# GATE CSE 2002

 Question 1
The rank of the matrix $\begin{bmatrix} 1 & 1\\ 0& 0 \end{bmatrix}$ is
 A 4 B 2 C 1 D 0
Engineering Mathematics   Linear Algebra
Question 1 Explanation:
 Question 2
The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree
 A 0 but not 1 B 1 but not 0 C 0 or 1 D 2
Engineering Mathematics   Numerical Method
Question 2 Explanation:

 Question 3
The solution to the recurrence equation $T(2^{k})=3T(2^{k-1})+1,T(1)=1$ is
 A $2^{k}$ B $\frac{3^{k+1}-1}{2}$ C $3^{log_{2}^{k}}$ D $2^{log_{3}^{k}}$
Algorithm   Recurrence Relation
Question 3 Explanation:
 Question 4
The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have same colour is.
 A 2 B 3 C 4 D $n-2[\frac{n}{2}]+2$
Discrete Mathematics   Graph Theory
Question 4 Explanation:
 Question 5
In the worst case, the number of comparisons needed to search a single linked list of length n for a given element is
 A log n B n/2 C $log_{2}^{n}-1$ D n