GATE 2026 EE PYQ: all 65 questions with official answers

Q1 · General Aptitude · MCQ · 1 mark

‘The shopkeeper sells lemons.’

In this sentence, the word ‘lemons’ is the ________.

(A)
object
(B)
subject
(C)
predicate
(D)
verb

Answer (official key): A

Worked solution: in your report after you take this paper.

Q2 · General Aptitude · MCQ · 1 mark

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?

(A)
P
(B)
Q
(C)
R
(D)
S

Answer (official key): A

Worked solution: in your report after you take this paper.

Q3 · General Aptitude · MCQ · 1 mark

At how many points will the curves $y = x^2$ and $y = -x^2 - 2x - 1$ intersect in the real $(x, y)$ plane?

(A)
0
(B)
1
(C)
2
(D)
3

Answer (official key): A

Worked solution: in your report after you take this paper.

Q4 · General Aptitude · MCQ · 1 mark

‘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.

Answer (official key): C

Worked solution: in your report after you take this paper.

Q5 · General Aptitude · MCQ · 1 mark

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

(A)
P
(B)
Q
(C)
R
(D)
S

Answer (official key): B

Worked solution: in your report after you take this paper.

Q6 · General Aptitude · MCQ · 2 marks

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)

Answer (official key): A

Worked solution: in your report after you take this paper.

Q7 · General Aptitude · MCQ · 2 marks

In the given figure, $\overline{PQ}$ is the diameter of a circle with center $O$ . Two points $R$ and $S$ are chosen on the circle such that $\angle ROS = 80^\circ$ . When $\overline{PR}$ and $\overline{QS}$ are extended, they meet at $T$ . The value of $\angle RTS$ is _________________

(A)
40°
(B)
50°
(C)
60°
(D)
80°

Answer (official key): B

Worked solution: in your report after you take this paper.

Q8 · General Aptitude · MCQ · 2 marks

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

Answer (official key): A

Worked solution: in your report after you take this paper.

Q9 · General Aptitude · MCQ · 2 marks

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 previous Step is turned ON.
Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
The state of any bulb not meeting the conditions above is left unchanged.

The 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 ______

(A)
5
(B)
4
(C)
3
(D)
0

Answer (official key): B

Worked solution: in your report after you take this paper.

Q10 · General Aptitude · MCQ · 2 marks

$P$ and $Q$ are two positive integers such that $P^2 = Q^2 + 13$ .

The product of the numbers $P$ and $Q$ is _________

(A)
13
(B)
26
(C)
39
(D)
42

Answer (official key): D

Worked solution: in your report after you take this paper.

Q11 · Signals and Systems · MCQ · 1 mark

Consider the infinite-length, discrete-time sequence $x[n] = 0.9^{|n|}$ , where $n$ is an integer. The region of convergence of its Z-transform $X(z)$ is given by:

(Note: $z$ is a complex variable)

(A)
$|z| > 0.9$
(B)
$|z| < 0.9$
(C)
$0.9 < |z| < 1/0.9$
(D)
$\{z \text{ such that } |z| < 0.9\} \cup \{z \text{ such that } |z| > 1/0.9\}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q12 · Signals and Systems · MCQ · 1 mark

Let $x_c(t)$ be any continuous-time periodic signal with period $T$ . It is sampled uniformly with a sampling period $T_s$ where $T_s \neq T$ , resulting in the discrete sequence

x[n] = x_c(nT_s),

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 $T/T_s$ for all values of $T/T_s$
(B)
$x[n]$ will always be periodic with period 1 for all values of $T/T_s$
(C)
$x[n]$ will never be periodic
(D)
$x[n]$ will be periodic if and only if $T/T_s$ is a rational number

Answer (official key): D

Worked solution: in your report after you take this paper.

Q13 · Control Systems · MCQ · 1 mark

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

Y(s) = \frac{100}{s(s + 100)}

The rise time is defined as the time taken for the response to go from 0.1 to 0.9 of its final value. The settling time is defined as the time taken for the response to reach 0.98 of its final value.

For this system, the rise time ( $T_r$ ), settling time ( $T_s$ ), and time constant ( $T_c$ ), all expressed in seconds, are

(A)
$T_r = 0.022$ , $T_s = 0.04$ , $T_c = 0.01$
(B)
$T_r = 0.22$ , $T_s = 0.404$ , $T_c = 0.01$
(C)
$T_r = 2.2$ , $T_s = 4.04$ , $T_c = 1.01$
(D)
$T_r = 22$ , $T_s = 40.4$ , $T_c = 10.1$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q14 · Differential Equations · MCQ · 1 mark

Consider the following differential equation:

t^{2}\frac{d^{2}y}{dt^{2}} + 7t\frac{dy}{dt} + 8t\,y = 10\sin(t)

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

Answer (official key): A

Worked solution: in your report after you take this paper.

