Use selection changed event for item dropdownlist, and get the selected item id when item dropdown list changing, use this id to pass with sql to get the rate of the corresponding item.
protected void ddlitems_SelectedIndexChanged(object sender, EventArgs e)
{
ListItem objItem = ddlitems.SelectedItem;
string selectedItemId = objItem.Text;
SqlConnection con = new SqlConnection("Data Source=MICKEY\\SQLEXPRESS;Initial Catalog=rr;Integrated Security=True");
SqlCommand com = new SqlCommand("select RATE from mrp where item = '" + selectedItemId + "'", con);
DataTable PriceTable = new DataTable();
SqlDataAdapter da = new SqlDataAdapter(com);
con.Open();
da.Fill(PriceTable);
con.Close();
TextBox1.Text = PriceTable.Rows[0][0].ToString().Trim();
}