# 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
Question 5 Explanation:
 Question 6
Which of the following is true?
 A The set of all rational negative numbers forms a group under multiplication. B The set of all non-singular matrices forms a group under multiplication. C The set of all matrices forms a group under multiplication. D Both B and C are true.
Discrete Mathematics   Group Theory
Question 6 Explanation:
 Question 7
The language accepted by a Pushdown Automaton in which the stack is limited to 10 items is best described as
 A Context free B Regular C Deterministic context D Recursive
Theory of Computation   Push-down Automata
Question 7 Explanation:
 Question 8
"If X then Y unless Z" is represented by which of the following formulas in prepositional logic? ($"\neg"$, is negation, $"\wedge "$ is conjunction, and $"\rightarrow "$ is implication)
 A $(X\wedge \neg Z)\rightarrow Y$ B $(X\wedge Y)\rightarrow \neg Z$ C $X\rightarrow (Y \wedge \neg Z)$ D $(X\rightarrow Y )\wedge \neg Z$
Discrete Mathematics   Propositional Logic
Question 8 Explanation:
 Question 9
A device employing INTR line for device interrupt puts the CALL instruction on the data bus while
 A $\overline{INTA}$ is active B HOLD is active C READY is active D None of the above
Computer Organization   Interrupt
Question 9 Explanation:
 Question 10
In 8085 which of the following modifies the program counter ?
 A Only PCHL instruction B Only ADD instructions C Only JMP and CALL instructions D All instructions
Computer Organization   Machine Instruction
Question 10 Explanation:
There are 10 questions to complete.