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GATE EE 2026 Set 1

All 65 solved GATE EE 2026 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

Paper marks

100

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MCQ · NAT · MSQ

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Difficulty mixEasy 20Medium 37Hard 8

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65 of 65 questions

Question typeDifficultyYour progress

General Aptitude (GA)

1
Q1MCQ1 markEasy
‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the ________.
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Question
$‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the________.$
Your answer
Choose one option, then check your answer.
A. $object$ B. $subject$ C. $predicate$ D. $verb$
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$Correct answer (A) object Step-by-step solution In the sentence "The shopkeeper sells lemons", "The shopkeeper" is the subject (the doer of the action), "sells" is the transitive verb, and "lemons" is the direct object (the entity receiving the action). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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2
Q2MCQ1 markEasy
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…
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Question
$The figure below is supposed to show three non-overlapping shapes - one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by ‘?’ and completes the oval and the two triangles?$
Your answer
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A. $P$ B. $Q$ C. $R$ D. $S$
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$Correct answer (A) P [figure] Step-by-step solution By analyzing the missing segments required to complete the three shapes: the top part of the missing square needs a curved segment to complete the oval, and the bottom corners need specific triangular segments to complete the two triangles. Figure P provides the exact segments that align with the existing parts to form a complete oval and two complete triangles without any overlaps. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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3
Q3MCQ1 markEasy
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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Question
$y = x^2$
Your answer
Choose one option, then check your answer.
A. $0$ B. $1$ C. $2$ D. $3$
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$x^2 = -x^2 - 2x - 1$
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4
Q4MCQ1 markEasy
‘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.…
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Question
$‘If Anish had scored hundred runs in today’s match, he would have been made the captain of his team. He would have then become the youngest captain in his team’s history. Unfortunately, he got out without scoring any runs. Hence, there won’t be any change in the captaincy for now.’ Based on the paragraph above, which one of the following statements is true?$
Your answer
Choose one option, then check your answer.
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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$Correct answer (C) The current captain is older than Anish. Step-by-step solution The passage states that if Anish had scored a hundred runs, he would have become the youngest captain in the team's history. Since he did not score any runs, he did not become the captain. This implies that the current captain is not Anish and must be older than Anish would have been as the 'youngest' captain. Therefore, the current captain is older than Anish. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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5
Q5MCQ1 markEasy
Which one of the following figures P, Q, R, or S, correctly shows the $45^\circ$ clockwise-rotated version of figure (I)? [figure] [figure]
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Question
$45^\circ$
Your answer
Choose one option, then check your answer.
A. $P$ B. $Q$ C. $R$ D. $S$
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$45^\circ$
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6
Q6MCQ2 marksEasy
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…
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Question
$Match the words in Column I with their synonyms in Column II. Column I Column II (i) Lonely (p) Verbatim (ii) Literal (q) Solitary (iii) Lousy (r) Deadly (iv) Lethal (s) Terrible$
Your answer
Choose one option, then check your answer.
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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$Correct answer (A) (i)-(q); (ii)-(p); (iii)-(s); (iv)-(r) Step-by-step solution The correct matches for the synonyms are: (i) Lonely: Solitary (q) (ii) Literal: Verbatim (p) (iii) Lousy: Terrible (s) (iv) Lethal: Deadly (r) This corresponds to the sequence (i)-(q); (ii)-(p); (iii)-(s); (iv)-(r), which is option (A). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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7
Q7MCQ2 marksMedium
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…
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Question
$\overline{PQ}$
Your answer
Choose one option, then check your answer.
A. $40^\circ$ B. $50^\circ$ C. $60^\circ$ D. $80^\circ$
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$PQ$
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8
Q8MCQ2 marksMedium
Based on the relationship between each polygon and the number inside it, the value of ‘X’ is ______ [figure]
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Question
$Based on the relationship between each polygon and the number inside it, the value of ‘X’ is______$
Your answer
Choose one option, then check your answer.
A. $720$ B. $596$ C. $24$ D. $240$
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$n$
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9
Q9MCQ2 marksMedium
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…
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Question
$Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules: Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON. Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF. The state of any bulb not meeting the conditions above is left unchanged. The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure. The number of bulbs which are ON at the end of Step 8 is______$
Your answer
Choose one option, then check your answer.
