# GATE CSE 2015 SET-1

 Question 1
If $g(x)=1-x$ and $h(x)=\frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is:
 A $\frac{h(x)}{g(x)}$ B $\frac{-1}{x}$ C $\frac{g(x)}{h(x)}$ D $\frac{x}{(1-x)^{2}}$
Discrete Mathematics   Functions
Question 1 Explanation:
 Question 2
$\lim_{x\rightarrow \infty }x^{1/x}$ is
 A $\infty$ B 0 C 1 D Not defined
Engineering Mathematics   Calculus
Question 2 Explanation:

 Question 3
Match the following:
 A P-iii, Q-ii, R-iv, S-i B P-i, Q-ii, R-iv, S-iii C P-ii, Q-iii, R-iv, S-i D P-ii, Q-i, R-iii, S-iv
Algorithm   Divide and Conquer
Question 3 Explanation:
 Question 4
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n ( $\geq$2) numbers? In the recurrence equations given in the options below, c is a constant.
 A T(n)=2T(n/2)+cn B T(n)=T(n-1)+T(1)+cn C T(n)=2T(n-1)+cn D T(n)=T(n/2)+cn
Algorithm   Sorting
Question 4 Explanation:
 Question 5
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
 A 63 and 6, respectively B 64 and 5, respectively C 32 and 6, respectively D 31 and 5, respectively
Data Structure   Binary Tree
Question 5 Explanation:

There are 5 questions to complete.