1
GATE EE 2008
+2
-0.6
A general filter circuit is shown in figure

The output of the filter in above is given to the circuit shown in figure The gain $${V_S}$$ frequency characteristic of the $$0/p$$ $$\left( {{V_0}} \right)$$ will be

A
B
C
D
2
GATE EE 2008
+2
-0.6
A waveform generator circuit using $$OPAMPs$$ is shown in the figure. It produces a triangular wave at point $$'P'$$ with a peak to peak voltage of $$5V$$ for $${v_1} = 0\,V.$$

If the voltage $${v_1}$$ is made $$+2.5$$ $$V,$$ the voltage waveform at $$'P'$$ will become.

A
B
C
D
3
GATE EE 2008
+2
-0.6
The truth of a monoshot shown in the figure is given in the table below:

Two monoshots, one positive edge triggered and other negative edge triggered, are connected as shown in the figure. The pulse widths of the two monoshot options, $${Q_1}$$ and $${Q_2}$$ are $${T_{O{N_1}}}$$ and $${T_{O{N_2}}}$$ respectively.

The frequency and the duty cycle of the signal at $${Q_1}$$ will respectively be

A
$$F = {1 \over {{T_{ON1}} + {T_{ON2}}}},{\mkern 1mu} D = {{{T_{O{N_1}}}} \over {{T_{O{N_1}}} + {T_{O{N_2}}}}}$$
B
$$F = {1 \over {{T_{O{N_1}}} + {T_{O{N_2}}}}},{\mkern 1mu} D = {{{T_{O{N_2}}}} \over {{T_{O{N_1}}} + {T_{O{N_2}}}}}$$
C
$$F = {1 \over {{T_{O{N_1}}}}},{\mkern 1mu} D = {{{T_{O{N_1}}}} \over {{T_{O{N_1}}} + {T_{O{N_2}}}}}$$
D
$$F = {1 \over {{T_{O{N_2}}}}},{\mkern 1mu} D = {{{T_{O{N_1}}}} \over {{T_{O{N_1}}} + {T_{O{N_2}}}}}$$
4
GATE EE 2008
+1
-0.3
A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$

Where $$\delta \left( t \right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by $$u(t),y(t)$$ can be of the form

A
$${e^{ t}}$$
B
$${e^{ - t}}$$
C
$${e^{ t}}$$$$u(t)$$
D
$${e^{ - t}}$$$$u(t)$$
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