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1
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Which one of the following options is the correct Fourier series of the periodic function $f(x)$ described below:

$$ f(x)=\left\{\begin{array}{cl} 0 & \text { if }-2 < x < -1 \\ 2 k & \text { if }-1 < x < 1 \text {; period }=4 \\ 0 & \text { if }-1 < x < 2 \end{array}\right. $$

A
$f(x)=\frac{k}{2}+\frac{2 k}{\pi}\left(\cos \frac{\pi}{2} x-\frac{1}{3} \cos \frac{3 \pi}{2} x+\frac{1}{5} \cos \frac{5 \pi}{2} x-+\ldots\right)$
B
$f(x)=\frac{k}{2}+\frac{2 k}{\pi}\left(\sin \frac{\pi}{2} x-\frac{1}{3} \sin \frac{3 \pi}{2} x+\frac{1}{5} \sin \frac{5 \pi}{2} x-+\ldots\right)$
C
$f(x)=k+\frac{4 k}{\pi}\left(\cos \frac{\pi}{2} x-\frac{1}{3} \cos \frac{3 \pi}{2} x+\frac{1}{5} \cos \frac{5 \pi}{2} x-+\ldots\right)$
D
$f(x)=k+\frac{4 k}{\pi}\left(\sin \frac{\pi}{2} x-\frac{1}{3} \sin \frac{3 \pi}{2} x+\frac{1}{5} \sin \frac{5 \pi}{2} x-+\ldots\right)$
2
GATE CE 2022 Set 1
Numerical
+1
-0

The Fourier cosine series of a function is given by :

$$f(x) = \sum\limits_{n = 0}^\infty {{f_n}\cos nx} $$

For f(x) = cos4x, the numerical value of (f4 + f5) is _________. (round off to three decimal places)

Your input ____
3
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exists for $$t>0$$ then the convolution $$z\left( t \right) = x\left( t \right) * y\left( t \right)$$ is ____________.
A
$${e^{ - t}} - {e^{ - 2t}}$$
B
$${e^{ - 2t}}$$
C
$${e^{ - t}}$$
D
$${e^{ - t}} + {e^{ - 3t}}$$
4
GATE CE 2009
MCQ (Single Correct Answer)
+1
-0.3
Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is
A
$${a \over {{s^2} - {a^2}}}$$
B
$${s \over {{s^2} - {a^2}}}$$
C
$${a \over {{s^2} + {a^2}}}$$
D
$${s \over {{s^2} + {a^2}}}$$
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Questions Asked from Marks 1
GATE CE 2025 Set 1 (1) GATE CE 2022 Set 1 (1) GATE CE 2011 (1) GATE CE 2009 (1) GATE CE 2005 (1) GATE CE 2004 (1) GATE CE 2003 (1) GATE CE 2001 (1) GATE CE 1999 (1) GATE CE 1998 (2) GATE CE 1995 (1)
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude