GATE CSE 1996
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GATE CSE

1
Which of the following is false?
2
The minimum number of interchanges needed to convert the array

89, 19, 40, 17, 12, 10, 2, 5, 7, 11, 6, 9, 70

into a heap with the maximum element at the root is
3
The average number of key comparisons done on a successful sequential search in list of length n is
4
Quicksort is run on two inputs shown below to sort in ascending order taking first element as pivot
i) 1, 2, 3,......., n
ii) n, n-1, n-2,......, 2, 1
Let C1 and C2 be the number of comparisons made for the inputs (i) and (ii) respectively. Then,
5
The recurrence relation
T(1) = 2
T(n) = 3T(n/4) + n
has the solution, T(n) equals to
6
A binary search tree is generated by inserting in order the following integers:

50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24

The number of nodes in the left subtree and right subtree of the root respectively is
7
The pass numbers for each of the following activities

(i) object code generation
(ii) literals added to literal table
(iii) listing printed
(iv) address resolution of local symbols that occur in a two pass assembler respectively are

8
A $$ROM$$ is used to store the table for multiplication of two $$8$$ bit unsigned integers. The size of $$ROM$$ required is
9
A computer system has a three level memory hierarchy, with access time and hit ratios as shown below: GATE CSE 1996 Computer Organization - Memory Interfacing Question 24 English 1 GATE CSE 1996 Computer Organization - Memory Interfacing Question 24 English 2 GATE CSE 1996 Computer Organization - Memory Interfacing Question 24 English 3

(i) What should be the minimum size of level $$1$$ and $$2$$ memories to achieve an average access time of less than $$100$$ nsec?

(ii) What is the average access time achieved using the chosen sizes of level $$1$$ and level $$2$$ memories?

10
It gives non-uniform priority to various devices.
11
Both’s algorithm for integer multiplication gives worst performance when the multiplier pattern is
12
Consider the following floating point number representation GATE CSE 1996 Computer Organization - Computer Arithmetic Question 12 English

The exponent is in $$2’s$$ complement representation and mantissa is in the sign magnitude representation. The range of the magnitude of the normalized mantissa in this representation is

13
Consider the following statements:
(i) First-in-first out types of computations are efficiently supported by STACKS.
(ii) Implementing LISTS on linked lists is more efficient than implementing LISTS on an array for almost all the basic LIST operations.
(iii) Implementing QUEUES on a circular array is more efficient than implementing QUEUES on a linear array with two indices.
(iv) Last-in-first-out type of computations are efficiently supported by QUEUES.
14
Which of the following sequences denotes the post order traversal sequence of the tree of previous question?
15
In the balanced binary tree in Fig. given below, how many nodes will become unbalanced when a node is inserted as a child of the node “g”? GATE CSE 1996 Data Structures - Trees Question 76 English
16
A binary search tree is generated by inserting in order the following integers: 50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24 The number of nodes in the left subtree and right subtree of the root respectively is
17
An advantage of chained hash table (external hashing) over the open addressing scheme is
18
A binary search tree is used to locate the number 43. Which of the following probe sequences are not possible?
19

A library relational database system uses the following schema

USERS (User #, User Name, Home Town)

BOOKS (Books # Book Title, Author Name)

ISSUED (Book #, User #, Date)

Explain in one English sentence, what each of the following relational algebra queries is designed to determine.

(a) $$\sigma_{ \text{User#}=6}\left(\pi_{\text{User#, Book Title}}\left(\left(\text{USERS} \bowtie \text{ISSUED}\right) \bowtie \text{BOOKS}\right)\right)$$

(b) $$\pi_{\text{Author Name}}\left(\text{BOOKS} \bowtie \sigma_{\text{Home Town=Delhi}} \left(\text{USERS} \bowtie \text{ISSUED}\right)\right)$$
20
Consider the circuit in Fig. Which has a four bit binary number $${b_3}\,{b_2}\,{b_1}\,{b_0}\,$$ as input and a five bit binary number $${d_3}\,{d_2}\,{d_1}\,{d_0}\,$$ as output. The circuit implements: GATE CSE 1996 Digital Logic - Combinational Circuits Question 12 English
21
Consider the circuit in fig shown $$f$$ implements GATE CSE 1996 Digital Logic - Combinational Circuits Question 11 English
22
Consider the synchronous sequential circuit in fig. GATE CSE 1996 Digital Logic - Sequential Circuits Question 11 English 1

(a) Draw a state diagram which is implemented by the circuit. Use the following names for the states corresponding to the values of flip-flops as given below.