A. $5$ B. $4$ C. $3$ D. $0$
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$Correct answer (B) 4 Step-by-step solution Let's represent ON as 1 and OFF as 0 for the 7 bulbs: Initial : 0 0 0 1 0 0 0 Step 1 : B3 and B5 turn ON (Rule 1: exactly one ON neighbor). B4 stays ON (Rule 3: no condition met). Result: 0 0 1 1 1 0 0 Step 2 : B2 and B6 turn ON (Rule 1: exactly one ON neighbor). B4 turns OFF (Rule 2: both neighbors ON). Result: 0 1 1 0 1 1 0 Step 3 : B1 and B7 turn ON (Rule 1: exactly one ON neighbor). B4 stays OFF (Rule 1: has two ON neighbors, not exactly one). Result: 1 1 1 0 1 1 1 Step 4 : B2 and B6 turn OFF (Rule 2: both neighbors ON). B1, B3, B5, B7 stay ON (Rule 3). Result: 1 0 1 0 1 0 1 Step 5 : B2, B4, B6 stay OFF (Rule 1: each has two ON neighbors). B1, B3, B5, B7 stay ON (Rule 3). Result: 1 0 1 0 1 0 1 Since Step 5 is identical to Step 4, the system has reached a steady state. Thus, at Step 8, the configuration will still be 1 0 1 0 1 0 1. The number of ON bulbs is 4. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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10
Q10MCQ2 marksEasy
$P$ and $Q$ are two positive integers such that $P^2 = Q^2 + 13$ . The product of the numbers $P$ and $Q$ is _________
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Question
$P$
Your answer
Choose one option, then check your answer.
A. $13$ B. $26$ C. $39$ D. $42$
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$P^2 = Q^2 + 13 \Rightarrow P^2 - Q^2 = 13 \Rightarrow (P - Q)(P + Q) = 13$
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Column I	Column II
(i) Lonely	(p) Verbatim
(ii) Literal	(q) Solitary
(iii) Lousy	(r) Deadly
(iv) Lethal	(s) Terrible

Electrical Engineering (EE)

11
Q11MCQ1 markMedium
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…
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Question
$x[n] = 0.9^{|n|}$
Your answer
Choose one option, then check your answer.
A. $|z| > 0.9$ B. $|z| < 0.9$ C. $0.9 < |z| < 1/0.9$ D. $\{z \text{ such that } |z| < 0.9 \} \cup \{ z \text{ such that } |z| > 1/0.9 \}$
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$x[n] = 0.9^{|n|}$
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12
Q12MCQ1 markMedium
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…
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Question
$x_c(t)$
Your answer
Choose one option, then check your answer.
A. $x[n]$ B. $x[n]$ C. $x[n]$ D. $x[n]$
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$x[n]$
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13
Q13MCQ1 markMedium
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…
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Question
$Y(s) = \frac{100}{s(s + 100)}$
Your answer
Choose one option, then check your answer.
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. $T_r = 22, T_s = 40.4, T_c = 10.1$
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$Y(s) = \frac{100}{s(s+100)}$
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14
Q14MCQ1 markEasy
Consider the following differential equation: $t^2 \frac{d^2y}{dt^2} + 7t \frac{dy}{dt} + 8ty = 10 \sin(t)$ Which one of the following options is correct?
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Question
$t^2 \frac{d^2y}{dt^2} + 7t \frac{dy}{dt} + 8ty = 10 \sin(t)$
Your answer
Choose one option, then check your answer.
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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$t^2 \frac{d^2y}{dt^2} + 7t \frac{dy}{dt} + 8ty = 10 \sin(t)$
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15
Q15MCQ1 markEasy
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…
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Question
$R$
Your answer
Choose one option, then check your answer.
A. $\frac{Qq}{4\pi\epsilon R}$ B. $\frac{Qq}{4\pi\epsilon R^2}$ C. $0$ D. $\frac{q}{4\pi\epsilon R} \times \frac{Q}{2\pi R}$
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$dQ$
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16
Q16MCQ1 markEasy
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…
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Question
$\vec{v} = 5 \hat{x}$
Your answer
Choose one option, then check your answer.
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. $The magnetic field does not exert any force on the charge$
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$q$
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17
Q17MCQ1 markMedium
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?
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Question
$A 15 kVA, 1100 V/220 V, single-phase two-winding transformer is configured as a 1.32 kV/1.1 kV autotransformer. What will be the rating of the autotransformer?$
Your answer
Choose one option, then check your answer.
