Mechanical Engineering - GATE 2018 Paper Solution

“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

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“Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

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Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

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A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?

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A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

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For integers $a,\;b$ and $c$ what would be the minimum and maximum values respectively of $a+\;b+\;c$ if $\log\left|a\right|+\log\left|b\right|+\log\left|c\right|=0?$

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Given that $a\;$and $\;b$ are integers and  $a\;+a^2\;b^3$ is odd, which one of the following statements is correct ?

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From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

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Which of the following functions describe the graph shown in the below figure?

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Consider the following three statements:
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.

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

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Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is

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The rank of the matrix $\begin{bmatrix}-4&\;\;\;\;1&-1\\-1&-1&-1\\\;\;\;7&-3&\;\;\;1\;\end{bmatrix}$ is

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According to the Mean Value Theorem, for a continuous function $f\left(x\right)$ in the interval $\left[a,\;b\right],$ there exists a value $\xi$ in this interval such that $\int_a^bf\left(x\right)dx=$

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$F\left(z\right)$ is a function of the complex variable $z=x+iy$ given by

$F\left(z\right)=i\;z\;+\;k\;Re\;\left(z\right)+i\;Im\left(z\right)$.

For what value of k will $F\left(z\right)$ satisfy the Cauchy-Riemann equations?

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A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

The tensions in the strings are

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If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

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The equation of motion for a spring-mass system excited by a harmonic force is

$M\ddot x+Kx=F\;c\mathrm{os}\left(\omega t\right)$,

where $M$ is the mass, $K$ is the spring stiffness, $F$ is the force amplitude and $\omega$ is the angular frequency of excitation. Resonance occurs when $\omega$ is equal to

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For an Oldham coupling used between two shafts, which among the following statements are correct?
I.           Torsional load is transferred along shaft axis.
II.          A velocity ratio of 1:2 between shafts is obtained without using gears.
III.         Bending load is transferred transverse to shaft axis.
IV.         Rotation is transferred along shaft axis.

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For a two-dimensional incompressible flow field given by $\overset\rightharpoonup u=A\left(x\widehat i-y\widehat j\right)$, where $A>0$ , which one of the following statements is FALSE?

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Which one of the following statements is correct for a superheated vapour?