GATE CSE 1996 Digital Logic - Sequential Circuits Question 11 English 2

(b) Given that the initial state of the circuit is $${S_4},$$ identify the set of states which are not reachable.

23
A logic network has two data inputs $$A$$ and $$B,$$ and two control inputs $${C_0}$$ and $${C_1}$$. It implements the function $$F$$ according to the following Table. GATE CSE 1996 Digital Logic - Boolean Algebra Question 24 English

Implement the circuit using one $$4$$ to $$1$$ Multiplexor, one $$2$$-input Exclusive $$OR$$ gate, one $$2$$-input $$AND$$ gate, one $$2$$-input $$OR$$ gate and one Inverter.

24
What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in fig? GATE CSE 1996 Digital Logic - K Maps Question 8 English
25
Let $$A = \left[ {\matrix{ {{a_{11}}} & {{a_{12}}} \cr {{a_{21}}} & {{a_{22}}} \cr } } \right]\,\,$$ and $$B = \left[ {\matrix{ {{b_{11}}} & {{b_{12}}} \cr {{b_{21}}} & {{b_{22}}} \cr } } \right]\,\,$$ be
two matrices such that $$AB=1.$$
Let $$C = A\left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]$$ and $$CD=1.$$
Express the elements of $$D$$ in terms of the elements of $$B.$$
26
Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is
27
The probability that the top and bottom cards of a randomly shuffled deck are both access is
28
Let R be a non-emply relation on a collection of sets defined by $${A^R}\,B $$ if and only if $$A\, \cap \,B\, = \,\phi $$. Then, (pick the true statement)
29
Which one of the following is false?
30
Let R denote the set of real numbers. Let f: $$R\,x\,R \to \,R\,x\,R\,$$ be a bijective function defined by f (x, y ) = (x + y, x - y). The inverse function of f is given by
31
Let $$A$$ and $$B$$ be sets and let $${A^c}$$ and $${B^c}$$ denote the complements of the sets $$A$$ and $$B$$. The set $$\left( {A - B} \right) \cup \left( {B - A} \right) \cup \left( {A \cap B} \right)$$ is equal to
32
Let $$X$$ $$X = \left\{ {2,3,6,12,24} \right\}$$. Let $$ \le $$ the partial order defined by $$x \le y$$ if $$x$$ divides $$y$$. The number of edges in the Hasse diagram of $$\left( {X, \le } \right)$$ is
33
Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. It is given that there are exactly 97 functions from $$X$$ to $$Y$$. From this one can conclude that
34
Which of the following statements is false?
35
Let AX = B be a system of linear equations where A is an m x n matrix and B is a $$m\,\, \times \,\,1$$ column vector and X is a n x 1 column vector of unknowns. Which of the following is false?
36
The recurrence relation $$\,\,\,\,\,$$ $$T\left( 1 \right) = 2$$
$$T\left( n \right) = 3T\left( {{n \over 4}} \right) + n$$ has the solution $$T(n)$$ equal to
37
The matrices$$\left[ {\matrix{ {\cos \,\theta } & { - \sin \,\theta } \cr {\sin \,\,\theta } & {\cos \,\,\theta } \cr } } \right]\,\,and$$
$$\left[ {\matrix{ a & 0 \cr 0 & b \cr } } \right]\,$$ commute under multiplication
38
The formula used to compute an approximation for the second derivative of a function $$f$$ at a point $${x_0}$$ is
39
Which one of the following is false? Read $$ \wedge $$ as AND, $$ \vee $$ as OR, $$ \sim $$ as NOT, $$ \to $$ as one way implication and $$ \leftrightarrow $$ two way implication.
40
A ROM is sued to store the table for multiplication of two $$8$$-bit unsigned integers. The size of ROM required is
41
A solution to the Dining Philosophers Problem which avoids deadlock is
42
The concurrent programming constructs fork and join are as below: Fork (label) which creates a new process executing from the specified label join (variable) which decrements the specified synchronization variable (by 1) and terminates the process if the new value is not 0. Show the precedence graph for S1, S2, S3, S4 and S5 of the concurrent program below.
N = 2
M = 2
fork L3
fork L4
S1
L1 : join N
S3
L2: join M
S5
L3:S2
goto L1
L4:S4
goto L2
next:
43
A $$1000$$ Kbyte memory is managed using variable partitions but to compaction. It currently has two partitions of sizes $$200$$ Kbytes and $$260$$ Kbytes respectively. The smallest allocation request in Kbytes that could be denied is for
44
A demand paged virtual memory system uses $$16$$ bit virtual address, page size of $$256$$ bytes, and has $$1$$ Kbyte of main memory. $$LRU$$ page replacement is implemented using a list, whose current status (page numbers in decimal ) is GATE CSE 1996 Operating Systems - Memory Management Question 28 English
$$\eqalign{ & \,\, \uparrow \cr & LRU\,Page \cr} $$
For each hexa decimal address in the address sequence given below,
$$00FF,$$ $$010D,$$ $$10FF,$$ $$11B0$$
Indicate,
i) The new status of the list
ii) Page faults, if any, and
iii) Page replacements, if any
45
A file system with a one-level directory structure is implemented on a disk with disk block size of $$4$$ K bytes. The disk is used as follows:

