Is it possible to have a sine wave Distortion like this when we give +5v DC Offset to a 340khz sinusoidal signal where my function generator can output upto 3MHz signal or it's the problem of my function generator...same problem do arising in square and triangular wave also...plzz help

 

If by distortion you mean it jumping around then it is caused by your scope not triggering.
Either select auto-trigger or adjust the trigger level until you get a stable trace.

 

If by distortion you mean it jumping around then it is caused by your scope not triggering.
Either select auto-trigger or adjust the trigger level until you get a stable trace.

Thank u sir thanks a lot for ur help...I am just new in ECE and started learning things so I don't have that much of knowledge can u please explain why this happens and what trigger input actually is...??? BTW now it's working properly

 

This might help: https://www.electronics-notes.com/articles/test-methods/oscilloscope/oscilloscope-trigger.php

 

And AC couple your trigger signal. That's why you have that option.

 

You really need to sit down and learn the purpose and operation of each and every knob on your oscilloscope.
Read the manual.
Come here and ask if you don't understand.

 

One common confusion with oscilloscopes is the DC vs AC input coupling setting.
AC coupling is not used for all AC signals, it's only used when you want to look at an AC signal that has a large DC bias relative to its AC value.
All AC coupling does is connect a capacitor in series with the input to block the DC component.
The AC coupling acts as a high-pass filter and will rolloff or distort signal components below the corner frequency (such as causing droop in low frequency square-wave signals).
AC coupling will also shift the signal so the oscilloscope 0V point becomes the signals average value. Thus, for example, a 0-5V square-wave will look like a ±2.5V signal with AC coupling.

So you only want to use the AC setting when the signal is riding on a DC offset that you want to suppress/ignore.
Otherwise you use the DC setting.