GATE CSE 2015 SET-1

If g(x)=1-x and h(x)=\frac{x}{x-1}, then \frac{g(h(x))}{h(g(x))} is:

\lim_{x\rightarrow \infty }x^{1/x} is

Match the following:

Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n ( \geq2) numbers? In the recurrence equations given in the options below, c is a constant.

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

Match the following:

Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)?
I. 3, 5, 7, 8, 15, 19, 25
II. 5, 8, 9, 12, 10, 15, 25
III. 2, 7, 10, 8, 14, 16, 20
IV. 4, 6, 7, 9 18, 20, 25

Which one of the following is TRUE at any valid state in shift-reduce parsing?

Which one of the following is NOT equivalent to p\leftrightarrow q?

For a set A, the power set of A is denoted by 2^{A}. If A={5,{6},{7}}, which of the following options are TRUE?
I. \phi \in 2^{A}
II. \phi \subseteq 2^{A}
III. {5,{6}} \in 2^{A}
IV. {5,{6}}\subseteq 2^{A}