Q15 · Electromagnetic Fields · MCQ · 1 mark

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?

( $\epsilon$ is the permittivity of the medium)

(A)
$\dfrac{Qq}{4\pi\epsilon R}$
(B)
$\dfrac{Qq}{4\pi\epsilon R^2}$
(C)
0
(D)
$\dfrac{q}{4\pi\epsilon R}\times\dfrac{Q}{2\pi R}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q16 · Electromagnetic Fields · MCQ · 1 mark

A positive point charge with velocity $\vec{v} = 5\,\hat{x}$ enters a region having electric field $\vec{E} = 4\,\hat{y}$ and magnetic field $\vec{B} = -6\,\hat{z}$ . 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

Answer (official key): B

Worked solution: in your report after you take this paper.

Q17 · Electrical Machines · MCQ · 1 mark

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

Answer (official key): C

Worked solution: in your report after you take this paper.

Q18 · Power Systems · MCQ · 1 mark

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 method?

(A)
$2N \times 2N$
(B)
$(2N - 1 - P) \times (2N - 1 - P)$
(C)
$(2N - Q) \times (2N - Q)$
(D)
$(P + Q) \times (P + Q)$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q19 · Power Systems · MCQ · 1 mark

The initial three-phase voltage phasors ( $\bar{V}_A$ , $\bar{V}_B$ , and $\bar{V}_C$ ) 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 $\Delta\theta$ , 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

Answer (official key): D

Worked solution: in your report after you take this paper.

Q20 · Electrical Machines · MCQ · 1 mark

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?

(A)
2, 6
(B)
6, 2
(C)
4, 6
(D)
6, 4

Answer (official key): B

Worked solution: in your report after you take this paper.

Q21 · Electrical Machines · MCQ · 1 mark

Which one of the following options is correct regarding the typical double-squirrel-cage structure used in induction motors?

(A)
At starting, a larger portion of the rotor current flows in the outer cage
(B)
At starting, a larger portion of the rotor current flows in the inner cage
(C)
At rated speed, most of the rotor current flows in the outer cage
(D)
The purpose of the double-squirrel-cage structure is to lower the effective rotor resistance at starting

Answer (official key): A

Worked solution: in your report after you take this paper.

Q22 · Electrical Machines · MCQ · 1 mark

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.

$I_s$ 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

Answer (official key): C

Worked solution: in your report after you take this paper.

Q23 · Electric Circuits · MCQ · 1 mark

A circuit with ideal elements is shown.

Which one of the following options correctly identifies all the linear elements in the circuit?

(A)
R only
(B)
R, L, and C only
(C)
D only
(D)
L, C, and D only

Answer (official key): B

Worked solution: in your report after you take this paper.

Q24 · Electric Circuits · MCQ · 1 mark

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

(A)
$V_{TH}$ = 100 V, $R_{TH}$ = 10 kΩ
(B)
$V_{TH}$ = 140 V, $R_{TH}$ = 0 Ω
(C)
$V_{TH}$ = 100 V, $R_{TH}$ = 0 Ω
(D)
$V_{TH}$ = 140 V, $R_{TH}$ = 10 kΩ

Answer (official key): B

Worked solution: in your report after you take this paper.

Q25 · Electric Circuits · MCQ · 1 mark

Refer to the four circuits shown.

Which one of the following options for $k_1$ , $k_2$ , $k_3$ , and $k_4$ makes all of them realizable?

(A)
$k_1 = 1$ , $k_4 = -1/3$ , for all values of $k_2$ and $k_3$
(B)
$k_2 = -2$ , $k_3 = +1/3$ , for all values of $k_1$ and $k_4$
(C)
$k_1 = 2$ , $k_2 = 0.5$ , $k_3 = -2/3$ , $k_4 = -3$
(D)
$k_1 = 2$ , $k_2 = -0.5$ , $k_3 = -2/3$ , $k_4 = +3$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q26 · Electric Circuits · MCQ · 1 mark

A single-phase voltage source $v_s = 325\sin(2\pi 50 t)$ V delivers a current

i = 12\sin(2\pi 50 t) + 9\sin(2\pi 150 t)\ \text{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

Answer (official key): B

Worked solution: in your report after you take this paper.

