GATE CSE 1994 Previous-Year Questions (PYQ)
Read the following instructions carefully:
(i) This question paper consists of Two sections: A & B.
(ii) Section ‘A’ has EIGHT questions. Answer ALL questions in this Section.
(iii) Section ‘B’ has TWENTY questions. Answer any TEN questions in this Section.
(iv) Begin answer for this section on a fresh page.
(v) Answer to questions in each Section should appear together in the same sequence in which they appear in the question paper.
(vi) There will be no negative marking.
Section - A (100 Marks)
Choose one of the alternatives for the following questions:
Question 1.
FORTRAN implementations do not permit recursion because
(a) they use static allocation for variables
(b) they use dynamic allocation for variables
(c) stacks are not available on all machines
(d) it is not possible to implement recursion on all machines
Question 2.
Let A and B be real symmetric matrices of size n × n. Then which one of the following is true?
(a) AA’ = 1
(b) A = A-1
(c) AB = BA
(d) (AB)’ = BA
Question 3.
Backward Euler method for solving the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x}\)=f(x,y) is specified by, (choose one of the following).
(a) yn+1 = yn + hf(xn, yn)
(b) yn+1 = yn + hf(xn+1,yn+1)
(c) yn+1 = yn-1 + 2hf(xn,yn)
(d) yn+1 = (1+h)f(xn+1,yn+1)
Question 4.
Let A and B be any two arbitrary events. Which one of the following is true?
(a) P(A∩B) = P(A)P(B)
(b) P(A∪B) = P(A) + P(B)
(c) P(A|B) = P(A∩B)P(B)
(d) P(A∪B) ≤ P(A) + P(B)
Question 5.
An unrestricted use of the “goto” statement is harmful because
(a) it makes it more difficult to verify programs
(b) it increases the running time of the programs
(c) it increases the memory required for the programs
(d) it results in the compiler generating longer machine code
Question 6.
The number of distinct simple graphs with upto three nodes is
(a) 15
(b) 10
(c) 7
(d) 9
Question 7.
The recurrence relation that arises in relation with the complexity of binary search is:
(a) T(n) = T(\(\frac n2\)) + k, k a constant
(b) T(n) = 2T(\(\frac n2\)) + k, k a constant
(c) T(n) = T(\(\frac n2\)) + log n
(d) T(n) = T(\(\frac n2\)) + n
Question 8.
The logic expression for the output of the circuit shown in figure below is:
(a) \( \overline AC+\overline BC+CD\)
(b) \(A\overline C+B\overline C+CD\)
(c) \(ABC+\overline C\;\overline D\)
(d) \(\overline A\;\overline B+\overline B\;\overline C\;+\;CD\)
Question 9.
The rank of matrix \(\begin{bmatrix}0&0&-3\\9&3&5\\3&1&1\end{bmatrix}\) is
(a) 0
(b) 1
(c) 2
(d) 3
Question 10.
Some group (G,o) is known to be abelian. Then, which one of the following is true for G?
(a) g = g-1 for every g ∈ G
(b) g = g2 for every g ∈ G
(c) (goh)2 = g2oh2 for every g, h ∈ G
(d) G is of finite order
Question 11.
In a compact single dimensional array representation for lower triangular matrices (i.e all the elements above the diagonal are zero) of size , n × n non-zero elements (i.e elements of the lower triangle) of each row are stored one after another, starting from the first row, the index of the (i, j)th element of the lower triangular matrix in this new representation is:
(a) i + j
(b) i + j – 1
(c) \(j+\frac{i(i-1)}2\)
(d) \(i+\frac{j(j-1)}2\)
Question 12.
Generation of intermediate code based on an abstract machine model is useful in compilers because
(a) It makes implementation of lexical analysis and syntax analysis easier
(b) Syntax-directed translations can be written for intermediate code generation
(c) It enhances the portability of the front end of the compiler
(d) It is not possible to generate code for real machines directly from high level language programs
Question 13.
A memory page containing a heavily used variable that was initialized very early and is in constant use is removed when
(a) LRU page replacement algorithm is used
(b) FIFO page replacement algorithm is used
(c) LFU page replacement algorithm is used
(d) None of the above
Question 14.
Which of the following permutations can be obtained in the output (in the same order) using a stack assuming that the input is the sequence 1, 2, 3, 4, 5 in that order?
(a) 3, 4, 5, 1, 2
(b) 3, 4, 5, 2, 1
(c) 1, 5, 2, 3, 4
(d) 5, 4, 3, 1, 2
Question 15.
The number of substrings (of all lengths inclusive) that can be formed from a character string of length n is
(a) n
(b) n2
(c) \(\frac{n(n-1)}2\)
(d) \(\frac{n(n+1)}2\)
Question 16.
Which of the following conversions is not possible (algorithmically)?
(a) Regular grammar to context-free grammar
(b) Non-deterministic FSA to deterministic FSA
(c) Non-deterministic PDA to deterministic PDA
(d) Non-deterministic Turing machine to deterministic Turing machine
Question 17.
Linked lists are not suitable data structures of which one of the following problems?
(a) Insertion sort
(b) Binary search
(c) Radix sort
(d) Polynomial manipulation
Question 18.
Which of the following features cannot be captured by context-free grammars?
(a) Syntax of if-then-else statements
(b) Syntax of recursive procedures
(c) Whether a variable has been declared before its use
(d) Variable names of arbitrary length
Question 19.
Which of the following algorithm design techniques is used in the quicksort algorithm?
(a) Dynamic programming
(b) Backtracking
(c) Divide and conquer
(d) Greedy method
Question 20.
In which one of the following cases is it possible to obtain different results for call-by reference and call-by-name parameter passing methods?
(a) Passing a constant value as a parameter
(b) Passing the address of an array as a parameter
(c) Passing an array element as a parameter
(d) Passing an array following statements is true
Question 21.
Which one of the following statements is true?
(a) Macro definitions cannot appear within other macro definitions in assembly language programs
(b) Overlaying is used to run a program which is longer than the address space of computer
(c) Virtual memory can be used to accommodate a program which is longer than the address space of a computer
(d) It is not possible to write interrupt service routines in a high level language
Question 22.
Which one of the following statements is false?
(a) Optimal binary search tree construction can be performed efficiently using dynamic programming.
(b) Breadth-first search cannot be used to find connected components of a graph
(c) Given the prefix and postfix walks over a binary tree, the binary tree cannot be uniquely constructed.
(d) Depth-first search can be used to find connected components of a graph.
Question 23.
Consider the following two functions:
\(g_1(n)=\left\{\begin{array}{l}n^3\;\;for\;\;0\leq n\leq10,000\\n^2\;for\;\;n\geq10,000\end{array}\right.\)
\(g_2(n)=\left\{\begin{array}{l}n\;\;for\;\;0\leq n\leq100\\n^3\;for\;\;n>100\end{array}\right.\)
Which of the following is true?
(a) g1(n) is O(g2(n))
(b) g1(n) is O(n3)
(c) g2(n) is O(g1(n))
(d) g2(n) is O(n)
Question 24.
Consider the following heap (figure) in which blank regions are not in use and hatched region are in used.
The sequence of requests for blocks of size 300, 25, 125, 50 can be satisfied if we use
(a) either first fit or best fit policy (any one)
(b) first fit but not best fit policy
(c) best fit but first fit policy
(d) None of the above
Question 25.
Fill in the blanks:
2.1 The number of flip-flops required to construct a binary modulo N counter is __________
2.2 On the set N of non-negative integers, the binary operation __________ is associative and non-commutative.
2.3 Amongst the properties {reflexivity, symmetry, anti-symmetry, transitivity} the relation R ={(x,y) ∈ N2| x ≠ y} satisfies __________
2.4 The number of subsets {1,2,……n} with odd cardinality is __________
Question 24.
T