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GATE Mock Test Mechanical Engineering (ME) - 6 - Mechanical Engineering MCQ


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30 Questions MCQ Test GATE Mechanical (ME) Mock Test Series 2025 - GATE Mock Test Mechanical Engineering (ME) - 6

GATE Mock Test Mechanical Engineering (ME) - 6 for Mechanical Engineering 2024 is part of GATE Mechanical (ME) Mock Test Series 2025 preparation. The GATE Mock Test Mechanical Engineering (ME) - 6 questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The GATE Mock Test Mechanical Engineering (ME) - 6 MCQs are made for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for GATE Mock Test Mechanical Engineering (ME) - 6 below.
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GATE Mock Test Mechanical Engineering (ME) - 6 - Question 1

Fill in the blank with the correct

The police were unable to the crowd.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 1
To prevent somebody/something from moving forward or crossing.
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 2

Directions: Out of the following figures, three are similar in a certain way. One figure is not like the other three. Find out the figure that does not belong to the group.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 2
All the figures, except figure (a), are actually the same, but only rotated through different angles. That is, except (a), all the other figures are the different orientations of the same figure.
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GATE Mock Test Mechanical Engineering (ME) - 6 - Question 3

Fill in the blank with the correct word.

State ownership of the country's productive resources may unfortunately rather than ameliorate environmental problems.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 3
The use of the phrase 'rather than' implies that there is a contrast within the sentence. Therefore, in the phrase "may unfortunately rather than ameliorate (meaning improve)", the missing word should mean the opposite of ameliorate. So, the correct choice must have the meaning 'worsen'. Among the given choices, it is ' exacerbate' which has this meaning, and is the answer.
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 4

What is the chance that a leap year, selected at random, will contain 53 Sundays?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 4
There are 52 complete weeks in a calendar year i.e. 52 x 7 = 364 days

Number of days in a leap year = 366

∴ Probability of 53 Sundays = 2/7

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 5

How many squares on (a) chess board?


Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 5
Number of squares on a chess board = 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82

= 204

Alternate Method:

For n x n grid = n x (n + 1) x (2n + 1)/6 = (8 x 9 x 17)/6 = 204

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 6

In a group, the ratio of the number of boys to the number of girls is P. The ratio of the number of girls to the number of boys is Q, then P + Q is always

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 6
We know that (x + 1/x) is always greater than or equal to 2.

Now, let x be the number of boys and y be the number of girls, then

x/y = P and y/x = Q

So, P + Q = (x/y) + (y/x) ≥ 2

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 7

In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 7
Let the age of mother be x years

∴ Age of the son = x/2 years

and the age of the daughter = 3(x/2 - 7) years

and the age of the father = (x/2 - 7) years

3(x/2 - 7) = 9

3x/2 - x - 21 = 9

x/2 = 9 + 21 = 30

x = 30 x 2 = 60 years

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 8

Directions: Out of the given figures, three are similar in a certain way. One figure is not like the other three. Find out the figure which does not belong to the group.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 8
Each one of the figures, except figure (b), contains one complete square, one cup-shaped element with three sides, one L-shaped element with two sides, and one straight line.
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 9

The collection may improve only if the govemment raises taxes.

  1. Whenever the taxes are raised, the collections improve.

  2. The collections never improve when taxes are raised.

  3. The collections will not improve if the taxes are not raised.

Which of the following can be logically inferred from the above statement?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 9
The use of the word 'only if' implies that the condition that the taxes be raised is 'necessary' but the use of the word 'may' implies that it is not 'sufficient' for the collections to improve. In other words, the sentence implies that collections are not going to improve without tax raise, while if taxes were indeed raised, it may or may not improve. Consequent to this, the evaluations of the three inferences are

1. data inadequate

2. definitely false

3. definitely true

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 10

Directions: In the question given below, a statement is followed by three courses of action labelled (A), (B) and (C). A course of action is a step or administrative decision to be taken for improvement, follow-up or further action in regard to the problem, policy, etc. On the basis of the information given in the statement, you have to assume everything in the statement to be true and then decide which of the suggested courses of action logically follow(s) for pursuing.

Statement: Many political activists have decided to stage demonstrations and block traffic movement in the city during peak hours to protest against the steep rise in prices of essential commodities.

Courses of action:

(A) The Govt. should immediately ban all forms of agitations in the country.

(B) The police authority of the city should deploy additional forces all over the city to help traffic movement in the city.

(C) The state administration should carry out preventive arrests of the known criminals staying in the city.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 10
(A) is not feasible in a democracy. (C) is not followed because the problem is not concerned with criminals. (B) is the only course that authorities can resort to.
*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 11

To drill a 20 mm diameter hole in CI work piece at 450 rpm and 0.2 mm feed. The specific power is 0.03 kW - min/ cm3 and motor efficiency is 90%. Then the power of electric motor (in kW) for a drilling machine is___________.


Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 11
Volume of metal removed during drilling operation = V

∴ V= π/4 X D2 X f X N = π/4 X (2)2 X 0.02 x 450

= 28.274 cm3 /min

Power required at the drill = V x S

= 28.274 x 0.03

= 0.848 kW

Power of electric motor = 0.848/η = 0.848/0.9 = 0.942 kW

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 12

If A is a 2 x 2 non-singular square matrix, then adj(adj A) is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 12
We know that,

adj(adj(A)) = |A|n–2.A

Here, n = 2

So, we get

adj(adj(A)) = |A|2–2.A

= |A|0.A = I.A = A

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 13

An air-water vapour mixture is contained in a rigid closed vessel with a volume of 35 m3 at 1.5 bar, 120°C and Φ = 10%. The specific volume of water vapour (in m3/kg) in air is______.

(At 120°C, Psat = 1.985 bar)


Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 13
Pv = Φ x Psat

= 0.1 x 1.985

= 0.1985 bar

= 19.85 kPa

V = R/Mv x T/Pv = (8.314/18) X (393/19.85 ) = 9.145 m3/kg

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 14

In inventory control theory, the order size that minimizes total inventory holding cost and ordering cost is known as

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 14
Economic order quantity (EOQ) is the order size which minimizes total annual inventory holding cost and cost of ordering. EOQ applies only when demand for a product is constant over the year and each new order is delivered in full when inventory reaches zero. There is a fixed cost for each order placed, regardless of the number of units ordered. There is also a cost for each unit held in storage, sometimes expressed as a percentage of the purchase cost of the item.
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 15

Which one of the following is correct for an ideal gas in a closed system?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 15
TdS = dU + PdV

⇒ dU = TdS - PdV

TdS = dH - VdP

⇒ dH = TdS + VdP

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 16

A velocity field of a flow is given by V = (y − 1) i + (y − 2) j, where V is in m/s and x and y are in metres. What will be the equation of stream line passing through the point (5, 3)?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 16
V = (y − 1) i + (y − 2) j ...(i)

From equation (i), the velocity components are

u = y − 1, v = y − 2, w = 0

From the equation of stream line

On integrating, we get

(y – 2) + 2 In (y – 2) – In (y – 2) = x + C

Let (y – 2 = t) and solve

(y – 2) + In (y – 2) = x + C

At (5, 3) 1 + In (1) = 5 + C

C = 1 – 5 = – 4

Hence, equation of stream line becomes

y – 2 + In (y – 2) = x – 4

x = y + In (y – 2) + 2

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 17

An adiabatic process for an ideal gas is represented on a PV diagram by

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 17


An adiabatic process for an ideal gas is not represented on a PV diagram by a circle, a hyperbola or a parabola.

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 18

Consider the following statements:

  1. A kinematic chain is the combination of kinematic pairs joined in such a way that the relative motion between them is completely constrained.

  2. The degree of freedom of a kinematic pair is given by the number of independent coordinates required to completely specify the relative movement.

Which of the above statements is/are correct?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 18
A kinematic chain is the combination of kinematic pairs joined in such a way that each link forms a part of two pairs and the relative motion between the links is completely or successfully constrained.

The degree of freedom of a kinematic pair is given by the number of independent coordinates required to completely specify the relative movement.

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 19

A dc servomotor is coupled to a lad screw which drives the table of a CNC machine tool. A digital encoder, mounted at the end of the screw emits 500 pulses per revolution. If the pitch is 5 mm/rev, and motor speed 600 rpm. Then the table speed (in m/min) is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 19
Table speed V = p x rpm

= 5 x 600

= 3000 mm/min

= 3 m/min

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 20

The function x1/x is decreasing if

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 20
f(x) = x1/x

Let y = x1/x

Taking log on both side

Diff. w.r.t x

So,

f (x) is decreasing if f'(x) < />

1 - log x < />

log x > 1

Thus, x > e

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 21

System with mass 20 kg and equivalent stiffness of 2 kN/m is modified by attaching the viscous damper which is parallel with spring. Damping factor of system is 0.32. Modified system will have maximum magnification factor when frequency of exciting force is equal to k times of natural frequency of system. The value of k is_________ . (up to two decimal places)


Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 21

According to question, ω/ωn = k

For MF to be maximum, (1 - k2)2 + (2ξk)2 should be minimum.

So, for the denominator to be minimum,

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 22

Match List - I (Mechanical properties) with List - II (Related terms) and select the correct answer using the codes given below the list.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 22
Malleability is a physical property of metals that defines the ability to be hammered, pressed or rolled into thin sheets without breaking.

Resilience is the property of a material to absorb energy and to resist shock and impact loads. It is measured by the amount of energy absorbed per unit volume within elastic limit. This property is essential for designing the spring materials.

Hardness is the property of a metal, which gives it the ability to resist being permanent, deformed (bent, broken, or have its shape changed) when a load is applied. The greater the hardness of the metal, the greater resistance it has to deformation. It also means the ability of a metal to cut other metal.

Isotropy is a common term in materials science that means uniform in all directions. Isotropic materials exhibit the same material properties in all directions. Metals and glasses tend to be isotropic.