Q27 · Power Electronics · MCQ · 1 mark

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.

What is the power loss in the diode?

(A)
32.8 W
(B)
21.2 W
(C)
18.6 W
(D)
23.1 W

Answer (official key): C

Worked solution: in your report after you take this paper.

Q28 · Power Electronics · MCQ · 1 mark

Consider the circuit shown in Figure (a). A gate pulse $v_g$ is applied between time instants $t_0$ and $t_1$ . After $t_1$ , during the MOSFET turn OFF process, it experiences a voltage overshoot.

Based on the $v_{ds}$ waveforms shown in Figure (b), which one of the following options is correct?

(A)
$R_1 > R_2 > R_3$
(B)
$R_1 > R_3 > R_2$
(C)
$R_3 > R_2 > R_1$
(D)
$R_2 > R_3 > R_1$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q29 · Control Systems · MCQ · 1 mark

The asymptotic Bode magnitude plot of a system is shown.

Which one of the following options best represents the transfer function of the system?

(A)
$G(s) = \dfrac{1 + \frac{s}{\omega_0}}{\frac{s}{\omega_0}}$
(B)
$G(s) = \dfrac{\frac{s}{\omega_0}}{1 + \frac{s}{\omega_0}}$
(C)
$G(s) = \dfrac{1 + \frac{s}{\omega_0}}{1 - \frac{s}{\omega_0}}$
(D)
$G(s) = \dfrac{1 - \frac{s}{\omega_0}}{1 + \frac{s}{\omega_0}}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q30 · Linear Algebra · MSQ · 1 mark

Two $n \times n$ 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 $n \times n$ identity matrix.)

(A)
Determinant $(A - 2I) = 0$
(B)
Determinant $(B - 2I) = 0$
(C)
Determinant $(A + B - 2I) = 0$
(D)
Determinant $(A + B - 4I) = 0$

Answer (official key): A, B, D

Worked solution: in your report after you take this paper.

Q31 · Electrical Machines · MSQ · 1 mark

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?

(A)
No-load current drawn would be smaller for operation in the USA compared to that in India
(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
(D)
The eddy current losses in the core would be approximately 44% higher while operating in the USA compared to that in India

Answer (official key): A

Read the worked solution

Q32 · Calculus · Numerical · 1 mark

Given that $\vec{F}(x,y,z) = \sin(y)\,\hat{x} + \cos(x)\,\hat{y} + 5\,\hat{z}$ , the integral

\oiint_{S} \vec{F}(x,y,z)\cdot d\vec{s}

over the unit sphere $S$ centered at the origin evaluates to ________

(Round off to one decimal place)

Answer (official key): 0

Worked solution: in your report after you take this paper.

Q33 · Analog and Digital Electronics · Numerical · 1 mark

In the linear regulator circuit shown, the base to emitter voltage $V_{BE}$ 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)

Answer (official key): 47.5 to 48

Worked solution: in your report after you take this paper.

Q34 · Power Electronics · Numerical · 1 mark

Consider the circuit shown. Assume that the diode D is ideal. The supply voltage $v_s = 325\sin(2\pi 50 t)$ V, $L = 500$ µH, and $R = 10\ \Omega$ . The peak diode current (in amperes) is ______________

(Round off to one decimal place)

Answer (official key): 32.3 to 32.5

Worked solution: in your report after you take this paper.

Q35 · Linear Algebra · Numerical · 1 mark

$A$ is an $m \times m$ skew-symmetric matrix with real-valued entries, and $x$ is an $m$ -dimensional column vector with real-valued entries such that $x^{T}x = 1$ .

The quantity $x^{T}Ax$ evaluates to _________

(Answer in integer)

Answer (official key): 0

Worked solution: in your report after you take this paper.

Q36 · Calculus · MCQ · 2 marks

A time-limited waveform $g(x)$ is specified as follows:

g(x) = \begin{cases} -k, & -\pi < x \le 0 \\ +k, & 0 < x \le \pi \\ 0, & \text{otherwise} \end{cases}

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

f(x) = \sum_{m=-\infty}^{\infty} g(x + 2\pi m), \quad \text{for all } x \in \mathbb{R}

The sum of the coefficients of the third harmonics of the sine and cosine terms in the trigonometric Fourier series expansion of $f(x)$ is $\dfrac{2}{3\pi}$ .

What is the value of $k$ ?

