Past Year Paper - Mechanical Engineering GATE : 2022 (Session - 1) - Mechanical Engineering MCQ

In first filler we need to mention number so option (A) and (B) are eliminated and in second filler we are getting the sense of exhausted, so it should be ‘too’ Hence, the correct option is (D).

Given,
Average salary of M,N,S = Rs. 4000
Average salary of N,S,P = Rs 5000
Monthly salary of P = Rs. 6000
M + N+ S / 3 = 4000
N +S + P / 3 = 5000
M + N + S = 12000
N + S + P = 15000
Monthly salary of P = 6000
N + S + 6000 = 15000
N + S =  9000
M + 9000 = 12000
M = 3000
Percentage salary of M with respect to
= 3000 / 6000 x 100%
= 50%
Hence, the correct option is (A). 

Given,
Total distance covered by a person = 80 km
Total time taken by that person = 6 hours
Speed of first part of journey = 10 kmph
Speed of second part of journey = 18 kmph
Assume, time taken for 1st part = t hrs
Time taken for 2nd part = (6 - t) hrs
Distance = Speed ´ Time
80 = 10t +18(6 -t) 80
= 10t +108 - 8t
-28 = -8t t
= 3.5 hrs
Distance travelled with speed 10 kmph
10 x 3.5= 35 km
Percentage of the total distance is
Travelled at a uniform speed of 10 kmph
= 35 / 80 x 100
= 43.75%
Hence, the correct option is (C).

Given :
P is learning French and Dutch
Q is learning Chinese and Japanese
R is learning Spanish and French
S is learning Dutch and Japanese
French < Dutch … (i)
Chinese > Japanese … (ii)
Japanese > Dutch … (iii)
French > Spanish … (iv)
By equation (i), (ii), (iii) and (iv)
Chinese > Japanese > Dutch > French > Span according to the difficulty level arrangement Girl Q is learning most difficult pair of languages, which is Chinese and Japanese.
Hence, the correct option is (B).

Given:

The correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow, 

Hence, the correct option is (A).

Option (B) is correct logical inference as wallets with a key are more likely to be returned because people relate to suffering of others as mentioned in the passage “the primary reason for this behavior is compassion and empathy”.
Hence, the correct option is (B).

Let ABCD be the square of unit length and P, Q, R, S be midpoints of AB, BC, CD, DA respectively

Let O be centre of circle
OR = OQ = 1/2 units

SP = PQ = RQ = PS (rhombus)
Area of ΔORQ = 1/2OROQ
= 1/2O x RQ

Diameter = 2r = 1/√2
Hence, the correct option is (A). 

Let, equilateral ∆ of side a
square of side b
radius of circle = r

Ratio of perimeters, 3a : 4b : 2πr

Hence, the correct option is (B).

Given : 

Conclusion I. No engineer is professor 
As no information is provided for some part of engineers, they can be part of professors and cannot be part of professors.
Hence, it can be inferred from statement.
Conclusion II. Some engineers are professor. As no information is provided for some part of engineers, they can be part of professors and cannot be part of professors.
Hence, it can be inferred from statement.
Conclusion III. No male is a teacher.
Can be inferred from statement as we can see in the diagram.
All part of teacher is inside of professors and no professor is male. Hence teachers are also not male.
Hence, the correct option is (A). 

In a 12 hour duration second, minute and hour hands of clock can be coincide, 11 times.
In every 1 hour hands of a clock will coincide one time and in 12 hour period hands of a clock will coincide only for 11 time as between 11 to 1 hands will be coincided only for 1 time at exactly 12.
Hence, the correct option is (A).

Given : The limit
 
It has finite value for real a.


It becomes ∞ but according to question the limit has finite value.
That means, 3π² + aπ should be zero to become (0/0) form, so that we can apply L’ hospital rule.
3π² + aπ = 0
aπ = -3π²
a = 3π
Now, putting the value a = 3π,

We can apply L’ hospital rule,

p = π
Hence, the correct option is (A).

