Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 1) - Mechanical Engineering MCQ

Let ‘a’ be the side of square, then length and breadth of rectangle are ‘a+10 and ‘a+5’ respectively.
Given that,
Area of rectangle= Area of Square+650
(a + 10)(a + 5) = a² + 650
a² + 15a + 50 = a² + 650
15a = 600
a = 40
Area of rectangle=a² + 650
Area of rectangle=1600+650=2250

Let one’s digit is y and ten’s digit is x
Hence the number becomes ‘10x +y’ and the reverse number will be ‘10y+x’
x + y = 9 … (i)
10x + y− 10y − x = 45
x − y = 5 …. (ii)
Adding (i) and (ii)
x = 7
Subtracting (i) and (ii)
y = 2
Therefore the number is 72.

Time taken by a machine to make a toy will be independent of how many machines are making toys in parallel.
From given data, it takes 7 minutes for a machine to make a toy. If hundred such machines are running parallel to make a toy each, the time will remain same 7 minutes.
7 machine → 7 toys → 7 minutes
1 machine → 1 toy → 7 minutes
Because one machine takes 7 minute for making 1 toy.
So, 100 machines will take 7 minute for making 100 toys.

The statement suggests that some weak condition of the person is depicted. And this  weak condition should not be taken as being miser.
Miser: A person reluctant to spend.
Frugal: A person who is economically weak.

Principle – Truth/Proposition serving as foundation of person’s belief.
Principal – The most important person in an organization. Here it refers to school Principal

Given: a and b are integers
a + a²b³ is odd
Taking a common
a(1+ab³) is odd
Odd number is obtained after multiplication if both numbers multiplied are odd.
Hence, a is odd and 1+ab³ is also odd.
1+ab³ is odd, so ab³ will be even. (odd-1= even quantity)
Because a is odd so for ab³ to be even b must be even.
So, a is odd and b is even.

Solving by options
Option A: Even if statement 2^nd is false, i.e. All red flowers do not fade quickly, that does not mean that some roses won’t fade quickly.

Option B: There can be a possibility that no rose fade quickly

Option C: This is true in all possibilities.

Option D: There can be a possibility that some roses do fade quickly.

Hence option C is the only correct option.

Hence only B option prevails.

log| a|+ log| b |+ log| c | = 0
It is possible only,
If | a |,| b | and | c | all are equal to 1.
So, a, b, c may be respectively ‘+1’ or ‘-1’.
For minimum value all three will be negative.
So, minimum value = - 3
For maximum value all three will be positive.
So, maximum value = + 3.

Train speed = 54 km/h
Time = 25 sec for travelling length of train and length of platform
Man speed = 9 km/h
Relative speed of train with respect to man = 45 km/h
Time = 14 sec
So, length of train = time x speed

Length of train = 35 x 5 m = 175 m
Length of platform + length of train = speed x time

Length of platform 375 -175 = 200 m

This has to be solved through options
Continuity equation for 2D incompressible flow

A − A = 0
It satisfies continuity equation.

As y →  velocity vector field will not be defined along y axis.
So flow will be along x-axis i.e. 1-D flow.
⇒ Stream line equation for 2D

Ideal gas
State 1 : T₁ = 300 K, P₁ = 100 kPa
State 2 : T₂ = 600 K,P₂ = 500 kPa

Change in specific entropy

Comments: This can also be inferred from fact that if T₁ is finite then the bar will not remain horizontal.

In Pelton wheel turbine for maximum efficiency,

A dice is rolled 5 times

Probability of getting 1 ‘at least’ 4 times will include probability of getting 1- “4
times+5times”
The probability distribution is binomial distribution.

Taylor’s Tool life equation is VTⁿ=Constant
Let subscript 1 represent the initial conditions and subscript 2 represent the final conditions.

Grinding ratio is defined as ratio of Volume of work material removed to the ratio of wheel material removed.

Grinding wheel wears 1/200 (= 0.005) times the volume of material removed.

The figure represents fillet weld on T joint.

Where H= height of specimen and L= Length of Sine bar (length between center of two rollers)

As interpolator provides two functions:
1. It computes individual axis velocities to drive the tool along the programmed path at given feed rate.
2. It generates intermediate coordinate positions along the programmed path.

Stiffness of helical spring

Where, d=Spring Wire diameter
D= Mean Coil diameter
n= Number of coils
G= Shear Modulus
d increased by 2% i.e. d’=1.02d

Grashoff’s law is satisfied.
350 mm link is fixed, i.e. adjacent to shortest link is fixed.
The mechanism obtained will be crank rocker mechanism, it means only one link (crank) will fully rotate.

Probability that all the three balls are red is


Alter:
The required probability can also be obtained as,
Probability=

Converting the matrix into Echelon form,




Now since the matrix is in Echelon
Rank=Number of non-zero rows=2

This implies that within interval [a,b] there exists a value   such that 

Assuming length of plate as B
Let in infinitely small time ‘dt’ the plate is displaced with ‘dh’
So,

As per continuity,
Rate of mass displaced through plate= Rate of mass displaced between plates and wall


Since the flow is 2D the velocity of flow in direction perpendicular to plane of paper is
zero.

Where u = (kx − y) and v = (x + y)
According to Cauchy Riemann Equations,

From first condition k=1.

Maximum shear stress at a point is given by =

‘Simple moving average method’ is generally also called ‘Moving average method’ which gives equal weightage to all data points for period ‘M’ on which it is defined.