(A)
1
(B)
$\dfrac{1}{2}$
(C)
$\dfrac{1}{3}$
(D)
$\dfrac{1}{4}$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q37 · Analog and Digital Electronics · MCQ · 2 marks

In the circuit shown, the open loop gain of the operational amplifier is $A_0 = 105$ .

What is the voltage gain of the circuit?

(Round off to two decimal places)

(A)
–16.67
(B)
–20.00
(C)
–21.00
(D)
–12.67

Answer (official key): A

Worked solution: in your report after you take this paper.

Q38 · Electrical Machines · MCQ · 2 marks

Three single-phase 11 kV/3.3 kV 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

Answer (official key): D

Worked solution: in your report after you take this paper.

Q39 · Power Systems · MCQ · 2 marks

In the circuit shown, the phase currents are

\bar{I}_A = 572.812 + j\,50.115\ \text{A}

\bar{I}_B = -254.525 - j\,459.175\ \text{A}

\bar{I}_C = -207.083 + j\,444.091\ \text{A}

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 ( $\text{Y}_n\Delta$ ) is 2:1 on every phase, the value of $\bar{I}_{RA}$ , rounded off to three decimal places, is:

(A)
0 A
(B)
$0.653\angle 17.556^\circ$ A
(C)
$537.240\angle 4.105^\circ$ A
(D)
$8.954\angle 4.105^\circ$ A

Answer (official key): D

Worked solution: in your report after you take this paper.

Q40 · Power Systems · MCQ · 2 marks

The operating characteristic of a reactance relay is given by

X \le 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 $\mho$ ) is given by:

(A)
$G^{2} + (B + 0.5)^{2} = \dfrac{1}{4}$
(B)
$B \le 1$
(C)
$G^{2} + (B + 1)^{2} = \dfrac{1}{2}$
(D)
$G^{2} + (B - 1)^{2} = \dfrac{1}{2}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q41 · Power Systems · MCQ · 2 marks

A three-phase two-winding transformer has a voltage transformation ratio $\dfrac{V_P}{V_S} = 0.866 + j\,0.5$ , where $V_P$ is the primary side voltage in p.u., and $V_S$ is the 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 corresponding to the leakage impedance of the transformer referred to the secondary is $y_t$ p.u. Neglect the magnetizing branch.

The $Y_{bus}$ representation of this transformer is:

(A)
$\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} \dfrac{y_t}{0.866 + j0.5} & \dfrac{-y_t}{0.866 + j0.5} \\[6pt] \dfrac{-y_t}{0.866 - j0.5} & \dfrac{y_t}{0.866 - j0.5} \end{bmatrix}\begin{bmatrix} V_P \\ V_S \end{bmatrix}$
(B)
$\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} y_t & -y_t \\ -y_t & y_t \end{bmatrix}\begin{bmatrix} V_P \\ V_S \end{bmatrix}$
(C)
$\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} y_t & \dfrac{-y_t}{0.866 - j0.5} \\[6pt] \dfrac{-y_t}{0.866 + j0.5} & y_t \end{bmatrix}\begin{bmatrix} V_P \\ V_S \end{bmatrix}$
(D)
$\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} y_t & \dfrac{-y_t}{0.866 + j0.5} \\[6pt] \dfrac{-y_t}{0.866 - j0.5} & y_t \end{bmatrix}\begin{bmatrix} V_P \\ V_S \end{bmatrix}$

Answer (official key): D

Worked solution: in your report after you take this paper.

Q42 · Electric Circuits · MCQ · 2 marks

An electrical component has voltage drop $v = V_m \sin(\omega t)$ , when the current through it is $i = I_m \sin(\omega t - \phi)$ .

What is the average power dissipated over a half cycle corresponding to $\phi$ ?

(A)
0
(B)
$V_m I_m \cos\phi$
(C)
$\dfrac{V_m I_m \cos\phi}{2}$
(D)
$\dfrac{V_m I_m \cos\phi}{4}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q43 · Electric Circuits · MCQ · 2 marks

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

The voltage across the capacitor at time instants (in seconds) $t = 0^{+}$ , $t = 0.50$ , and $t = \infty$ , respectively, is:

(A)
8.00 V, 28.00 V, 26.36 V
(B)
8.00 V, 26.36 V, 28.00 V
(C)
10.00 V, 26.36 V, 28.00 V
(D)
10.00 V, 28.00 V, 26.36 V

Answer (official key): B

Worked solution: in your report after you take this paper.

Q44 · Electric Circuits · MCQ · 2 marks

The terminal voltage and current of a linear electrical network shown in Figure (a) are given in the table.

