After doing some analysis on OOB search the following is the code which we came up with.

The technique is use the query string with query items “k=query”, “cs=This List” & “u=list’s absolute url”. Underlined items are the items which change dynamically.

http://server/sites/site/_layouts/OSSSearchResults.aspx?k=MyQuery&cs=This List&u=http://server/sites/site/MyLibrary

<div>
    <script type="text/javascript">
        function Search() {
            var libraryName = 'Library'; //Library Name            
            var url = window.location.protocol + "//" + window.location.host + _spPageContextInfo.siteServerRelativeUrl; //http://server/sites/<sitecollection> orhttp://server/sites/<sitecollection>/site
            var searchUrl = url + '/_layouts/OSSSearchResults.aspx';

            var queryText = document.getElementById('querybox').value;
            var queryUrl = searchUrl + '?k=' + queryText + '&cs=This List&u=' + url + '/' + libraryName; //http://server/sites/<sitecollection>/_layouts/OSSSearchResults.aspx?k=<Query from input box>&cs=This List&u=http://server/sites/<site>/<Library Name>

            window.navigate(queryUrl);
            //alert(queryUrl);
        }            
    </script>
    <input id="querybox" name="querybox" />
    <input onclick="Search()" name="SearchInLibrary" value="Search In Adapter Document Library" type="button" />
</div>

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