# GATE CSE 1997

 Question 1
The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. What is the probability that it will rain today and tomorrow?
 A 0.3 B 0.25 C 0.35 D 0.4
Discrete Mathematics   Probability Theory
Question 1 Explanation:
 Question 2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will
 A converge to -1 B converge to $\sqrt{2}$ C converge to $\sqrt{-2}$ D not converge
Engineering Mathematics   Numerical Method
Question 2 Explanation:
 Question 3
The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$
 A 11 B -48 C 0 D -24
Engineering Mathematics   Linear Algebra
Question 3 Explanation:
 Question 4
The concatenation of two lists is to be performed on O(1) time. Which of the following implementations of a list should be used?
 A Singly linked list B Doubly linked list C Circular doubly linked list D Array implementation of list
Question 4 Explanation:
 Question 5
The correct matching for the following pairs is
$\begin{array}{ll|ll}\hline \text{A.} & \text{All pairs shortest path} & \text{1.} & \text{Greedy} \\\hline \text{B.} & \text{Quick Sort} & \text{2.}& \text{Depth-First Search} \\\hline \text{C.}& \text{Minimum weight spanning tree} & \text{3.} & \text{Dynamic Programming} \\\hline \text{D.} & \text{Connected Components} &\text{4.} & \text{Divide and Conquer} \\\hline \end{array}$
 A A-2 B-4 C-1 D-3 B A-3 B-4 C-1 D-2 C A-3 B-4 C-2 D-1 D A-4 B-1 C-2 D-3
Algorithm   Minimum Spanning Tree
Question 5 Explanation:
 Question 6
In the following grammar
\begin{aligned} X &::= X \oplus Y \mid Y \\ Y&::= Z * Y \mid Z\\ Z&::= id \end{aligned}
Which of the following is true?
 A '$\oplus$' is left associative while '*' is right associative B Both '$\oplus$' and '*' are left associative C '$\oplus$' is right associative while '*' is left associative D None of the above
Compiler Design   Parsing
Question 6 Explanation:
 Question 7
Which of the following is essential for converting an infix expression to the postfix form efficiently?
 A An operator stack B An operand stack C An operand stack and an operator stack D A parse tree
Data Structure   Stack
Question 7 Explanation:
 Question 8
A language L allows declaration of arrays whose sizes are not known during compilation. It is required to make efficient use of memory. Which one of the following is true?
 A A compiler using static memory allocation can be written for L B A compiler cannot be written for L; an interpreter must be used C A compiler using dynamic memory allocation can be written for L D None of the above
Compiler Design   Runtime Environment
Question 8 Explanation:
 Question 9
The conditional expansion facility of macro processor is provided to
 A test a condition during the execution of the expanded program B to expand certain model statements depending upon the value of a condition during the execution of the expanded program C to implement recursion D to expand certain model statements depending upon the value of a condition during the process of macro expansion
C Programming   Conditional Statement
Question 9 Explanation:
 Question 10
Heap allocation is required for languages.
 A that support recursion B that support dynamic data structure C that use dynamic scope rules D None of the above
Compiler Design   Runtime Environment
Question 10 Explanation:
There are 10 questions to complete.