A. $60 kVA$ B. $75 kVA$ C. $90 kVA$ D. $100 kVA$
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$S_{2w} = 15$
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18
Q18MCQ1 markMedium
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…
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Question
$N$
Your answer
Choose one option, then check your answer.
A. $2N \times 2N$ B. $(2N - 1 - P) \times (2N - 1 - P)$ C. $(2N - Q) \times (2N - Q)$ D. $(P + Q) \times (P + Q)$
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$N$
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19
Q19MCQ1 markMedium
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…
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Question
$\bar{V}_A$
Your answer
Choose one option, then check your answer.
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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$V_0 = \frac{1}{3}(V_A + V_B + V_C)$
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20
Q20MCQ1 markEasy
A certain application requires power at a frequency of $16.67\text{ Hz}$ , while the available grid frequency is $50\text{ Hz}$ . A 3-phase synchronous motor connected to the…
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Question
$16.67\text{ Hz}$
Your answer
Choose one option, then check your answer.
A. $2, 6$ B. $6, 2$ C. $4, 6$ D. $6, 4$
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$N_s$
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21
Q21MCQ1 markEasy
Which one of the following options is correct regarding the typical double-squirrel-cage structure used in induction motors?
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Question
$Which one of the following options is correct regarding the typical double-squirrel-cage structure used in induction motors?$
Your answer
Choose one option, then check your answer.
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. $The purpose of the double-squirrel-cage structure is to lower the effective rotor resistance at starting$
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$Correct answer (A) At starting, a larger portion of the rotor current flows in the outer cage Step-by-step solution In a double-squirrel-cage induction motor, the outer cage is designed with high resistance and low reactance, while the inner cage has low resistance and high reactance. At starting, the rotor frequency is high (equal to the supply frequency), which makes the reactance of the inner cage very high. Consequently, the rotor current is forced to flow primarily through the outer cage. This high-resistance path provides the high starting torque required. At rated speed, the slip and rotor frequency are low, making the reactance of the inner cage small, so the current flows through the low-resistance inner cage for efficient operation. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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22
Q22MCQ1 markMedium
The figure shows the single-line diagram of a synchronous generator delivering $P = 50\text{ MW}$ of power at unity power factor to an infinite bus. [figure] $I_s$ denotes the…
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Question
$P = 50\text{ MW}$
Your answer
Choose one option, then check your answer.
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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$P = \frac{EV}{X_s} \sin \delta$
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23
Q23MCQ1 markEasy
A circuit with ideal elements is shown. [figure] Which one of the following options correctly identifies all the linear elements in the circuit?
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Question
$A circuit with ideal elements is shown. Which one of the following options correctly identifies all the linear elements in the circuit?$
Your answer
Choose one option, then check your answer.
A. $R only$ B. $R, L, and C only$ C. $D only$ D. $L, C, and D only$
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$R$
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24
Q24MCQ1 markMedium
For the circuit shown, which one of the following options correctly identifies the Thevenin’s equivalent parameters between nodes Y and Z? [figure]
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Question
$For the circuit shown, which one of the following options correctly identifies the Thevenin’s equivalent parameters between nodes Y and Z?$
Your answer
Choose one option, then check your answer.
A. $V_{TH} = 100\text{ V}, R_{TH} = 10\text{ k}\Omega$ B. $V_{TH} = 140\text{ V}, R_{TH} = 0\text{ }\Omega$ C. $V_{TH} = 100\text{ V}, R_{TH} = 0\text{ }\Omega$ D. $V_{TH} = 140\text{ V}, R_{TH} = 10\text{ k}\Omega$
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$V_{TH}$
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25
Q25MCQ1 markMedium
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? [figure]
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Question
$k_1, k_2, k_3,$
Your answer
Choose one option, then check your answer.
A. $k_1 = 1, k_4 = -1/3,$ B. $k_2 = -2, k_3 = +1/3,$ C. $k_1 = 2, k_2 = 0.5, k_3 = -2/3, k_4 = -3$ D. $k_1 = 2, k_2 = -0.5, k_3 = -2/3, k_4 = +3$
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$V_D = V_X$
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26
Q26MCQ1 markMedium
A single-phase voltage source $v_s = 325 \sin(2\pi 50t)$ V delivers a current, $i = 12 \sin(2\pi 50t) + 9 \sin(2\pi 150t)$ A to a load. The load power factor, correct up to two…
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Question
$v_s = 325 \sin(2\pi 50t)$
Your answer
Choose one option, then check your answer.
