# GATE Mechanical Engineering 2020 SET-1

 Question 1
Multiplication of real valued square matrices of same dimension is
 A associative B commutative C always positive definite D not always possible to compute
Engineering Mathematics   Linear Algebra
Question 1 Explanation:
Matrix multiplication is associative.
 Question 2
The value of $\lim_{x \to 1} \left ( \frac{1-e^{-c(1-x)}}{1-xe^{-c(1-x)}} \right )$ is
 A c B c+1 C $\frac{c}{c+1}$ D $\frac{c+1}{c}$
Engineering Mathematics   Calculus
Question 2 Explanation:
Applying L Hospital rule
$\lim_{x \to 1}\left ( \frac{1-e^{-c(1-x)}}{1-xe^{-c(1-x)}} \right )=\lim_{x \to 1}\left ( \frac{1-e^{-c+cx}}{-x(ce^{-c+x})-(e^{-c+cx})} \right ) =\frac{-c}{-c-1}=\frac{c}{c+1}$

 Question 3
The Laplace transform of a function f(t) is $L(f)=\frac{1}{s^2+\omega ^2}$. Then f(t) is
 A $f(t)=\frac{1}{\omega ^2}(1-\cos \omega t)$ B $f(t)=\frac{1}{\omega} \cos \omega t$ C $f(t)=\frac{1}{\omega} \sin \omega t$ D $f(t)=\frac{1}{\omega ^2}(1-\sin \omega t)$
Engineering Mathematics   Differential Equations
Question 3 Explanation:
$L(t)=\frac{1}{s^{2}+\omega ^{2}}$
$f(t)=L^{-1}\left \{ \frac{1}{s^{2}+\omega ^{2}} \right \}=\frac{1}{\omega }\sin \omega t$
 Question 4
Which of the following function f(z), of the complex variable z, is NOT analytic at all the points of the complex plane?
 A $f(z)=z^2$ B $f(z)=e^z$ C $f(z)=\sin z$ D $f(z)=\log z$
Engineering Mathematics   Complex Variables
Question 4 Explanation:
logz is not analytic at all points.
 Question 5
The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load $P \gt 0$ with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are A BF and DH only B BF, DH and GC only C BF, DH, GC, CD and DE only D BF, DH, GC, FG and GH only
Engineering Mechanics   FBD, Equilirbium, Plane Trusses and Virtual work
Question 5 Explanation:
If at any joint three forces are acting out of which two of them are collinear then force in third member must be zero.
For member ED look at joint E. Similarity look for other members.

There are 5 questions to complete.