglect the ripple in the output voltage. What is the input voltage Vdc?

(A) 10.0 V

(B) 15.0 V

(C) 7.5 V

(D) 12.5 V

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m
m .co

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a
Q.49 Which one of the following statements is ALWAYS correct about a collection of
𝑝 column vectors, each having n real-valued entries?

m
m .co
(A)
.co
If 𝑝 > n, then the column vectors must be linearly dependent
s e m
s em l a
(B)
gIfla
𝑝 > n, then the column vectors must be linearly independent ag
a
(C) If 𝑝 = n, then the column vectors must be orthogonal

(D) If 𝑝 < n, then the column vectors must be linearly independent

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.50 Consider the second-order differential equation

𝑑 2 𝑦 𝑑𝑦
+ +𝑦 =0
𝑑𝑥 2 𝑑𝑥
with initial conditions
𝑑𝑦
𝑦(0) = 1, | = 1
𝑑𝑥 𝑥=0
The solution is given by

(A)
√3𝑥 √3𝑥
𝑦(𝑥) = exp(−𝑥/2) (cos ( ) + √3sin ( ))
2 2

(B)
√3𝑥 1 √3𝑥
𝑦(𝑥) = exp(−𝑥/2) (cos ( ) + sin ( ))
2 √3 2

(C)
√3𝑥 1 √3𝑥
𝑦(𝑥) = exp(−𝑥/2) (cos ( ) − sin ( ))
2 √3 2

(D)
√3𝑥 √3𝑥
𝑦(𝑥) = exp(−𝑥/2) (cos ( ) − √3sin ( ))
2 2

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m .co

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a
Q.51 The figure shows an arbitrarily shaped planar conducting loop A in the XY plane.
Two nonintersecting regions with areas 𝑎1 and 𝑎2 within the loop are subjected to
⃗⃗1 = 𝑚 sin(𝜔𝑡) (1 𝑥̂ + 0 𝑦̂ + 1 𝑧̂ ) , and
magnetic fields 𝐵
√2
𝑛
⃗⃗
𝐵2 = − cos(2𝜔𝑡 + 𝜋/4) (0 𝑥̂ + 1 𝑦̂ + 1 𝑧̂ ) , respectively.
√2

m
m .co
m .co s e m
s e l a
g l a ag
a

What is the expression for the induced rms voltage in loop A?

m
m .co
s e
(A)
g la
𝑎2 𝜔 2 𝑚2 + 4𝑎22 𝜔 2 𝑛2
√ 1
4
a

(B)
𝑎2 𝜔 2 𝑚2 + 4𝑎22 𝜔 2 𝑛2
√ 1
2

m
.co
(C)
m 𝑎2 𝜔 2 𝑚2 − 2𝑎22 𝜔 2 𝑛2
.co
√ 1
2
e m
e m l as
las ag
ag (D)
√𝑎12 𝜔 2 𝑚2 + 2𝑎22 𝜔 2 𝑛2

m .
.co s e m
s em l a
la
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Q.52 A system is characterized by the following state equation and output equation (𝑢 :
input, 𝐱: state vector, 𝑦: output)

𝑎 𝑏 1
𝐱̇ = [ ]𝐱 + [ ]𝑢
−𝑎 0 0
𝑦 = [1 2] 𝐱
What are the values of 𝑎 and 𝑏 for which the poles of the transfer function are at
–2 + j3 and –2 – j3 ?