A. $1.00$ B. $0.80$ C. $0.65$ D. $0.57$
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$P$
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27
Q27MCQ1 markEasy
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. [figure] What…
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Question
$The figure shows a straight-line approximation for the forward characteristics of a power diode. A continuous on-state current of 15 A is flowing through the diode. What is the power loss in the diode?$
Your answer
Choose one option, then check your answer.
A. $32.8 W$ B. $21.2 W$ C. $18.6 W$ D. $23.1 W$
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$V_0 = 1.0$
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28
Q28MCQ1 markMedium
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…
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Question
$v_g$
Your answer
Choose one option, then check your answer.
A. $R_1 > R_2 > R_3$ B. $R_1 > R_3 > R_2$ C. $R_3 > R_2 > R_1$ D. $R_2 > R_3 > R_1$
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$D$
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29
Q29MCQ1 markEasy
The asymptotic Bode magnitude plot of a system is shown. [figure] Which one of the following options best represents the transfer function of the system?
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Question
$The asymptotic Bode magnitude plot of a system is shown. Which one of the following options best represents the transfer function of the system?$
Your answer
Choose one option, then check your answer.
A. $G(s) = \frac{1 + \frac{s}{\omega_0}}{\frac{s}{\omega_0}}$ B. $G(s) = \frac{\frac{s}{\omega_0}}{1 + \frac{s}{\omega_0}}$ C. $G(s) = \frac{1 + \frac{s}{\omega_0}}{1 - \frac{s}{\omega_0}}$ D. $G(s) = \frac{1 - \frac{s}{\omega_0}}{1 + \frac{s}{\omega_0}}$
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$-20$
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30
Q30MSQ1 markMedium
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…
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Question
$n \times n$
Your answer
Select all that apply, then check your answer.
A. $( A - 2I ) = 0$ B. $( B - 2I ) = 0$ C. $( A + B - 2I ) = 0$ D. $( A + B - 4I ) = 0$
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$\mathbf{x} \neq 0$
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31
Q31MSQ1 markMedium
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…
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Question
$A 220V/12V single-phase transformer is designed for use in India and rated 100 VA at 50 Hz. Later, this unit is shipped to the USA where it is used as a 110V/6V transformer at 60 Hz. Which of the following statements is/are correct?$
Your answer
Select all that apply, then check your answer.
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. $The eddy current losses in the core would be approximately 44% higher while operating in the USA compared to that in India$
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$B_m$
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32
Q32NAT1 markEasy
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…
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Question
$\vec{F}(x, y, z) = \sin(y) \hat{x} + \cos(x) \hat{y} + 5 \hat{z}$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
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$\oiint_S \vec{F} \cdot d\vec{s} = \iiint_V (\nabla \cdot \vec{F}) dV$
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33
Q33NAT1 markMedium
In the linear regulator circuit shown, the base to emitter voltage $V_{BE}$ of the BJT is $0.6\text{ V}$ . The Zener diode clamps the base voltage to $5.4\text{ V}$ . Ignore the…
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Question
$V_{BE}$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
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$V_{out}$
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34
Q34NAT1 markMedium
Consider the circuit shown. Assume that the diode $D$ is ideal. The supply voltage $v_s = 325 \sin(2\pi 50t)$ V, $L = 500 \mu\text{H}$ , and $R = 10 \Omega$ . The peak diode current…
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Question
$D$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
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$R-L$
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35
Q35NAT1 markEasy
$A$ 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…
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Question
$A$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
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$A$
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36
Q36MCQ2 marksMedium
A time-limited waveform $g(x)$ is specified as follows: $g(x) = \begin{cases} -k, & -\pi < x \leq 0 \\ +k, & 0 < x \leq \pi \\ 0, & \text{otherwise} \end{cases}$ A new waveform…
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Question
$g(x)$
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A. $1$ B. $\frac{1}{2}$ C. $\frac{1}{3}$ D. $\frac{1}{4}$
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$f(x)$
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37
Q37MCQ2 marksMedium
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) [figure]
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Question
$A_0 = 105$
Your answer