Terminal voltage ( $v_t$ )	Terminal current ( $i_t$ )
18 V	–0.5 A
30 V	0.5 A
36 V	1.0 A

The correct choice for the parameters ( $I_N$ , $R_N$ ) of the Norton equivalent circuit shown in Figure (b) is:

(A)
$I_N$ = 3.0 A, $R_N$ = 24.0 Ω
(B)
$I_N$ = 12.0 A, $R_N$ = 2.0 Ω
(C)
$I_N$ = 2.0 A, $R_N$ = 12.0 Ω
(D)
$I_N$ = 2.0 A, $R_N$ = 24.0 Ω

Answer (official key): C

Worked solution: in your report after you take this paper.

Q45 · Analog and Digital Electronics · MCQ · 2 marks

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

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

(A)
$\overline{\bar{x}y\bar{z}}$
(B)
0
(C)
$\bar{x}(y + z)$
(D)
1

Answer (official key): B

Read the worked solution

Q46 · Analog and Digital Electronics · MCQ · 2 marks

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 = $\overline{\overline{AB} + C}$ , P = 5 mW
(B)
OUT = $\overline{(\bar{A} + \bar{B})C}$ , P = 5 mW
(C)
OUT = $\overline{AB}\,\bar{C} + \bar{C}$ , P = 7.5 mW
(D)
OUT = $\overline{AB}\,C$ , P = 7.5 mW

Answer (official key): D

Read the worked solution

Q47 · Power Electronics · MCQ · 2 marks

Consider the single-phase voltage source inverter circuit feeding an inductive load ( $L$ ). Assume that the power MOSFET switches are ideal. $S_1$ and $S_2$ are switched on during the first 10 µs, and $S_3$ and $S_4$ 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 current ( $i_L$ ) in the steady state is triangular with a peak value of 5 A as shown.

The rms value of the current through the switch $S_1$ is:

(A)
2.88 A
(B)
2.04 A
(C)
3.54 A
(D)
2.50 A

Answer (official key): B

Worked solution: in your report after you take this paper.

Q48 · Power Electronics · MCQ · 2 marks

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 $V_{dc}$ ?

(A)
10.0 V
(B)
15.0 V
(C)
7.5 V
(D)
12.5 V

Answer (official key): C

Worked solution: in your report after you take this paper.

Q49 · Linear Algebra · MCQ · 2 marks

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

(A)
If $p > n$ , then the column vectors must be linearly dependent
(B)
If $p > n$ , then the column vectors must be linearly independent
(C)
If $p = n$ , then the column vectors must be orthogonal
(D)
If $p < n$ , then the column vectors must be linearly independent

Answer (official key): A

Worked solution: in your report after you take this paper.

Q50 · Differential Equations · MCQ · 2 marks

Consider the second-order differential equation

\frac{d^{2}y}{dx^{2}} + \frac{dy}{dx} + y = 0

with initial conditions

y(0) = 1, \qquad \left.\frac{dy}{dx}\right|_{x=0} = 1

The solution is given by

(A)
$y(x) = \exp(-x/2)\left(\cos\left(\frac{\sqrt3 x}{2}\right) + \sqrt3\sin\left(\frac{\sqrt3 x}{2}\right)\right)$
(B)
$y(x) = \exp(-x/2)\left(\cos\left(\frac{\sqrt3 x}{2}\right) + \frac{1}{\sqrt3}\sin\left(\frac{\sqrt3 x}{2}\right)\right)$
(C)
$y(x) = \exp(-x/2)\left(\cos\left(\frac{\sqrt3 x}{2}\right) - \frac{1}{\sqrt3}\sin\left(\frac{\sqrt3 x}{2}\right)\right)$
(D)
$y(x) = \exp(-x/2)\left(\cos\left(\frac{\sqrt3 x}{2}\right) - \sqrt3\sin\left(\frac{\sqrt3 x}{2}\right)\right)$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q51 · Electromagnetic Fields · MCQ · 2 marks

The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two nonintersecting regions with areas $a_1$ and $a_2$ within the loop are subjected to magnetic fields

\vec{B}_1 = \frac{m}{\sqrt2}\sin(\omega t)\,(1\hat{x} + 0\hat{y} + 1\hat{z}),

\vec{B}_2 = -\frac{n}{\sqrt2}\cos(2\omega t + \pi/4)\,(0\hat{x} + 1\hat{y} + 1\hat{z}),

respectively.

