Mechanical Engineering Gate Yearwise 


Mechanical Engineering Gate 2022 Set-2 Questions with Answer

Ques 27 GATE 2022 SET-2

A cylindrical billet of 100 mm diameter and 100 mm length is extruded by a direct extrusion process to produce a bar of L-section. The cross sectional dimensions of this L-section bar are shown in the figure. The total extrusion pressure (𝑝) in MPa for the above process is related to extrusion ratio (𝑟) as

where σ0 is the mean flow strength of the billet material in MPa, l is the portion of the billet length remaining to be extruded in mm, d0 is the initial diameter of the billet in mm, and K0 is the die shape factor.

If the mean flow strength of the billet material is 50 MPa and the die shape factor is 1.05, then the maximum force required at the start of extrusion is ________ kN (round off to one decimal place).

A

a

B

a

C

a

D

a


() is the correct answer.

Ques 28 GATE 2022 SET-2

A straight-teeth horizontal slab milling cutter is shown in the figure. It has 4 teeth and diameter (D) of 200 mm. The rotational speed of the cutter is 100 rpm and the linear feed given to the workpiece is 1000 mm/minute. The width of the workpiece (w) is 100 mm, and the entire width is milled in a single pass of the cutter. The cutting force/tooth is given by F = Ktcw, where specific cutting force K = 10 N/mm2, w is the width of cut, and tc is the uncut chip thickness.
The depth of cut (d) is D/2, and hence the assumption of d/D<<1 is invalid. The maximum cutting force required is ______ KN (round off to one decimal place).


() is the correct answer.

Ques 29 GATE 2022 SET-2

In an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is 0.5 mm and the shear angle is 15°. The orthogonal rake angle of the tool is 0° and the width of cut is 2 mm. The workpiece material is perfectly plastic and its yield shear strength is 500 MPa. The cutting force is _______ N (round off to the nearest integer)


() is the correct answer.

Ques 30 GATE 2022 SET-2

The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch (𝑝) and included angle of the thread are 4 mm and 60º, respectively.The diameter of the best size wire is ___________ mm (round off to 2 decimal places).


() is the correct answer.

Ques 31 GATE 2022 SET-2

In an direct current arc welding process, the power source has an open circuit voltage of 100 V and short circuit current of 1000 A. Assume a linear relationship between voltage and current. The arc voltage (V) varies with the arc length (l) as V = 10 + 5l, where V is in volts and l is in mm. The maximum available arc power during the process is _________ kVA (in integer).


() is the correct answer.

Ques 32 GATE 2022 SET-2

Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?

A

Stress value where the stress-strain curve transitions from elastic to plastic behavior

B

The maximum load attained divided by the original cross-sectional area

C

The maximum load attained divided by the corresponding instantaneous cross-sectional area

D

Stress where the specimen fractures


(b) is the correct answer.

Ques 33 GATE 2022 SET-2

A structural member under loading has a uniform state of plane stress which in usual notations is given by σx = 3P, σy = -2P and τxy = √2 P, where P > 0. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of P at which yielding starts (according to the maximum distortion energy theory) is

A

70 MPa

B

90 MPa

C

120 MPa

D

75 MPa


(c) is the correct answer.

Ques 34 GATE 2022 SET-2

Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components A and B is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, including the solidus and liquidus lines, are straight lines. If this binary alloy with 15 weight % of B is poured into a mould at a pouring temperature of 800 ºC, then the solidification range is

A

400 ºC

B

250 ºC

C

800 ºC

D

150 ºC


(b) is the correct answer.

Ques 35 Gate 2022 Set-2

If f(x) = 2ln(√e), what is the area bounded by f(x) for the interval [0, 2] on the x-axis?

A

1/2

B

1

C

2

D

4


(c) is the correct answer.

Ques 36 GATE 2022 SET-2

Consider the following functions for non-zero positive integers, p and q.

Which one of the following options is correct based on the above?

A

f(2,2) = g(2,2)

B

f(g(2,2), 2) < f(2, g(2,2))

C

g(2,1) ≠ f(2,1)

D

f(3,2) > g(3,2)


(b) is the correct answer.

Ques 37 GATE 2022 SET-2

F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of F(t)?

A

1

B

2

C

3

D

4


(b) is the correct answer.

Ques 38 GATE 2022 SET-2

Consider a cube of unit edge length and sides parallel to coordinate axes, with its centroid at the point (1, 2, 3). The surface integral ∫A 𝑭⃗ ⋅𝑑𝑨⃗ of a vector field 𝑭⃗ = 3xi + 5yj + 6zk over the entire surface A of the cube is ______.

A

14

B

27

C

28

D

31


(c) is the correct answer.

Ques 39 GATE 2022 SET-2

Consider the definite integral

Let Ie be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is Is. The percentage error is defined as e = 100 × (Ie − Is)/Ie. The value of e is

A

2.5

B

3.5

C

1.2

D

0


(b) is the correct answer.

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