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A. $-16.67$ B. $-20.00$ C. $-21.00$ D. $-12.67$
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$A_0 = 105$
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38
Q38MCQ2 marksHard
Three single-phase $11\text{ kV}/3.3\text{ kV}$ transformers are connected to form a three-phase transformer bank with connections as shown. [figure] Considering ABC phase…
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Question
$11\text{ kV}/3.3\text{ kV}$
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A. $Dd0$ B. $Dd4$ C. $Dd6$ D. $Dd10$
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$V_{AB}$
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39
Q39MCQ2 marksHard
In the circuit shown, the phase currents are $I_A = 572.812 + j50.115$ A $I_B = -254.525 - j459.175$ A $I_C = -207.083 + j444.091$ A [figure] Given that the CTs are ideal with no…
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Question
$I_A = 572.812 + j50.115$
Your answer
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A. $0 A$ B. $0.653 \angle 17.556^o$ C. $537.240 \angle 4.105^o$ D. $8.954 \angle 4.105^o$
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$I_0$
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40
Q40MCQ2 marksMedium
The operating characteristic of a reactance relay is given by $X \leq 1 \Omega$ , where $X$ is the reactance calculated by the relay. Its operating characteristic in the admittance…
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Question
$X \leq 1 \Omega$
Your answer
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A. $G^2 + (B + 0.5)^2 \geq \frac{1}{4}$ B. $B \geq 1$ C. $(G - 1)^2 + B^2 \leq \frac{1}{2}$ D. $G^2 + (B - 1)^2 \geq \frac{1}{2}$
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$X$
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41
Q41MCQ2 marksHard
A three-phase two-winding transformer has a voltage transformation ratio $\frac{V_P}{V_S} = 0.866 + j0.5$ , where $V_P$ is the primary side voltage in p.u., and $V_S$ is the…
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Question
$\frac{V_P}{V_S} = 0.866 + j0.5$
Your answer
Choose one option, then check your answer.
A. $\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} \frac{y_t}{0.866 + j0.5} & -\frac{y_t}{0.866 + j0.5} \\ -\frac{y_t}{0.866 + j0.5} & \frac{y_t}{0.866 + j0.5} \end{bmatrix} \begin{bmatrix} V_P \\ V_S \end{bmatrix}$ 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. $\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} y_t & -\frac{y_t}{0.866 + j0.5} \\ -\frac{y_t}{0.866 + j0.5} & y_t \end{bmatrix} \begin{bmatrix} V_P \\ V_S \end{bmatrix}$ D. $\begin{bmatrix} I_P \\ I_S \end{bmatrix} = \begin{bmatrix} y_t & -\frac{y_t}{0.866 - j0.5} \\ -\frac{y_t}{0.866 + j0.5} & y_t \end{bmatrix} \begin{bmatrix} V_P \\ V_S \end{bmatrix}$
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$a = \frac{V_P}{V_S}$
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42
Q42MCQ2 marksMedium
An electrical component has voltage drop $v = V_m \sin(\omega t)$ , when the current through it is $i = I_m \sin(\omega t - \theta)$ . What is the average power dissipated over a…
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Question
$v = V_m \sin(\omega t)$
Your answer
Choose one option, then check your answer.
A. $0$ B. $V_m I_m \cos \theta$ C. $\frac{V_m I_m}{2} \cos \theta$ D. $\frac{V_m I_m}{4} \cos \theta$
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$p(t)$
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43
Q43MCQ2 marksMedium
The electrical network shown has an independent voltage source ( $10 \text{ V}$ ) and a current source ( $1 \text{ u}(t) \text{ mA}$ ). The voltage across the capacitor at time…
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Question
$10 \text{ V}$
Your answer
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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. $10.00 V, 28.00 V, 26.36 V$
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$10 \text{ V}$
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44
Q44MCQ2 marksMedium
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 ( $i_t$ ) |…
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Question
$v_t$
Your answer
Choose one option, then check your answer.
A. $I_N = 3.0 \text{ A}$ B. $I_N = 12.0 \text{ A}$ C. $I_N = 2.0 \text{ A}$ D. $I_N = 2.0 \text{ A}$
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$v_t$
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45
Q45MCQ2 marksMedium
The digital circuit shown has 3 inputs ( $x$ , $y$ , and $z$ ). The simplified logical expression for the output (OUT) is:
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$x$
Your answer
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A. $\bar{x}yz$ B. $0$ C. $x(y+z)$ D. $1$
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$x, y, z$
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46
Q46MCQ2 marksMedium
The MOSFET switches shown in the circuit are ideal. [figure] Which of the following is the correct option for Boolean logical expression of the output (OUT), and the maximum…
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Question
$The MOSFET switches shown in the circuit are ideal. Which of the following is the correct option for Boolean logical expression of the output (OUT), and the maximum possible power (P) consumed by the circuit?$
Your answer
Choose one option, then check your answer.