(A) 𝑎 = 4, 𝑏 = 3.25

(B) 𝑎 = – 4, 𝑏 = 3.25

(C) 𝑎 = 4, 𝑏 = – 3.25

(D) 𝑎 = – 4, 𝑏 = – 3.25

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m .co

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a
Q.53 A system is represented in state-space form as follows:
(𝑢: input, 𝐱: state vector, 𝑦: output)

1 2 1
𝐱̇ = [ ]𝐱 + [ ]𝑢
−3 0 2
m
.co
𝑦 = [1 2 ] 𝐱
o m m
. c 2 1
s e
em
new state vector 𝐳 = [ ] 𝐱
Consider the
s −1 0
g l a
l a a
agvector 𝐳 ?
What is the state-space representation of the system in terms of the new state

(A) −1 4 4
𝐳̇ = [ ]𝐳 + [ ]𝑢
−1 −2 −1
m
𝑦 = [2 3] 𝐳
m .co
s e
(B)
𝐳̇ = [
2 3
] 𝐳 + [ ] 𝑢 gl
3 a
0 3 5 a
𝑦 = [2 3] 𝐳

(C) 4 9 4
𝐳̇ = [ ]𝐳 + [ ]𝑢
−2 −3 −1
𝑦 = [2 3] 𝐳
m
m
c. o(D) m.co
m 𝐳̇ = [
2 1 4
]𝐳 + [ ]𝑢 s e
s e −4 1 −1
g l a
g la 𝑦 = [4 −1] 𝐳 a
a

m .
.co s e m
s em l a
la
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Q.54 For the balanced 3-phase transmission line shown, consider the following cases:

Case-1: |𝑉1 | = 1.1 p. u. , |𝑉2 | = 0.9 p. 𝑢. , 𝑍 = 0.75∠0𝑜 𝑝. 𝑢. and
𝜃12 = 𝜃1 − 𝜃2 = 0𝑜

Case-2: |𝑉1 | = 1.1 p. u. , |𝑉2 | = 0.9 p. u. , 𝑍 = 0.75∠90𝑜 𝑝. 𝑢. and
𝜃12 = 𝜃1 − 𝜃2 = 90𝑜

Which of the following statements is/are correct about real power loss and
reactive power loss in the line?

(A) Real power loss in Case-1 is more than that in Case-2

(B) Real power loss in Case-2 is more than that in Case-1

(C) Reactive power loss in Case-1 is more than that in Case-2

(D) Reactive power loss in Case-2 is more than that in Case-1

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m
m .co

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a
Q.55 Consider an n × n orthogonal matrix 𝐴 with real entries and each column
having unit Euclidean norm.

Which of the following statements is/are correct?

m
m .co
.co s e m
(A)
s emThe value of the determinant of 𝐴 is either +1 or –1
l a
g la ag
(B) a The eigenvalues of 𝐴 have modulus 1

(C) ∥ 𝐴𝒙 ∥ = ∥ 𝒙 ∥, for all x ∈ 𝑅 𝑛 , where ∥ 𝒙 ∥ denotes the Euclidean norm of 𝒙, and
(𝐴𝒙)𝑇 (𝐴𝒚) ≠ 𝒙𝑇 𝒚, for all distinct x, y ∈ 𝑅 𝑛

(D) ∥ 𝐴𝒙 ∥ = ∥ 𝒙 ∥, for all x ∈ 𝑅 𝑛 , where ∥ 𝒙 ∥ denotes the Euclidean norm of 𝒙, and
(𝐴𝒙)𝑇 (𝐴𝒚) = 𝒙𝑇 𝒚, for all x, y ∈ 𝑅 𝑛 m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.56 Consider the system of linear equations: Ax = b, where A is an n × n matrix,
and x and b are n-dimensional column vectors.

Suppose this system of equations has a unique solution. Which of the following
statements is/are correct?

(A) A-1 exists

(B) The system of equations Amx = b also has a unique solution for
m = 1, 2, 3,…

(C) rank(A) = rank(Am), for m = 1, 2, 3,…

(D) rank(A) < rank([A | b ]), where [A | b ] denotes the augmented matrix.