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

(A)
$\sqrt{\dfrac{a_1^{2}\omega^{2}m^{2} + 4a_2^{2}\omega^{2}n^{2}}{4}}$
(B)
$\sqrt{\dfrac{a_1^{2}\omega^{2}m^{2} + 4a_2^{2}\omega^{2}n^{2}}{2}}$
(C)
$\sqrt{\dfrac{a_1^{2}\omega^{2}m^{2} - 2a_2^{2}\omega^{2}n^{2}}{2}}$
(D)
$\sqrt{a_1^{2}\omega^{2}m^{2} + 2a_2^{2}\omega^{2}n^{2}}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q52 · Control Systems · MCQ · 2 marks

A system is characterized by the following state equation and output equation ( $u$ : input, $\mathbf{x}$ : state vector, $y$ : output)

\dot{\mathbf{x}} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}\mathbf{x} + \begin{bmatrix} 1 \\ 0 \end{bmatrix}u

y = \begin{bmatrix} 1 & 2 \end{bmatrix}\mathbf{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)
$a = -4$ , $b = -3.25$

Answer (official key): D

Worked solution: in your report after you take this paper.

Q53 · Control Systems · MCQ · 2 marks

A system is represented in state-space form as follows: ( $u$ : input, $\mathbf{x}$ : state vector, $y$ : output)

\dot{\mathbf{x}} = \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix}\mathbf{x} + \begin{bmatrix} 1 \\ 2 \end{bmatrix}u

y = \begin{bmatrix} 1 & 2 \end{bmatrix}\mathbf{x}

Consider the new state vector $\mathbf{z} = \begin{bmatrix} 2 & 1 \\ -1 & 0 \end{bmatrix}\mathbf{x}$

What is the state-space representation of the system in terms of the new state vector $\mathbf{z}$ ?

(A)
$\dot{\mathbf{z}} = \begin{bmatrix} -1 & 4 \\ -1 & -2 \end{bmatrix}\mathbf{z} + \begin{bmatrix} 4 \\ -1 \end{bmatrix}u$ , $y = \begin{bmatrix} 2 & 3 \end{bmatrix}\mathbf{z}$
(B)
$\dot{\mathbf{z}} = \begin{bmatrix} 2 & 3 \\ 0 & 3 \end{bmatrix}\mathbf{z} + \begin{bmatrix} 3 \\ 5 \end{bmatrix}u$ , $y = \begin{bmatrix} 2 & 3 \end{bmatrix}\mathbf{z}$
(C)
$\dot{\mathbf{z}} = \begin{bmatrix} 4 & 9 \\ -2 & -3 \end{bmatrix}\mathbf{z} + \begin{bmatrix} 4 \\ -1 \end{bmatrix}u$ , $y = \begin{bmatrix} 2 & 3 \end{bmatrix}\mathbf{z}$
(D)
$\dot{\mathbf{z}} = \begin{bmatrix} 2 & 1 \\ -4 & 1 \end{bmatrix}\mathbf{z} + \begin{bmatrix} 4 \\ -1 \end{bmatrix}u$ , $y = \begin{bmatrix} 4 & -1 \end{bmatrix}\mathbf{z}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q54 · Power Systems · MSQ · 2 marks

For the balanced 3-phase transmission line shown, consider the following cases:

Case-1: $|V_1| = 1.1$ p.u., $|V_2| = 0.9$ p.u., $Z = 0.75\angle 0^\circ$ p.u. and $\theta_{12} = \theta_1 - \theta_2 = 0^\circ$

Case-2: $|V_1| = 1.1$ p.u., $|V_2| = 0.9$ p.u., $Z = 0.75\angle 90^\circ$ p.u. and $\theta_{12} = \theta_1 - \theta_2 = 90^\circ$

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

Answer (official key): A, D

Worked solution: in your report after you take this paper.

Q55 · Linear Algebra · MSQ · 2 marks

Consider an $n \times n$ orthogonal matrix $A$ with real entries and each column having unit Euclidean norm.

Which of the following statements is/are correct?

(A)
The value of the determinant of $A$ is either $+1$ or $-1$
(B)
The eigenvalues of $A$ have modulus 1
(C)
$\|A\mathbf{x}\| = \|\mathbf{x}\|$ for all $\mathbf{x} \in \mathbb{R}^n$ , and $(A\mathbf{x})^{T}(A\mathbf{y}) \ne \mathbf{x}^{T}\mathbf{y}$ for all distinct $\mathbf{x}, \mathbf{y} \in \mathbb{R}^n$
(D)
$\|A\mathbf{x}\| = \|\mathbf{x}\|$ for all $\mathbf{x} \in \mathbb{R}^n$ , and $(A\mathbf{x})^{T}(A\mathbf{y}) = \mathbf{x}^{T}\mathbf{y}$ for all $\mathbf{x}, \mathbf{y} \in \mathbb{R}^n$

Answer (official key): A, B, D

Worked solution: in your report after you take this paper.

