$(1)$ In a binary heap with $'n'$ elements with the smallest element at the root, the $7th$ smallest element can be found in time?
$A)\theta(nlogn)$ $B)\theta(n)$ $C)\theta(logn)$ $D)\theta(1)$
$(2)$ In binary max heap containing $'n'$ numbers, the smallest element can be found in time?
$A)\theta(n)$ $B)\theta(logn)$ $C)\theta(loglogn)$ $D)\theta(1)$
$(3)$ Consider the process of inserting an element into a max heap. If we perform a binary search on the path from new leaf to root, find the position of a newly inserted element, the number of comparisons performed are____________
$(4)$ We have a binary heap on $'n'$ elements and wish to insert $'n'$ more elements(not necessarily one after another) into this heap. The total time required for this is?
$A)\theta(logn)$ $B)\theta(n)$ $A)\theta(nlogn)$ $A)\theta(n^{2})$