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m .co

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a
Q.57 The resistance values of the Wheatstone bridge shown are:
P = 2000 Ω, Q = 500 Ω,R = 3000 Ω . The battery voltage E = 50V .
The battery has an internal resistance of 1  and the Galvanometer (G)
has a resistance of 50  .

m
m .co
m .co s e m
s e l a
g l a ag
a

The value of the resistance S for balanced condition is _____________ Ω
(Answer in integer)

m
Q.58
.co
A system with two generators G1 and G2 (without generator limits) is shown.
m
s e
g la
a

The total load on the system is 1184 MW. The expressions for the cost of
generation (𝐶1 and 𝐶2 ) and real power loss (𝑃𝐿𝑜𝑠𝑠 ) are as follows:

m
.co
𝐶1 (𝑃𝐺1 ) = 1000 + 50𝑃𝐺1 + 0.01(𝑃𝐺1 )2 Rs/MWh
m
m .co 𝐶2 (𝑃𝐺2 ) = 2000 + 50𝑃𝐺2 + 0.001(𝑃𝐺2 )2 Rs/MWh
s e m
s e g l a
la
𝑃𝐿𝑜𝑠𝑠 = 0.001(𝑃𝐺2 − 50)2 MW
g a
a When the generators are operating at their optimal generation, meeting the total
load requirement, the real power loss in the system is ________ MW (Round off
to one decimal place)

Consider the Lagrange multiplier 𝜆 = 70.25 for optimal generation.

m .
.co s e m
s em l a
la
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Q.59 A balanced three-phase supply is given to a 30 kW, 4-pole, 400 V, 50 Hz, wound
rotor induction motor with Y-connected stator and rotor windings. The motor is
driving a constant torque load. With shorted sliprings, the machine runs at 1476
rpm.

When an external non-inductive resistance of 0.27 Ω per phase is connected in
series in the rotor circuit, the steady-state speed drops to 1404 rpm.

Neglecting rotational losses, the actual per phase rotor winding resistance
is ____ Ω

(Round off to two decimal places)

Q.60 Consider the two-port network shown. For maximum power transfer to the
resistive load (RL), the value of RL should be__________ Ω
(Round off to two decimal places)

Q.61 Consider the circuit shown. Assume that the diode (D) is ideal.

Given vs = 100 sin(2𝜋50𝑡) V, 𝑉𝑑𝑐 = 50 V, and 𝑅 = 10 Ω, the average value
of the current through the diode is ___________ A

(Round off to two decimal places)

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Q.62 The magnitude of the contour integral

(𝑧+1)2
∮𝐶 ((𝑧−𝑖)(𝑧−2)) 𝑑𝑧

over the contour 𝐶: |𝑧 − 2 − 𝑖| = 3/2 is ______
m
m .co
.co
(Round off to two decimal places)
e m
em
Note: 𝑧 is a complex variable and 𝑖 = √−1
l as
las ag
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Q.63 a A uniform spherical volume charge distribution of radius 2 m, centered at
3
the origin, has a strength of × 10−6 C/m3. A point charge of strength 𝜋 ×
𝜋
8.854 × 10−12 C is moved from (– 3, 0, – 4) to (0, 0, 4) in Cartesian coordinate
system. The relative permittivity of the medium is 1 and the coordinate values are
in meters.

The work done during the process is ______ µJ

m
.co
(Round off to two decimal places)

e m
Q.64
las
Let X and Y be two real-valued random variables with

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E(X) = 1, E(Y) = 2, E(X2) = 4, E(Y2) = 9, and E(XY) = 0.9,
where E denotes the expectation operator.

The value of α that minimizes E( (X−αY)2 ) is __________

(Round off to one decimal place)

m
m .co
.co
Q.65 The integral
e m
e m 1 ∞
𝑥 2026
l as
las ∫
π 0 (1 + 𝑥 2026 )(1 + 𝑥 2 )
d𝑥
ag
ag
evaluates to _________

(Round off to two decimal places)

m .
.co s e m
s em l a
la
Organizing Institute: IIT Guwahati

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Page 55 of 55
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 55 of 55