1
GATE ECE 2015 Set 2
Numerical
+2
-0
The value of the integral $$\int_{ - \infty }^\infty {12\,\cos (2\pi )\,{{\sin (4\pi t)} \over {4\pi t}}\,dt\,}$$ is
2
GATE ECE 2015 Set 3
+2
-0.6
The complex envelope of the bandpass signal $$x(t)\, = \, - \sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right)\sin \left( {\pi t - {\pi \over 4}} \right),$$ centered about f = $${1 \over {2\,}}\,Hz,$$ is
A
$$\left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{j{\pi \over 4}}}$$
B
$$\left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{ - j{\pi \over 4}}}$$
C
$$\sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{j{\pi \over 4}}}$$
D
$$\sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{ - j{\pi \over 4}}}$$
3
GATE ECE 2014 Set 2
Numerical
+2
-0
The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}}$$ (5t) dt is
4
GATE ECE 2014 Set 1
+2
-0.6
For a function g(t), it is given that $$\int_{ - \infty }^\infty {g(t){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}}$$ for any real value $$\omega$$. If y(t)=$$\int_{ - \infty }^t {g(\tau )d\tau ,\,then\,\int_{ - \infty }^\infty {y(t)\,dt} \,}$$ is
A
0
B
- j
C
$$- {j \over 2}$$
D
$${j \over 2}$$
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