Disk-block $$0:$$ File Allocation Table, consisting of one $$8$$-bit entry per date block, representing the data block address of the next date block in the file:

Disk block $$1:$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ Directory, with one $$32$$ bit entry per file:
Disk block $$2:$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ Data block $$1;$$
Disk block $$3:$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ Data block $$2;$$ etc.

(a) What is the maximum possible number of files?
(b) What is the maximum possible file size in blocks?

46
A computer system uses the Banker’s Algorithm to deal with deadlocks. Its current state is shown in the tables below, where P0, P1, P2 are processes and R0, R1, R2 are resource types. GATE CSE 1996 Operating Systems - Deadlocks Question 10 English
(a) Show that the system can be in this state.
(b) What will the system do on a request by process P0 for one unit of resource type R1?
47
The process state transition diagram in Figure is representative of GATE CSE 1996 Operating Systems - Process Concepts and Cpu Scheduling Question 65 English
48
Which of the following is an example of spooled device?
49
Four jobs to be executed on a single processor system arrive at time $${0^ + }$$ in the order $$A, B, C, D.$$ their burst $$CPU$$ time requirements are $$4, 1, 8, 1$$ time units respectively. The completion time of A under round robin scheduling with time slice of one time units.
50
A critical section is a program segment
51
The correct matching for the following pairs is

List - I
(A) Activation record
(B) Location counter
(C) Reference counts
(D) Address relocation

List - II
(1) Linking loader
(2) Garbage collection
(3) Subroutine call
(4) Assembler

52
Which of the following statements is false?
53
Which two of the following four regular expressions are equivalent?
(i) $${\left( {00} \right)^ * }\left( {\varepsilon + 0} \right)$$
(ii) $${\left( {00} \right)^ * }$$
(iii) $${0^ * }$$
(iv) $$0\,\,{\left( {00} \right)^ * }$$
54
Let $$L \subseteq \sum {^{^ * }\,} $$ where $$\,\sum { = \,\,\left\{ {a,b} \right\}\,\,} $$ which of the following is true?
55
If $${L_1}$$ and $${L_2}$$ are context free languages and $$R$$ a regular set, one of the languages below is not necessarily a context free language. Which one?
56
Let $$G$$ be a context free grammar where $$G = \left( {\left\{ {S,A,.B,C} \right\},\left\{ {a,b,d} \right\},P,S} \right)$$ with productions $$P$$ given below
$$\eqalign{ & S \to ABAC\,\,\,\,\,\,\,\,\,S \to aA{\mkern 1mu} \left| \varepsilon \right. \cr & S \to bB{\mkern 1mu} \left| \varepsilon \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,C \to d \cr} $$

($$\varepsilon $$ denotes the null string). Transform the given grammar $$G$$ to an equivalent context- free grammar $${G^1}$$ that has no $$\varepsilon $$ productions ($$A$$ unit production is of the from $$x \to y,\,x$$ and $$y$$ are non terminals).

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