Q56 · Linear Algebra · MSQ · 2 marks

Consider the system of linear equations: $A\mathbf{x} = \mathbf{b}$ , where $A$ is an $n \times n$ matrix, and $\mathbf{x}$ and $\mathbf{b}$ 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 $A^{m}\mathbf{x} = \mathbf{b}$ also has a unique solution for $m = 1, 2, 3, \ldots$
(C)
$\operatorname{rank}(A) = \operatorname{rank}(A^{m})$ , for $m = 1, 2, 3, \ldots$
(D)
$\operatorname{rank}(A) < \operatorname{rank}([A \mid \mathbf{b}])$ , where $[A \mid \mathbf{b}]$ denotes the augmented matrix

Answer (official key): A, B, C

Worked solution: in your report after you take this paper.

Q57 · Electrical and Electronic Measurements · Numerical · 2 marks

The resistance values of the Wheatstone bridge shown are:

P = 2000\ \Omega, \quad Q = 500\ \Omega, \quad R = 3000\ \Omega .

The battery voltage $E$ = 50 V. The battery has an internal resistance of 1 Ω and the Galvanometer (G) has a resistance of 50 Ω.

The value of the resistance $S$ for balanced condition is _____________ Ω

(Answer in integer)

Answer (official key): 750

Worked solution: in your report after you take this paper.

Q58 · Power Systems · Numerical · 2 marks

A system with two generators G1 and G2 (without generator limits) is shown. The total load on the system is 1184 MW.

The expressions for the cost of generation ( $C_1$ and $C_2$ ) and real power loss ( $P_{Loss}$ ) are as follows:

C_1(P_{G1}) = 1000 + 50 P_{G1} + 0.01 P_{G1}^{2}\ \text{Rs/MWh}

C_2(P_{G2}) = 2000 + 50 P_{G2} + 0.001 P_{G2}^{2}\ \text{Rs/MWh}

P_{Loss} = 0.001 (P_{G2} - 50)^{2}\ \text{MW}

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 $\lambda = 70.25$ for optimal generation.

Answer (official key): Marks to all

Everyone who took this paper got the marks for this question. Marks to all in GATE

Worked solution: in your report after you take this paper.

Q59 · Electrical Machines · Numerical · 2 marks

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)

Answer (official key): 0.09

Worked solution: in your report after you take this paper.

Q60 · Electric Circuits · Numerical · 2 marks

Consider the two-port network shown. For maximum power transfer to the resistive load ( $R_L$ ), the value of $R_L$ should be__________ Ω

(Round off to two decimal places)

Answer (official key): 2.81 to 2.91

Read the worked solution

Q61 · Power Electronics · Numerical · 2 marks

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

Given $v_s = 100\sin(2\pi 50 t)$ V, $V_{dc} = 50$ V, and $R = 10\ \Omega$ , the average value of the current through the diode is ___________ A

(Round off to two decimal places)

Answer (official key): 1.04 to 1.14

Read the worked solution

Q62 · Complex Variables · Numerical · 2 marks

The magnitude of the contour integral

\oint_{C} \left(\frac{(z+1)^{2}}{(z-i)(z-2)}\right) dz

over the contour $C: |z - 2 - i| = 3/2$ is ______

(Round off to two decimal places)

Note: $z$ is a complex variable and $i = \sqrt{-1}$

Answer (official key): 25 to 25.6

Worked solution: in your report after you take this paper.

Q63 · Electromagnetic Fields · Numerical · 2 marks

A uniform spherical volume charge distribution of radius 2 m, centered at the origin, has a strength of $\dfrac{3}{\pi}\times 10^{-6}$ C/m³. A point charge of strength $\pi \times 8.854 \times 10^{-12}$ 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

(Round off to two decimal places)

Answer (official key): 0.38 to 0.42

Worked solution: in your report after you take this paper.

Q64 · Probability and Statistics · Numerical · 2 marks

Let $X$ and $Y$ be two real-valued random variables with

E(X) = 1,\quad E(Y) = 2,\quad E(X^{2}) = 4,\quad E(Y^{2}) = 9,\quad E(XY) = 0.9,

where $E$ denotes the expectation operator.

