GATE 2021 ME (Set 2) question paper PDF and answer key

The official GATE 2021 Mechanical Engineering (Set 2) paper, organised by IIT Bombay: 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 Bombay for GATE 2021 (official GATE site). Spotted a mistake? Email team@lemyte.com.

General Aptitude: 10 · 15 marks
Mechanical Engineering: 55 · 85 marks
MCQ / MSQ / NAT: 38 / 0 / 27
Marks to all: None

Where the marks were

GATE 2021 ME (Set 2) topic-wise marks

Mechanical Engineering questions only; General Aptitude adds 15 marks on top. The top three topics carried 33 of the 85 subject marks.

Topic	Questions	Marks
Manufacturing Engineering	10	16
Fluid Mechanics	7	10
Industrial Engineering	4	7
Mechanics of Materials	5	7
Theory of Machines	4	6
Heat Transfer	3	5
Applied Mechanics	3	5
Thermal Applications	3	5
Thermodynamics	3	4
Vibrations	2	4
Linear Algebra	2	3
Differential Equations	2	3
Numerical Methods	2	3
Calculus	1	2
Machine Design	1	2
Probability and Statistics	1	1
Engineering Materials	1	1
Complex Variables	1	1

Free solved questions

5 solved questions from GATE 2021 ME (Set 2)

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.

Q1 · General Aptitude · MCQ · 1 mark

Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

(A)
$2$
(B)
$3$
(C)
$4$
(D)
$5$

Answer (official key): B

Solution

R occupies position 2, so P and T must occupy positions 3 and 4. Applying the restriction that P cannot sit next to S gives the arrangements QRPTS, SRPTQ and SRTPQ. Thus there are $3$ arrangements, option B.

Q4 · General Aptitude · MCQ · 1 mark

If $\oplus\div\odot=2$ ; $\oplus\div\Delta=3$ ; $\odot+\Delta=5$ ; $\Delta\times\otimes=10$ ,

Then, the value of $(\otimes-\oplus)^2$ , is:

(A)
$0$
(B)
$1$
(C)
$4$
(D)
$16$

Answer (official key): B

Solution

Let the values represented by $\oplus,\odot,\Delta,\otimes$ be $a,b,c,d$ . Then $a=2b=3c$ and $b+c=5$ , giving $c=2$ , $b=3$ and $a=6$ . Since $cd=10$ , $d=5$ . Thus $(d-a)^2=(5-6)^2=1$ , option B.

Q42 · Theory of Machines · MCQ · 2 marks

A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.

Figure for GATE 2021 ME (Set 2) question 42 (Theory of Machines)

Diameters of pulleys of belt drive and number of teeth ( $T$ ) on the gears $2$ to $7$ are indicated in the figure. The speed and direction of rotation of gear $7$ , respectively, are

(A)
$255.68$ rpm; clockwise
(B)
$255.68$ rpm; anticlockwise
(C)
$575.28$ rpm; clockwise
(D)
$575.28$ rpm; anticlockwise

Answer (official key): A

Solution

The belt gives $N_2=2500(150/250)=1500$ rpm. Gears $3$ and $4$ share a shaft, as do $6$ and $7$ ; gear $5$ is an idler. Thus $N_7=1500(18/44)(15/36)=255.68$ rpm. The open belt preserves direction, and the three external gear meshes reverse it overall, giving clockwise rotation. Hence A.

Q43 · Vibrations · MCQ · 2 marks

A machine of mass $100$ kg is subjected to an external harmonic force with a frequency of $40$ rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( $K$ ) and damper (damping factor, $\xi$ ) in parallel. The designer has the following four isolators:

$K=640$ kN/m, $\xi=0.70$
$K=640$ kN/m, $\xi=0.07$
$K=22.5$ kN/m, $\xi=0.70$
$K=22.5$ kN/m, $\xi=0.07$

Arrange the isolators in the ascending order of the force transmitted to the foundation.

(A)
1-3-4-2
(B)
1-3-2-4
(C)
4-3-1-2
(D)
3-1-2-4

Answer (official key): C

Solution

Force transmissibility is $T_R=\sqrt{[1+(2\xi r)^2]/[(1-r^2)^2+(2\xi r)^2]}$ , where $r=\omega/\sqrt{K/m}$ . The frequency ratios are $0.5$ for isolators 1 and 2, and $8/3$ for 3 and 4. Their transmissibilities are approximately $1.190$ , $1.331$ , $0.540$ , and $0.174$ , respectively. The ascending order is 4-3-1-2, so C.

Q45 · Numerical Methods · Numerical · 2 marks

Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. If the starting guess ( $x_0$ ) is $2$ , the numerical value of the root after two iterations ( $x_2$ ) is _____________ (round off to two decimal places).

Answer (official key): 1.66 to 1.68

Solution

Newton-Raphson gives $x_{n+1}=x_n-(x_n^3-x_n-3)/(3x_n^2-1)$ . Starting at $x_0=2$ , $x_1=2-3/11=1.72727$ and $x_2\approx1.67369$ . After two iterations, the answer is $1.67$ .

The other 60 questions are solved in your report when you take GATE 2021 ME (Set 2) as a 3-hour test.

