GATE 2025 EC question paper PDF and answer key

The official GATE 2025 Electronics & Communication Engineering paper, organised by IIT Roorkee: 65 questions for 100 marks in 3 hours. Download the official question paper and answer key as PDFs. Below is how the marks were split by topic, the complete official answer key and 5 questions solved step by step.

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Question paper (PDF)Official answer key (PDF)

Source: the official paper and answer key published by IIT Roorkee for GATE 2025 (official GATE site). Spotted a mistake? Email team@lemyte.com.

General Aptitude: 10 · 15 marks
Electronics & Communication Engineering: 55 · 85 marks
MCQ / MSQ / NAT: 39 / 14 / 12
Marks to all: Q 8

Where the marks were

GATE 2025 EC topic-wise marks

Electronics & Communication Engineering questions only; General Aptitude adds 15 marks on top. The top three topics carried 36 of the 85 subject marks.

Topic	Questions	Marks
Networks, Signals and Systems	9	13
Analog Circuits	9	13
Control Systems	6	10
Probability and Statistics	5	9
Digital Circuits	6	9
Electromagnetics	4	8
Electronic Devices	4	7
Communications	5	6
Calculus	3	4
Linear Algebra	2	3
Complex Variables	1	2
Differential Equations	1	1

Free solved questions

5 solved questions from GATE 2025 EC

Question text and figures as in the official paper, the answer from the official key, and a worked solution. The other 60 solutions are in your report after you take the paper.

Q9 · General Aptitude · MCQ · 2 marks

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?

Nation	Gold	Silver	Bronze
USA	40	44	41
Canada	39	27	24
Japan	20	12	13
Australia	17	19	16
France	16	26	22

(A)
France will occupy the third place if the list were made on the basis of the total number of medals won.
(B)
The order of the top two nations will not change even if the list is made on the basis of the total number of medals won.
(C)
USA and Canada together have less than 50% of the medals awarded to the nations in the above table.
(D)
Canada has won twice as many total medals as Japan.

Answer (official key): C

Solution

Totals: USA 125, Canada 90, Japan 45, Australia 52, France 64; all together 376.

(A) France (64) is third: correct.
(B) USA and Canada stay first and second: correct.
(C) USA + Canada $= 215 > 188$ (50% of 376), so the statement is incorrect.
(D) $90 = 2 \times 45$ : correct.

Q10 · General Aptitude · MCQ · 2 marks

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to ₹ 5,00,000. For higher fees, the overhead is ₹ 1,00,000 plus 10% of the amount by which the fee exceeds ₹ 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than ₹ 10,00,000, what is the maximum consulting fee that the employee can charge?

(A)
₹ 7,01,438
(B)
₹ 7,24,961
(C)
₹ 7,51,232
(D)
₹ 7,75,784

Answer (official key): B

Solution

For a fee $F > 5{,}00{,}000$ , the overhead is $1{,}00{,}000 + 0.1(F - 5{,}00{,}000) = 0.1F + 50{,}000$ . The total billed is $1.18\,(F + 0.1F + 50{,}000) = 1.18\,(1.1F + 50{,}000) \le 10{,}00{,}000$ $1.1F \le 8{,}47{,}457.6 - 50{,}000 \Rightarrow F \le 7{,}24{,}961$

Q39 · Networks, Signals and Systems · MCQ · 2 marks

In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t) = 100\cos(200t)$ .

What should be the value of the variable capacitor $C$ such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A, respectively?

Figure for GATE 2025 EC question 39 (Networks, Signals and Systems)

(A)
25 µF
(B)
4 µF
(C)
0.25 µF
(D)
Insufficient information to find $C$

Answer (official key): A

Solution

$M_1$ reads the voltage across the series R–C–L branch and $M_2$ its current, so $|Z| = 25/5 = 5\ \Omega = R$ . The reactances must cancel (series resonance): $\omega^2 LC = 1 \Rightarrow C = \frac{1}{(200)^2(1)} = 25\ \mu\text{F}$ The LTI network between the source and the branch does not matter.

