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 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 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 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 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
Data Structure   Link List
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 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 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 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 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
There are 10 questions to complete.

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