The value of $\alpha$ that minimizes $E\!\left[(X - \alpha Y)^{2}\right]$ is __________

(Round off to one decimal place)

Answer (official key): 0.1

Worked solution: in your report after you take this paper.

Q65 · Calculus · Numerical · 2 marks

The integral

\frac{1}{\pi}\int_{0}^{\infty} \frac{x^{2026}}{(1 + x^{2026})(1 + x^{2})}\,dx

evaluates to _________

(Round off to two decimal places)

Answer (official key): 0.25

Worked solution: in your report after you take this paper.

All 65 questions of GATE 2026 EE

Q1 · General Aptitude · MCQ · 1 mark

Q2 · General Aptitude · MCQ · 1 mark

Q3 · General Aptitude · MCQ · 1 mark

Q4 · General Aptitude · MCQ · 1 mark

Q5 · General Aptitude · MCQ · 1 mark

Q6 · General Aptitude · MCQ · 2 marks

Q7 · General Aptitude · MCQ · 2 marks

Q8 · General Aptitude · MCQ · 2 marks

Q9 · General Aptitude · MCQ · 2 marks

Q10 · General Aptitude · MCQ · 2 marks

Q11 · Signals and Systems · MCQ · 1 mark

Q12 · Signals and Systems · MCQ · 1 mark

Q13 · Control Systems · MCQ · 1 mark

Q14 · Differential Equations · MCQ · 1 mark

Q15 · Electromagnetic Fields · MCQ · 1 mark

Q16 · Electromagnetic Fields · MCQ · 1 mark

Q17 · Electrical Machines · MCQ · 1 mark

Q18 · Power Systems · MCQ · 1 mark

Q19 · Power Systems · MCQ · 1 mark

Q20 · Electrical Machines · MCQ · 1 mark

Q21 · Electrical Machines · MCQ · 1 mark

Q22 · Electrical Machines · MCQ · 1 mark

Q23 · Electric Circuits · MCQ · 1 mark

Q24 · Electric Circuits · MCQ · 1 mark

Q25 · Electric Circuits · MCQ · 1 mark

Q26 · Electric Circuits · MCQ · 1 mark

Q27 · Power Electronics · MCQ · 1 mark

Q28 · Power Electronics · MCQ · 1 mark

Q29 · Control Systems · MCQ · 1 mark

Q30 · Linear Algebra · MSQ · 1 mark

Q31 · Electrical Machines · MSQ · 1 mark

Q32 · Calculus · Numerical · 1 mark

Q33 · Analog and Digital Electronics · Numerical · 1 mark

Q34 · Power Electronics · Numerical · 1 mark

Q35 · Linear Algebra · Numerical · 1 mark

Q36 · Calculus · MCQ · 2 marks

Q37 · Analog and Digital Electronics · MCQ · 2 marks

Q38 · Electrical Machines · MCQ · 2 marks

Q39 · Power Systems · MCQ · 2 marks

Q40 · Power Systems · MCQ · 2 marks

Q41 · Power Systems · MCQ · 2 marks

Q42 · Electric Circuits · MCQ · 2 marks

Q43 · Electric Circuits · MCQ · 2 marks

Q44 · Electric Circuits · MCQ · 2 marks

Q45 · Analog and Digital Electronics · MCQ · 2 marks

Q46 · Analog and Digital Electronics · MCQ · 2 marks

Q47 · Power Electronics · MCQ · 2 marks

Q48 · Power Electronics · MCQ · 2 marks

Q49 · Linear Algebra · MCQ · 2 marks

Q50 · Differential Equations · MCQ · 2 marks

Q51 · Electromagnetic Fields · MCQ · 2 marks

Q52 · Control Systems · MCQ · 2 marks

Q53 · Control Systems · MCQ · 2 marks

Q54 · Power Systems · MSQ · 2 marks

Q55 · Linear Algebra · MSQ · 2 marks

Q56 · Linear Algebra · MSQ · 2 marks

Q57 · Electrical and Electronic Measurements · Numerical · 2 marks

Q58 · Power Systems · Numerical · 2 marks

Q59 · Electrical Machines · Numerical · 2 marks

Q60 · Electric Circuits · Numerical · 2 marks

Q61 · Power Electronics · Numerical · 2 marks

Q62 · Complex Variables · Numerical · 2 marks

Q63 · Electromagnetic Fields · Numerical · 2 marks

Q64 · Probability and Statistics · Numerical · 2 marks

Q65 · Calculus · Numerical · 2 marks