Find output voltage of Op-amp with Input Vio or VOS/ Analog Integrated circuit

The input offset voltage (vio or VOS) is defined as the voltage that must be applied between the two input terminals of the op-amp to obtain zero volts at the output. VOS is symbolically represented by a voltage source that is in series with either the positive or negative input terminal (it is mathematically equivalent either way). VOS is considered to be a DC error and is present from the moment that power is applied until it is turned off, with or without an input signal. It occurs during the biasing of the op-amp and its effect can only be reduced, not eliminated.
The reason for VOS is mostly due to the inherent mismatch of the input transistors and components during the fabrication of the silicon die but stresses placed on the die during the packaging process have a minor contribution. These effects collectively produce a mismatch of the bias currents that flow through the input circuit, and primarily the input devices, resulting in a voltage differential at the input terminals of the op-amp. VOS has been reduced with modern manufacturing processes through increased matching and improved package materials and assembly.
An Operational Amplifier, or op-amp for short, is fundamentally a voltage-amplifying device designed to be used with external feedback components such as resistors and capacitors between its output and input terminals.
These feedback components determine the resulting function or “operation” of the amplifier and by virtue of the different feedback configurations whether resistive, capacitive, or both, the amplifier can perform a variety of different operations, giving rise to its name of “Operational Amplifier”.
In a linear operational amplifier, the output signal is the amplification factor, known as the amplifier gain ( A ) multiplied by the value of the input signal, and depending on the nature of these input and output signals, there can be four different classifications of operational amplifier gain.