1
GATE EE 2016 Set 1
+2
-0.6
The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is the input signal. A signal z(t) is called eigen-signal of the system T, when T{z(t)}= yz(t), where $$\gamma$$ is a complex number, in general, and is called an eigen value of T. suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?
A
cos(t) is and eigen-signal but sin(t) is not
B
cos(t) is and sin(t) are both eigen-signal but with different eigen values
C
sin(t) is an eigen-signal but cos(t) is not
D
cos(t) and sin(t) are both eigen-signal with identical eigen values
2
GATE EE 2014 Set 3
+2
-0.6
A continuous-time LTI system with system function H($$\omega$$) has the following pole-zero plot. For this system, which of the alternatives is TRUE? A
$$\left|H\left(0\right)\right|\;>\;\left|H\left(\omega\right)\right|;\;\left|\omega\right|\;>0$$
B
$$\left|H\left(\omega\right)\right|$$ has multiple maxima,at $$\omega_1\;and\;\omega_2$$
C
$$\left|H\left(0\right)\right|\;<\;\left|H\left(\omega\right)\right|;\;\left|\omega\right|\;>0$$
D
$$\left|H\left(\omega\right)\right|=\;cons\;\tan\;t;\;-\infty\;<\;\omega\;<\;\infty$$
3
GATE EE 2010
+2
-0.6
Given f(t) and g(t)as shown below: The Laplace transform of g(t) is
A
$$\frac1s\left(e^{3s}\;-\;e^{5s}\right)$$
B
$$\frac1s\left(e^{-5s}\;-\;e^{-3s}\right)$$
C
$$\frac{e^{-3s}}s\left(1\;-\;e^{-2s}\right)$$
D
$$\frac1s\left(e^{5s}\;-\;e^{3s}\right)$$
4
GATE EE 2010
+2
-0.6
Given f(t) and g(t)as shown below: g(t) can be expressed as
A
g(t) = f(2t - 3)
B
g(t) = $$f\left(\frac t2-3\right)$$
C
g(t) = $$f\left(2t-\frac32\right)$$
D
g(t) = $$f\left(\frac t2-\frac32\right)$$
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement
EXAM MAP
Joint Entrance Examination