EC GATE 2013 (Test 6)



Tag: ec gate 2013
Q.1
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t > 0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t > 0, we need to
A. change the initial condition to -y(t) and the forcing function to 2x(t)
B. change the initial condition to 2y(0) and the forcing function to -x(t)
C. change the initial condition to j√2y(0) and the forcing function to j√2x(t)
D. change the initial condition to -2y(0) and the forcing function to -2x(t)
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.2
Consider two identically distributed zero-mean random variables U and V. Let the cumulative distribution functions of U and 2V be F(x) and G(x) respectively. Then, for all values of x
A. F(x) - G(x) ≤ 0
B. F(x) - G(x) ≥ 0
C. (F(x) - G(x)).x ≤ 0
D. (F(x) - G(x)).x ≥ 0
Answer : Option C
Explaination / Solution:
No Explaination.


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