Take GATE 2021 ME (Set 2) as a test

Official answer key

GATE 2021 ME (Set 2) answer key

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

Download the official GATE 2021 ME (Set 2) answer key (PDF)

Q	Topic	Type	Marks	Answer
1	Analytical Aptitude	MCQ	1	B
2	Verbal Aptitude	MCQ	1	A
3	Quantitative Aptitude	MCQ	1	A
4	Quantitative Aptitude	MCQ	1	B
5	Spatial Aptitude	MCQ	1	D
6	Analytical Aptitude	MCQ	2	C
7	Quantitative Aptitude	MCQ	2	B
8	Quantitative Aptitude	MCQ	2	C
9	Spatial Aptitude	MCQ	2	B
10	Verbal Aptitude	MCQ	2	D
11	Linear Algebra	MCQ	1	D
12	Differential Equations	MCQ	1	C
13	Probability and Statistics	MCQ	1	D
14	Engineering Materials	MCQ	1	D
15	Manufacturing Engineering	MCQ	1	A
16	Manufacturing Engineering	MCQ	1	D
17	Manufacturing Engineering	MCQ	1	D
18	Industrial Engineering	MCQ	1	B
19	Manufacturing Engineering	MCQ	1	C
20	Heat Transfer	MCQ	1	A
21	Fluid Mechanics	MCQ	1	D
22	Fluid Mechanics	MCQ	1	B
23	Fluid Mechanics	MCQ	1	B
24	Applied Mechanics	MCQ	1	B
25	Theory of Machines	MCQ	1	D
26	Theory of Machines	MCQ	1	B
27	Mechanics of Materials	MCQ	1	D
28	Numerical Methods	MCQ	1	A
29	Complex Variables	MCQ	1	B
30	Thermodynamics	Numerical	1	373 to 377
31	Thermal Applications	Numerical	1	165
32	Thermodynamics	Numerical	1	134 to 136
33	Fluid Mechanics	Numerical	1	228 to 230
34	Mechanics of Materials	Numerical	1	800 to 840
35	Mechanics of Materials	Numerical	1	0.08 to 0.12
36	Calculus	MCQ	2	B
37	Linear Algebra	MCQ	2	B
38	Differential Equations	MCQ	2	C
39	Industrial Engineering	MCQ	2	A
40	Thermal Applications	MCQ	2	D
41	Mechanics of Materials	MCQ	2	B
42	Theory of Machines	MCQ	2	A
43	Vibrations	MCQ	2	C
44	Vibrations	MCQ	2	B
45	Numerical Methods	Numerical	2	1.66 to 1.68
46	Industrial Engineering	Numerical	2	40200 to 40300
47	Manufacturing Engineering	Numerical	2	2.6 to 3
48	Manufacturing Engineering	Numerical	2	39 to 40
49	Manufacturing Engineering	Numerical	2	38 to 39
50	Manufacturing Engineering	Numerical	2	388 to 400
51	Manufacturing Engineering	Numerical	2	3880 to 3886
52	Manufacturing Engineering	Numerical	2	200 to 206
53	Industrial Engineering	Numerical	2	6 to 10
54	Heat Transfer	Numerical	2	337 to 341
55	Heat Transfer	Numerical	2	10
56	Fluid Mechanics	Numerical	2	2257 to 2259
57	Thermal Applications	Numerical	2	25 to 25.4
58	Fluid Mechanics	Numerical	2	130 to 134
59	Fluid Mechanics	Numerical	2	90 to 92
60	Thermodynamics	Numerical	2	2.1 to 2.3
61	Applied Mechanics	Numerical	2	0.16 to 0.19
62	Applied Mechanics	Numerical	2	1.3 to 1.4
63	Mechanics of Materials	Numerical	2	48 to 52
64	Theory of Machines	Numerical	2	560 to 580
65	Machine Design	Numerical	2	152000 to 165000

Questions about GATE 2021 ME (Set 2)

How many questions are in the GATE 2021 ME (Set 2) paper?

65 questions for 100 marks: 10 General Aptitude questions worth 15 marks and 55 Mechanical Engineering questions worth 85 marks. By type, there were 38 MCQs, 27 numerical answer (NAT) questions. The paper lasted 3 hours.

Is there negative marking in GATE 2021 ME (Set 2)?

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 2021 ME (Set 2)?

Outside General Aptitude, the biggest topics were Manufacturing Engineering (16 marks), Fluid Mechanics (10 marks), Industrial Engineering (7 marks). The full topic-wise split is in the table on this page.

Were any GATE 2021 ME (Set 2) questions awarded marks to all?

No. Every question was graded with the answer in the official key.

Where does this GATE 2021 ME (Set 2) answer key come from?

From the official answer key published by IIT Bombay, which organised GATE 2021. 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 2021 ME (Set 2) question paper PDF and answer key

GATE 2021 ME (Set 2) topic-wise marks

5 solved questions from GATE 2021 ME (Set 2)

GATE 2021 ME (Set 2) answer key

Questions about GATE 2021 ME (Set 2)

How many questions are in the GATE 2021 ME (Set 2) paper?

Is there negative marking in GATE 2021 ME (Set 2)?

Which topics carried the most marks in GATE 2021 ME (Set 2)?

Were any GATE 2021 ME (Set 2) questions awarded marks to all?

Where does this GATE 2021 ME (Set 2) answer key come from?

More GATE papers