Two Sinusoidal signal $$p\left( {{\omega _1}t} \right) = A\,\sin \omega t,$$ and $$q\left( {{\omega _2}t} \right)$$ are applied to $$X$$ and $$Y$$ inputs of a dual channel $$C.R.O,$$ the lissajous figure displayed on the screen is shown below. The signal $$q\left( {{\omega _2}t} \right)$$ will be represented as

The simultaneous application of signals $$x(t)$$ and $$y(t)$$ to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-$$8$$ display. If $$P$$ and $$Q$$ are constants, and $$x(t)=P$$ $$sin(4t+30),$$ then $$y(t)$$ is equal to

A $$CRO$$ probe has an impedance of $$500k\Omega $$ in parallel with a capacitance of $$10pF$$. The probe is used to measure the voltage between $$P$$ and $$Q$$ as shown in Fig. The measured voltage will be

List $$-$$ $${\rm I}$$ represents the figures obtained on a $$CRO$$ screen when the voltage signals $$\,{V_X}\,\, = \,\,{V_{Xm}}\sin \,\,\omega t\,\,$$ and $$V_y^ \cdot \,\, = \,\,{V_{ym}}\sin \,\,\left( {\omega t + \Phi } \right)\,\,$$ are given to its $$X$$ and $$Y$$ plates respectively and $$\Phi $$ is changed. Choose the correct value of $$\Phi $$ from List $$-$$ $${\rm I}$$ to match with the corresponding figure of List $$-$$ $${\rm II}$$.