A. $OUT = \overline{AB} + \overline{C}, P = 5 \text{ mW}$ B. $OUT = \overline{(A + B)\overline{C}}, P = 5 \text{ mW}$ C. $OUT = A\overline{B}\overline{C} + \overline{C}, P = 7.5 \text{ mW}$ D. $OUT = \overline{A}\overline{B}C, P = 7.5 \text{ mW}$
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$V_{DD} = 5 \text{ V}$
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47
Q47MCQ2 marksMedium
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…
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Question
$L$
Your answer
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A. $2.88\text{ A}$ B. $2.04\text{ A}$ C. $3.54\text{ A}$ D. $2.50\text{ A}$
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$S_1$
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48
Q48MCQ2 marksHard
Consider the boost converter circuit shown. Assume that the semiconductor devices are ideal. In steady state, the inductor current rises linearly from $0\text{ A}$ to $6\text{ A}$ …
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Question
$0\text{ A}$
Your answer
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A. $10.0 V$ B. $15.0 V$ C. $7.5 V$ D. $12.5 V$
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$i_L$
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49
Q49MCQ2 marksEasy
Which one of the following statements is ALWAYS correct about a collection of $p$ column vectors, each having $n$ real-valued entries?
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$p$
Your answer
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A. $p > n$ B. $p > n$ C. $p = n$ D. $p < n$
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$n$
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50
Q50MCQ2 marksEasy
Consider the second-order differential equation $\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$ with initial conditions $y(0) = 1, \quad \left. \frac{dy}{dx} \right|_{x=0} = 1$ …
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Question
$\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$
Your answer
Choose one option, then check your answer.
A. $y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) + \sqrt{3} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)$ B. $y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) + \frac{1}{\sqrt{3}} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)$ C. $y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) - \frac{1}{\sqrt{3}} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)$ D. $y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) - \sqrt{3} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)$
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$m^2 + m + 1 = 0$
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51
Q51MCQ2 marksHard
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…
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Question
$a_1$
Your answer
Choose one option, then check your answer.
A. $\sqrt{\frac{a_1^2 \omega^2 m^2 + 4 a_2^2 \omega^2 n^2}{4}}$ B. $\sqrt{\frac{a_1^2 \omega^2 m^2 + 4 a_2^2 \omega^2 n^2}{2}}$ C. $\sqrt{\frac{a_1^2 \omega^2 m^2 - 2 a_2^2 \omega^2 n^2}{2}}$ D. $\sqrt{a_1^2 \omega^2 m^2 + 2 a_2^2 \omega^2 n^2}$
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$d\vec{A} = dA \hat{z}$
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52
Q52MCQ2 marksMedium
A system is characterized by the following state equation and output equation ( $u$ : input, $\mathbf{x}$ : state vector, $y$ : output)…
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Question
$u$
Your answer
Choose one option, then check your answer.
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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$A = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}$
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53
Q53MCQ2 marksMedium
A system is represented in state-space form as follows: ( $u$ : input, $\mathbf{x}$ : state vector, $y$ : output)…
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Question
$u$
Your answer
Choose one option, then check your answer.
A. $\dot{\mathbf{z}} = \begin{bmatrix} -1 & 4 \\ -1 & -2 \end{bmatrix} \mathbf{z} + \begin{bmatrix} 4 \\ -1 \end{bmatrix} u$ B. $\dot{\mathbf{z}} = \begin{bmatrix} 2 & 3 \\ 0 & 3 \end{bmatrix} \mathbf{z} + \begin{bmatrix} 3 \\ 5 \end{bmatrix} u$ C. $\dot{\mathbf{z}} = \begin{bmatrix} 4 & 9 \\ -2 & -3 \end{bmatrix} \mathbf{z} + \begin{bmatrix} 4 \\ -1 \end{bmatrix} u$ D. $\dot{\mathbf{z}} = \begin{bmatrix} 2 & 1 \\ -4 & 1 \end{bmatrix} \mathbf{z} + \begin{bmatrix} 4 \\ -1 \end{bmatrix} u$
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$\mathbf{z} = T\mathbf{x}$
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54
Q54MSQ2 marksMedium
For the balanced 3-phase transmission line shown, consider the following cases: [figure] **Case-1:**…
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Question
$|V_1| = 1.1 \text{ p.u.}, |V_2| = 0.9 \text{ p.u.}, Z = 0.75 \angle 0^\circ \text{ p.u.}$
Your answer
Select all that apply, then check your answer.
