After some search and advice from many individual I finally found some logic and understood the expression in Doctrine. Below I have given all the expression with an example. Code to be tested.
$ex1 = $qry->expr()->like('e.user', "'".$user."'");
$ex2 = $qry->expr()->orX(
$qry->expr()->between('e.datetime', "'".$datetimefrom."'", "'".$datetimeto."'")
);
$ex3 = $qry->expr()->in('e.country', $country);
$final_expression = $qry->expr()->andX($ex1,$ex2,$ex3);
You can also refer the below issue and solution which helped me to solve the above Question by me.
REF Multiple Query in Doctrine with NAND,NOR,NOT,AND Operators