For the circuit given in the figure, the voltage
VC
(in volts) across the capacitor is :
A
1.25$$\sqrt 2 $$ sin(5t - 0.25$$\pi $$)
B
1.25$$\sqrt 2 $$ sin(5t - 0.125$$\pi $$)
C
2.5$$\sqrt 2 $$ sin(5t - 0.25$$\pi $$)
D
2.5$$\sqrt 2 $$ sin(5t - 0.125$$\pi $$)
2
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let the input be
u
and the output be
y
of a system, and the other parameters are real
constants. Identify which among the following systems is not a linear system:
The same function 𝑥(𝑡) can also be considered as a periodic function with period T' = 40.
Let bk be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16$$, then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} = 16$$ is equal to
A
256
B
64
C
16
D
4
4
GATE ECE 2018
Numerical
+2
-0
Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n],
where X[k] = $$\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]{e^{ - j2\pi nk/N}}} $$.
The value (correct to two decimal places) of $$\sum\limits_{n = 0}^3 {x\left[ {2n} \right]} $$ is ___________.