Given : Laplace equation ∇²T = 0 , (0 < x < 1, 0 < y < 1)
T ( x, 0) = x, T (0, y) = y, T (x,1) = 1+ x, T (1, y) = 1+ y
Solution of Laplace equation is given by,
T ( x, y) = (C₁x + C₂) (C₃y + C₄) ......(i)
Using boundary condition,
T ( x, 0) = (C₁x + C₂ ) (C₄ ) = x ......(ii)
T (0, y) = C₂ (C₃y + C₄ ) = y ......(iii)
T ( x,1) = (C₁x + C₂) (C₃ + C₄) = 1 + x ......(iv)
T (1, y) = (C₁+ C₂) (C₃y + C₄) = 1 + y ......(v)
By solving equations (ii), (iii), (iv) and (v),
C₁ = 1, C₃ = 1, C₂ = 0 and C₄ = 0
Therefore, the solution is given by equation (i),
T ( x, y) = x+ y
Hence, the correct option is (B).

Given : A function  in three dimensional cartesian space.
Surface integral,

where, S is the surface of sphere of unit radius and is the outward unit normal vector on S.


then, surface integral

By divergence theorem,

I = 3V
Volume of sphere,  (with r = 1 )

Hence, the correct option is (A).

Given : Function f ( x) = x³ ; -1 ≤ x < 1
The above function f (x) is odd.
We know that, odd function contains only odd terms,

a₀ and a_n will be zero.
Therefore, the given function f (x) contains only sine term.
Hence, the correct option is (A).

Given : Matrix  is symmetric matrix.
A matrix  is to be symmetric if  [A] = [A^T] or a₁₂ =a₂₁
That means, 2K + 5 = 3K - 3 5 + 3 = 3K - 2K
K = 8
Hence, the correct option is (A).

F.B.D. at point B


F_BC sin 30^o = W
F_BC = 2 W .........(i)

F_AB = F_BC cos 30^o

F_AB = √3 W.........(ii)
Buckling load 
 .........(iii)
From equation (ii) and (iii)


β = 0.092
Hence, the correct option is (A). 

ω² = g / h or watt governor
(ω ∝ N)
N² = g / h 

h₁ = 400 Given

ω₂ = 2ω₁

h₂ = 100
Hence, the correct option is (B).

Given : Load = W
Applied force = F
The efficiency of square thread salent is

Hence, the correct option is (A).

1/600 x Pitch = BLU
5/600mm = BLU

Or,

= 10, 000 Hz = 10 kHz
Hence, the correct option is (B). 

For shaft, Upper limit = 25.01
Lower limit = 24.99
For hole Upper limit = 25.03
Lower limit = 25

It is a transition fit.
Hence, the correct option is (B). 

In linear programming problem, if a resource is not fully utilized, the shadow price of that resource will be zero.
Hence the correct option is (C).

CNC machines are not a form of inventory
Hence the correct option is (D).

Clausius inequality

Is hold good for any cycle hence the correct option is (B).
Hence, the correct option is (B).

T = 2x² + xy +4t Find dγ/dt at x = 1, γ = 1,t = 1
Using relation:

= 4 + 2(4 +1) + (1+ 3) x 1
= 4 +10 + 4 = 18
Hence, the correct option is (C). 

We know that 
Buoyancy force,

Hence, the correct option is (D). 

For homogeneous, isotropy & linear elastic.
(A) A body is subjected to hydrostatic pressure has no shear stress.

τ = 0 (In case of hydrostatic loading)
(B) If a long solid rod is subjected to tensile load then volume increases.

We know that the value of Possions ratio for elastic material is less than 0.5
From equation (i) The value of  is positive when (μ < 0.5) so, ε_v is also positive.
Hence, volume increases
Hence, the correct option is (A,B). 

Heat treatment process is/are used for surface hardening of steel

• Cyaniding
• Carbonitriding
• Carburizing

Note :  Surface hardening process → Cyaniding, Carbonitriding, Carburizing.
Surface softening process → Annealing.
Hence, the correct option is (A,B,C).

Wire is used as feed stock material in two manufacturing technique which are :

• Fused deposition modelling
• Directed energy deposition processes.

Hence, the correct option is (B,D). 

Method which can improve fatigue strength of a circular mild steel shaft are :

• Enhancing surface finish.
• Shot peening of the shaft.
• Reducing relative humidity

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

In a purely convergent nozzle with a steady inviscid compressible flow of an ideal gas.

• Mass flow rate through the nozzle will increase.
  
• Mach number at the exit plane of the nozzle will remain unchanged at unity. 

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