Top-level control cannot be added to a control

Use this:

private void frmInitialEntryBooks_Load(object sender, EventArgs e)
{
    frmSujbect objForm = new frmSujbect();
    objForm.TopLevel = false;
    pnl.Controls.Add(objForm);
    objForm.FormBorderStyle = System.Windows.Forms.FormBorderStyle.None;
    objForm.Dock = DockStyle.Fill;
    objForm.Show();
}

You are missing objForm.TopLevel = false;

Set TopLevel = False in frmsubject then try

frmSujbect objForm = new frmSujbect();
pnl.Controls.Add(objForm);
objForm.Show();