1
GATE ECE 2018
MCQ (Single Correct Answer)
+2
-0.67
For the circuit given in the figure, the voltage VC (in volts) across the capacitor is : GATE ECE 2018 Network Theory - Sinusoidal Steady State Response Question 3 English
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:
A
GATE ECE 2018 Signals and Systems - Representation of Continuous Time Signal Fourier Series Question 2 English Option 1
B
$$y\left( t \right) = \int\limits_0^t {{e^{\alpha \left( {t - \tau } \right)}}} \beta u\left( \tau \right)d\tau $$
C
y = au + b, b $$ \ne $$ 0
D
y = au
3
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎𝑘, that is

$$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}} {e^{jk{{2\pi } \over T}t}}$$

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
-0.67
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 ___________.
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