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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$I = \frac{V_1 \angle \theta_{12} - V_2 \angle 0}{Z \angle \theta_z}$
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55
Q55MSQ2 marksMedium
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?
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Question
$n \times n$
Your answer
Select all that apply, then check your answer.
A. $A$ B. $A$ C. $\| A\mathbf{x} \| = \| \mathbf{x} \|$ D. $\| A\mathbf{x} \| = \| \mathbf{x} \|$
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$A$
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56
Q56MSQ2 marksMedium
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.…
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Question
$A\mathbf{x} = \mathbf{b}$
Your answer
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A. $A^{-1}$ B. $A^m\mathbf{x} = \mathbf{b}$ C. $\text{rank}(A) = \text{rank}(A^m)$ D. $\text{rank}(A) < \text{rank}([A \mid \mathbf{b}])$
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$n \times n$
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57
Q57NAT2 marksEasy
The resistance values of the Wheatstone bridge shown are: $P = 2000\ \Omega$ , $Q = 500\ \Omega$ , $R = 3000\ \Omega$ . The battery voltage $E = 50\text{V}$ . The battery has an…
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Question
$P = 2000\ \Omega$
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$\frac{P}{Q} = \frac{R}{S}$
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58
Q58NAT2 marksHard
A system with two generators G1 and G2 (without generator limits) is shown. [figure] The total load on the system is 1184 MW. The expressions for the cost of generation ( $C_1$ and…
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Question
$C_1$
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$\frac{dC_i}{dP_{Gi}} = \lambda \left(1 - \frac{\partial P_{Loss}}{\partial P_{Gi}}\right)$
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59
Q59NAT2 marksMedium
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…
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Question
$\Omega$
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Numerical answer
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$N_s = \frac{120f}{P} = \frac{120 \times 50}{4} = 1500 \text{ rpm}$
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60
Q60NAT2 marksMedium
Consider the two-port network shown. For maximum power transfer to the resistive load ( $R_L$ ), the value of $R_L$ should be__________ $\Omega$ (Round off to two decimal places)…
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$R_L$
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$R_L$
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61
Q61NAT2 marksMedium
Consider the circuit shown. Assume that the diode ( $D$ ) is ideal. Given $v_s = 100 \sin(2\pi 50t)$ V, $V_{dc} = 50$ V, and $R = 10 \Omega$ , the average value of the current…
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$D$
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$I_{avg}$
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62
Q62NAT2 marksMedium
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)…
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Question
$\oint_C \left( \frac{(z+1)^2}{(z-i)(z-2)} \right) dz$
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$f(z) = \frac{(z+1)^2}{(z-i)(z-2)}$
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63
Q63NAT2 marksHard
A uniform spherical volume charge distribution of radius $2$ m, centered at the origin, has a strength of $\frac{3}{\pi} \times 10^{-6}$ C/m $^3$ . A point charge of strength…
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$2$
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$Q = \rho \cdot \frac{4}{3}\pi R^3 = (\frac{3}{\pi} \times 10^{-6}) \cdot \frac{4}{3}\pi (2)^3 = 32 \times 10^{-6}$
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64
Q64NAT2 marksMedium
Let $X$ and $Y$ be two real-valued random variables with $E(X) = 1, E(Y) = 2, E(X^2) = 4, E(Y^2) = 9$ , and $E(XY) = 0.9$ , where $E$ denotes the expectation operator. The value of…
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$X$
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$E((X - \alpha Y)^2)$
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65
Q65NAT2 marksHard
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)
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Question
$\frac{1}{\pi} \int_{0}^{\infty} \frac{x^{2026}}{(1 + x^{2026})(1 + x^2)} dx$
Your answer
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$I = \int_{0}^{\infty} \frac{x^{2026}}{(1 + x^{2026})(1 + x^2)} dx$
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Terminal voltage ( $v_t$ )	Terminal current ( $i_t$ )
18 V	- 0.5 A
30 V	0.5 A
36 V	1.0 A

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