Past Year Paper - Mechanical Engineering GATE : 2022 (Session - 2) - Mechanical Engineering MCQ

Writing too many things on the board while teaching could make the students get bored.
Hence, the correct option is (B).

Hence, the correct option is (C).

Given : Function, 

Area bounded by f (x) for the interval [0, 2] on the x-axis,


= 2
Therefore, area will be 2.
Hence, the correct option is (C).

Given:
A person was born on the fifth Monday of February in a particular year.
Then,
That year should be a leap year, as in a leap year February month is of 29 days.
If 1^st February is Monday then next Monday is on 8^th, 15^th, 22^nd and 29^th of the month.
So 1^st and last day of the month February will be same.
Here, the 2nd February of that year is a Tuesday.
Hence, the correct option is (A).

Given :

The group that can be assembled to get the shape that is shown above is, according to option (B).

Hence, the correct option is (B).

Option (C) can be inferred, as having ultra black skin has both advantages and disadvantages to species S.
Hence, the correct option is (C).

Average production = all production till to day/m = 100
According today, average production = all production till to day + 180 / m + 1

= 110m +110 = 100m +180
=10m:70
∴ m = 7
Hence, the correct option is (C).

Given:

(A) f (2, 2) = 2² =  4
g (2, 2) = 2² = 4
f (2, 2) =g(2, 2)
∴ option (A) is correct
(B) f (4, 2) =f (2, 4)
4² = 2⁴
∴ option (B) is wrong
(C) g (2,1) = 2;f (2,1)= 2
∴ option (C) is wrong
(D) f (3, 2) = 3²= 9
g (3, 2) = 3³ = 27
∴ option (D) is wrong
Hence, the correct option is (A).

Travel time between two city is 1 hr.
Hence, the total Journey time R to Q = 1 hr
Wait at Q = 1 hr Q to P = 1 hr
Wait at P = 1 hr P to S = 1 hr
Wait at S = 30 min
S to R = 1 hr
Total Journey hours from R to R is 6 hr 30 m.
Hence, the correct option is (A).

Case M :

Diameter of a shaded circle = 1/2 cm
Radius of shaded circle = 1/4 cm
Area = π/16 cm²
So, Area of unshaded region = Area of square sheet – Area of 4 shaded circular region.
∴ Area of unshaded region

Case N :

diameter = 1/3 and radius = 1/6
∴ Area of unshaded region of case N = Area of square sheet – Area of shaded circular region.

∴ The ratio of the areas of unshaded region of case M to that of case N

= 1:1
Hence, the correct option is (B).​​​​​​​​​​​​​​

Given : F (t) is a periodic square wave function with time period T = 2 second.
Complete Fourier series is given by,

Constant term in Fourier is given by a₀/2

a₀ = 4
Thus, constant term, 
= 2
Hence, the correct option is (B).
 

Given : Vector field, 
Surface integral, 
where, A is entire surface A of the cube.
By divergence theorem,

By equation (i),

Volume of cube, V =a³ (with a = 1 unit edge length)
I = 14 x a³
I = 14 x 1
I = 14
Hence, the correct option is (A).

Given : Definite integral, 

Percentage error,  
where, I_e be the exact value of integral and I s be the value which is evaluated using Simpson’s 1/3 rule with 10 equal subintervals.
The given f ( x) = 4x² + 2 x + 6 is a quadratic equation, for which exact value ( I_e) is always equal to approximated value ( I_s) .
Therefore,

Hence, the correct option is (D).

Given :

We need to find the value of 
where, a and b are positive integers.

Let
x + b= t
dx = dt
For x = -∞ ⇒ t =  -∞ 
And For x = ∞ ⇒ t = ∞

Let
at² = p²
2atdt =2pdp

For t = -∞ ⇒ p =  -∞ 
And For t = ∞ ⇒ p = ∞

From equation (i),

Hence, the correct option is (B).

The given polynomial

For stationary point, 

Since, φ(s) has triple roots at s = -σ , ( s +σ)³ will be one of it factors and φ(-σ) = 0 .
There will be an inflection point on the curve of φ(S) . Therefore, the first order d/s φ(s) ds f and second order derivative  will be zero.
∴ 
Hence, the correct option is (B).

The definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen is the maximum load attained divided by the original cross-sectional area.
i.e. 
Where, σ_ult= ultimate tensile strength, 
P_max = maximum load obtained in a tensile test,
A₀ = original cross-sectional area before load applied
Hence, the correct option is (B).

