# Mechanical Engineering - GATE 2020 Paper Solution

He is known for his unscrupulous ways. He always sheds _______ tears to deceive people.

Jofra Archer, the England fast bowler, is _______ than accurate.

Select the word that fits the analogy:

Buid : Building : : Grow : _______

I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase "having said that" mean in the given text ?

Define [ x ] as the greatest integer less than or equal to x , for each $x\in\left(-\infty,\infty\right)$. If $y=\lbrack x\rbrack,$ then area under y for $x\in\lbrack1,4\rbrack$ is ________ .

Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding ?

P, Q, R and S are to be uniquely coded using $\mathrm\alpha$ and $\mathrm\beta$. If P is coded as $\alpha\alpha$ and Q as $\mathrm{αβ}$, then R and S, respectively, can be coded as _________ .

The sum of the first n terms in the sequence 8, 88, 888, 8888, ... is ________ .

Select the graph that schematically represents BOTH $y=x^m$ and $y=x^1/m$ properly in the interval $0\leq x\leq1$ , for integer values of m , where m > 1.

The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is _______ .

Multiplication of real valued square matrices of same dimension is

The value of

$\lim\limits_{x\rightarrow1}\left(\frac{1-e^{-c\left(1-x\right)}}{1-x\;e^{-c\left(1-x\right)}}\right)\;\mathrm{is}$

The Laplace transform of a function $f\left(t\right)$ is $\mathcal L\left(f\right)=\frac1{\left(s^2+\omega^2\right)}$. Then, $f\left(t\right)$ is

Which of the following function $f(z)$, of the complex variable z , is NOT analytic at all the points of the complex plane ?

The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are

A single-degree-of-freedom oscillator is subjected to harmonic excitation $F\left(t\right)=F_0\cos\left(\omega t\right)$ as shown in the figure.

The non-zero value of $\omega$, for which the amplitude of the force transmitted to the ground will be $F_0$ , is

The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the $\style{font-family:'Times New Roman'}{\sigma-\tau}$ plane is 1 MPa, the Mohr's circle representation of the state-of-stress is given by

A four mechanism is shown below.

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be

The crystal structure of $\gamma$ iron (austenite phase) is