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 23

If |z1| = |Z2| = |Z3| = |Z4| and Z1 + Z2 + Z3 + Z4 = 0 then the points Z1, Z2, Z3 and Z4 in the argand plane are certainly not the vertices of a ________.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 23

If z1 = x1 + iy1 (A)

z2 = x1 - iy1 (B)

z3 = -x1 - iy1 (C)

and z4 = -x1 + iy1 (D)

Then |z1| = |Z2| = |Z3| = |Z4|

also, Z1 + Z2 + Z3 + Z4 = 0

Also, AB = CD = 2y,

and BC = AD = 2x,

∴ ABCD cab be a rectangle

If x1 = y1

then AB = BC = CD = DA = 2x1 = 2y1

∴ ABCD can be a square also.

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 24

Consider the following statements:

  1. The relative humidity of air does not change with temperature as long as specific humidity remains constant.

  2. Dew-point temperature is the temperature at which air is cooled at constant volume.

  3. Saturated air passing over a water surface does not cause a change of air temperature.

  4. For saturated air, dry bulb, wet- bulb and dew point temperatures are identical.

Which of the above statements are correct?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 24
Every psychometric chart includes vertical lines that represent the dry bulb temperatures, diagonals line represents wet bulb temperature and curved lines represent relative humidity.

Dry Bulb Temperature: Actual temperature of gas or mixture of gasses.

Wet Bulb temperature: Temperature obtained by an accurate thermometer having a wick moistened with distilled water

Dew point temperature: Temperature at which the liquid droplets just appear when the moist air is cooled continuously.

Relative humidity along the saturation line is 100%.

Following observations can be made from the psychometric chart

If relative humidity has not to change with the temperature then its specific humidity will not remain constant.

If air is saturated then its relative humidity is 100% that means it can't absorb more moisture, therefore if it will be made to pass over the water it will not absorb the moisture consequently its temperature will not change.

If air is saturated then its dry bulb temperature, wet bulb temperature and dew point temperature all are the same.

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 25

Which one of the following functions is strictly bounded?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 25
From the graphs below, we can see that is strictly bounded

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 26

A sine bar is specified by

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 26
The most common type of sine bar consists of an accurately lapped steel bar which is stepped at the ends, with a roller secured in to each step by a screw which holds it in contact with both faces of the step. A sine bar is specified by the distance between the centres of two rollers, i.e. 100 mm or 250 mm. A 100 mm bar is very common.
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 27

A copper bar of 60 mm diameter are to be turned over a length of 170 mm with a depth of cut of 1.5 mm feed of 0.2 mm/ rev at 230 rpm by HSS. If the tool life equation is VT0.2f0.3d0.12 = 60, then the number of components to be turned regrinding the tool is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 27
D = 60 mm; L = 170 mm

Depth of cut d = 1.5 mm; Feed (f) = 0.2 mm/rev

Speed (N) = 230 rpm

Cutting speed V = πDN/1000 = π X 60 X 230/1000 = 43.354 m /min

Given modified Taylor's tool life equation = VTn fPdq =C

∴ VTn fP dq = 43.354 x T0.2 x 0.20.3 x 1.50.12 = 60

⇒ T = 44.505

Time required for turning one job = l/f x N = 170/0.2X230

= 3.6956 min

Number of jobs that may be turned in regrinding = 44.505/3.6956 = 12.042

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 28

Given the value of the line integral along the straight line c from (0,0,0) to (1,1,1) is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 28
Given,

∴The equations of the straight line from (0,0,0) to (1,1,1) is

⇒ x = y = z = t

⇒ dx = dy = dz = dt.

If (x, y, z) = (0,0,0) then t = 0

If (x, y, z) = (1,1,1) then t = 1

∴ The line integral

= (1 - 1 - 1) - (0 - 0 - 0) = -1.

GATE Mock Test Mechanical Engineering (ME) - 6 - Question 29

For steam at P = 10 bar, hf = 762 kJ/kg and hg = 2778 kJ/kg when 100 kJ/kg heat is lost at constant pressure from steam at 10 bar and 0.8 dryness. The final dryness fraction will be

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 29
Steam at state 1

P = 10 bar; hf = 762 kJ/kg

hg = 2778 kJ/kg

x1 = 0.8

Steam at state 2

P = 10 bar

hfg = 2778 - 762 = 2016 kJ/kg

Enthalpy of mixture h1 = hf + x1hfg ......... (1)

Enthalpy of mixture at state 2

h2 = hf + X2 hfg ....... (2)

And h2 - h1 = 100 kJ

Doing (2) — (1)

⇒ 100 = hfg(x1 — x2)

X1 - x2 = 100/2016 = 0.0496

⇒ x2 = 0.8 - 0.0496 = 0.75

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME) - 6 - Question 30

The steel tube (E = 200 GPa) shown in the figure is 5.0 m long. It has 100 mm outer diameter and 16 mm wall thickness. The critical load (in kN) of the tube is _____. (Answer up to the nearest integer)


Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 6 - Question 30
We have, co = 1/2do = 50 mm

ci = co - t = 50 - 16 = 34 mm

= 3.859 x 106 mm4 = 3.859 x 10-6 m4

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