Q.What is the use of bypass capacitor in CE amplifier?

The bypass capacitor is placed across the emitter resistor to give the AC current an easy path around it. …

[!TLDR]

The bypass capacitor keeps AC out of $R_E$ so gain stays high while DC stabilisation is retained.

The emitter resistor $R_E$ is needed for DC bias stability, but if AC also flowed through it, the resulting negative feedback would sharply reduce the voltage gain. A bypass capacitor $C_E$ connected across $R_E$ offers very low reactance to AC, so the AC emitter current is shunted through the capacitor instead of $R_E$. Thus $R_E$ provides DC stabilisation while the capacitor prevents any loss of AC gain. …