How to access content page function from master page in ASP.Net

Try This

in master page

<asp:DropDownList ID="ddlcategories" runat="server" AutoPostBack="True" OnSelectedIndexChanged="ddlcategories_SelectedIndexChanged">
    <asp:ListItem>One</asp:ListItem>
    <asp:ListItem>Two</asp:ListItem>
</asp:DropDownList>

Master page CS:

public string SelectedValue
{
    get
    {
        return ddlcategories.SelectedValue;
    }
    set
    {
        ddlcategories.SelectedValue= value;
    }
}

protected void ddlcategories_SelectedIndexChanged(object sender, EventArgs e)
{
    SelectedValue = ddlcategories.SelectedValue;
}

Content Page markup:

<%@ MasterType VirtualPath="~/Site1.Master" %>

<asp:Label ID="Label1" runat="server" Text="Label"></asp:Label>

Content page CS.

protectedvoidPage_PreRender(object sender,EventArgs e){Label1.Text=Master.SelectedValue;}