# 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

“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

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?

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?

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?

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

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

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?

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

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

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

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

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

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 $\int_a^bf\left(x\right)dx=$

$F\left(z\right)$ 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?

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

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

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

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.

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?