Q51 · Calculus · MSQ · 2 marks

Consider a non-negative function $f(x)$ which is continuous and bounded over the interval [2, 8]. Let $M$ and $m$ denote, respectively, the maximum and the minimum values of $f(x)$ over the interval.

Among the combinations of $\alpha$ and $\beta$ given below, choose the one(s) for which the inequality

$\beta \le \int_2^8 f(x)\,dx \le \alpha$

is guaranteed to hold.

(A)
$\beta = 5m,\ \alpha = 7M$
(B)
$\beta = 6m,\ \alpha = 5M$
(C)
$\beta = 7m,\ \alpha = 6M$
(D)
$\beta = 7m,\ \alpha = 5M$

Answer (official key): A

Solution

Over an interval of length 6, $6m \le \int_2^8 f\,dx \le 6M$ . The inequality is guaranteed only if $\beta \le 6m$ and $\alpha \ge 6M$ (with $m, M \ge 0$ ).

Only (A) ( $5m \le 6m$ and $7M \ge 6M$ ) satisfies both.

Q59 · Linear Algebra · Numerical · 2 marks

Consider the vectors

$\boldsymbol{a} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \qquad \boldsymbol{b} = \begin{bmatrix} 0 \\ 3\sqrt{2} \end{bmatrix}.$

For real-valued scalar variable $x$ , the value of

$\min_x \|\boldsymbol{a}x - \boldsymbol{b}\|_2$

is ____________ (rounded off to two decimal places).

$\|\cdot\|_2$ denotes the Euclidean norm, i.e., for $\boldsymbol{y} = \begin{bmatrix} y_1 \\ y_2 \end{bmatrix}$ , $\|\boldsymbol{y}\|_2 = \sqrt{y_1^2 + y_2^2}$ .

Answer (official key): 2.95 to 3.05

Solution

The least-squares solution is $x^* = \dfrac{\boldsymbol{a}^T\boldsymbol{b}}{\boldsymbol{a}^T\boldsymbol{a}} = \dfrac{3\sqrt{2}}{2}$ .

The residual is $\boldsymbol{b} - \boldsymbol{a}x^* = \left(-\tfrac{3\sqrt{2}}{2}, \tfrac{3\sqrt{2}}{2}\right)$ , with norm $\sqrt{9} = 3.00$ .

The other 60 questions are solved in your report when you take GATE 2025 EC as a 3-hour test.

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Official answer key

GATE 2025 EC answer key

All 65 answers from the official key. Numerical answers are ranges; “or” means the key accepts either answer.

Download the official GATE 2025 EC answer key (PDF)

Q	Topic	Type	Marks	Answer
1	Verbal Aptitude	MCQ	1	A
2	Verbal Aptitude	MCQ	1	D
3	Quantitative Aptitude	MCQ	1	B
4	Analytical Aptitude	MCQ	1	B
5	Quantitative Aptitude	MCQ	1	A
6	Verbal Aptitude	MCQ	2	B
7	Analytical Aptitude	MCQ	2	D
8	Analytical Aptitude	MCQ	2	Marks to all
9	Analytical Aptitude	MCQ	2	C
10	Quantitative Aptitude	MCQ	2	B
11	Linear Algebra	MCQ	1	A
12	Calculus	MCQ	1	B
13	Probability and Statistics	MCQ	1	A
14	Communications	MCQ	1	A
15	Communications	MCQ	1	A
16	Control Systems	MCQ	1	D
17	Networks, Signals and Systems	MCQ	1	D
18	Networks, Signals and Systems	MCQ	1	A
19	Networks, Signals and Systems	MCQ	1	A
20	Networks, Signals and Systems	MCQ	1	A
21	Analog Circuits	MCQ	1	A
22	Analog Circuits	MCQ	1	C
23	Digital Circuits	MCQ	1	A
24	Digital Circuits	MCQ	1	B
25	Calculus	MSQ	1	A, B
26	Control Systems	MSQ	1	C
27	Networks, Signals and Systems	MSQ	1	C, D
28	Communications	MSQ	1	A, D
29	Analog Circuits	MSQ	1	A, C
30	Analog Circuits	MSQ	1	B, D
31	Electronic Devices	MSQ	1	A, D
32	Differential Equations	Numerical	1	0.25
33	Communications	Numerical	1	3
34	Analog Circuits	Numerical	1	50
35	Digital Circuits	Numerical	1	250
36	Control Systems	MCQ	2	D
37	Control Systems	MCQ	2	A
38	Networks, Signals and Systems	MCQ	2	A
39	Networks, Signals and Systems	MCQ	2	A
40	Networks, Signals and Systems	MCQ	2	A
41	Communications	MCQ	2	D
42	Probability and Statistics	MCQ	2	A
43	Analog Circuits	MCQ	2	D
44	Digital Circuits	MCQ	2	A
45	Digital Circuits	MCQ	2	A
46	Electronic Devices	MCQ	2	B
47	Analog Circuits	MCQ	2	A
48	Electronic Devices	MCQ	2	B
49	Electromagnetics	MCQ	2	C
50	Electromagnetics	MCQ	2	A
51	Calculus	MSQ	2	A
52	Complex Variables	MSQ	2	A, B
53	Control Systems	MSQ	2	B
54	Probability and Statistics	MSQ	2	B, C
55	Networks, Signals and Systems	MSQ	2	A, D
56	Control Systems	MSQ	2	B
57	Analog Circuits	MSQ	2	A, D
58	Probability and Statistics	Numerical	2	6.95 to 7.05
59	Linear Algebra	Numerical	2	2.95 to 3.05
60	Probability and Statistics	Numerical	2	0
61	Analog Circuits	Numerical	2	13.32 to 13.34
62	Digital Circuits	Numerical	2	200
63	Electronic Devices	Numerical	2	0.23 to 0.24
64	Electromagnetics	Numerical	2	6.3 to 6.5
65	Electromagnetics	Numerical	2	0.62 to 0.63

Questions about GATE 2025 EC

How many questions are in the GATE 2025 EC paper?

65 questions for 100 marks: 10 General Aptitude questions worth 15 marks and 55 Electronics & Communication Engineering questions worth 85 marks. By type, there were 39 MCQs, 14 MSQs, 12 numerical answer (NAT) questions. The paper lasted 3 hours.

Is there negative marking in GATE 2025 EC?

Yes, for MCQs only. A wrong MCQ answer costs one-third of its marks (−⅓ for a 1-mark question, −⅔ for a 2-mark question). MSQ and numerical (NAT) questions have no negative marking, and an MSQ earns marks only when every correct option is chosen.

Which topics carried the most marks in GATE 2025 EC?

Outside General Aptitude, the biggest topics were Networks, Signals and Systems (13 marks), Analog Circuits (13 marks), Control Systems (10 marks). The full topic-wise split is in the table on this page.

Were any GATE 2025 EC questions awarded marks to all?

Yes. The official key awarded full marks to everyone for question 8.

Where does this GATE 2025 EC answer key come from?

From the official answer key published by IIT Roorkee, which organised GATE 2025. Range answers for numerical questions and questions with more than one accepted answer are kept exactly as the key gives them.

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GATE 2025 EC question paper PDF and answer key

GATE 2025 EC topic-wise marks

5 solved questions from GATE 2025 EC

GATE 2025 EC answer key

Questions about GATE 2025 EC

How many questions are in the GATE 2025 EC paper?

Is there negative marking in GATE 2025 EC?

Which topics carried the most marks in GATE 2025 EC?

Were any GATE 2025 EC questions awarded marks to all?

Where does this GATE 2025 EC answer key come from?

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