It is given that when view from rear disc rotates clock-wise, when string AB cut the point A goes down because C.G. of shaft away from C and towards A. So gyroscopic effect will be 

Angular velocity vector 

Rotate slowly (compared to ω) direction about the negative z-axis.
Hence, the correct option is (A). 

For the maximum distortion energy theory,

For actual condition, 
σ₃ = 0 (because 2D condition)
Radius of Mohr’s circle



R = 2.8722P
Now, principal stresses, 



And


σ₂ = -2.3722P
By putting in equation (i),



During tensile test failure,


Where, σ_f is tensile yield strength = 350 MPa.
So,
 
 … (iii)
Equating equation (ii) and (iii), 

P = 70 MPa
Hence, the correct option is (A).

Since, MN = 300, XY = 15, NO = 30 and XN = solidification range = ?
By linear interpolation,
In similar triangles ΔMXY and ΔMNO,

∴ For solidification range, XN = MN- MX
XN = 300-150
Solidification range, XN = 150⁰C
Hence, the correct option is (D).

1. Allowance – 0.04 mm (due to minimum clearance)
2. Maximum clearance → (0.07 + 0.02)= 0.09 mm
3. Maximum material limit for hole → lower limit g hole = 25 mm
Hence, the correct option is (A).

P. Fused deposition modelling – Filament of polymer
Q. Laminated object manufacturing – Sheet of thermoplastic or green compacted metal sheet
R. Selective laser sintering – Heat fusible powder
Hence, the correct option is (A).

Chain and sprocket cannot impart linear motion in a CNC machine.
Hence, the correct option is (D).

Density is an intensive property of a thermodynamic system.
Hence, the correct option is (B).

Within the distance of a mean free path, the flow passes from a supersonic to a subsonic state, the velocity decreases suddenly and the pressure rises sharply. A normal shock is said to have occurred if there is an abrupt reduction of velocity in the downstream in course of a supersonic flow in a passage or around a body.
Since, volume flow rate is constant, velocity at B is lower than velocity at A and pressure at location B is observed to be higher than that at an upstream location A. Therefore, it indicates the normal shock. Hence, the correct option is (B).

Nusselt number equal to the dimensionless temperature gradient at the surface, and it provides a measure of the convective heat transfer occurring at the surface.
Nusselt number, 

Where, k_fluid = thermal conductivity of fluid

Hence, the correct option is (C).

Configuration (P) :

Therefore, it is structure and stable system will be in equilibrium.
But, we know equilibrium is a state of the body where all the forces are of the same magnitude making the net resultant zero. This is called static concurrent equilibrium. i.e. 

But, the given square plate has couple moment c which will be the disturbing action for the concurrent forces and the square plate (configurations P) due to this action cannot be remain in equilibrium. Hence, cannot be remain in equilibrium.
Configuration (Q) :

Here, the forces acting on the square plate is countering the action of couple moment c. Due to this counter action of forces (F) to resist the couple moment c, the square plate will remain in equilibrium. i.e.

Forces (F) giving counter clockwise moment and couple moment c giving clockwise moment. Hence, will remain in equilibrium.
Configuration (R) :

Similarly as we discussed above, here also the forces (F) resisting the couple moment c which is in clockwise direction by providing the anticlockwise moment. i.e. 

Hence, will remain in equilibrium.
Configuration (S) :

In the above arrangement, due to couple moment c , the reactions forces will try to counter the clockwise rotation which in result bring the arrangement in equilibrium or stable position i.e.

Hence, will remain in equilibrium.
Hence the correct option is (B), (C), (D).

Here,

We know that,

⇒ Volume of riser ≥ Volume of casting

Hence, the correct option is (A, B).

In, electron beam machining, electrical discharge machining and Laser beam machining, involves melting in metallic workpiece.
Hence, the correct option is (B,C,D).

∵ 
4y - 4y= 0
0 = 0 (Flow is incompressible)
Now,  checking irrotational,

ω_z= 0 (Flow is irrotational) Now, checking the acceleration experienced by a fluid particle is zero at ( x = 0,y= 0) ,

At ( x = 0,y= 0) :
a_x = 0
And

At ( x = 0,y= 0) :
a_y = 0
∴ Total acceleration,


a_total = 0 (Acceleration experienced by a fluid particle is zero at x = 0,y= 0 ).
Since,  shows 4xy in direction and 2( x² -y² ) in direction i.e. velocity field is two dimensional.
Hence, the correct option is (B), (C) and (D).

Condition - I


Where angle of lap (θ) = π

Condition-II



On equating equation (i) and (ii)
T₃ = 50 N
For 50 N number of discs = 50/20 = 2.5
Hence minimum value of m required to prevent downward motion of the left side of platform is 3.