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How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women?
Which of the following statement(s) is/are false?
(a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
(b) A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c) A complete graph (Kn) has a Hamilton Circuit whenever n≥3
(d) A cycle over six vertices (C6) is not a bipartite graph but a complete graph over 3 vertices is bipartite.
Which of the following is/are not true?
(a) The set of negative integers is countable.
(b) The set of integers that are multiples of 7 is countable.
(c) The set of even integers is countable.
(d) The set of real numbers between 0 and 1/2 is countable.
Consider the graph given below:
The two distinct sets of vertices, which make the graph bipartite are:
A tree with n vertices is called graceful, if its vertices can be labelled with integers 1, 2, …,n such that the absolute value of the difference of the labels of adjacent vertices are all different. Which of the following trees are graceful?
Which of the following arguments are not valid?
(a) “If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard”.
(b) “Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty”.
(c) If n is a real number such that n>1, then n2>1. Suppose that n2>1, then n>1.
Let P(m,n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.
(a) ∃m ∀n P(m,n)
(b) ∀n P(1,n)
(c) ∀m ∀n P(m,n)
Match the following terms:
List – I List – II
(a) Vacuous proof (i) A proof that the implication p→q is true based on the fact that p is false
(b) Trivial proof (ii) A proof that the implication p→q is true based on the fact that q is true
(c) Direct proof (iii) A proof that the implication p→q is true that proceeds by showing that q must be true when p is true.
(d) Indirect proof (iv) A proof that the implication p→q is true that proceeds by showing that p must be false when q is false.
Consider the compound propositions given below as:
(a)p∨∼(p∧q)
(b)(p∧∼q)∨∼(p∧q)
(c)p∧(q∨r)
Which of the above propositions are tautologies?
Which of the following property/ies a Group G must hold, in order to be an Abelian group?
(a) The distributive property
(b) The commutative property
(c) The symmetric property
Consider the following program:
#include
main()
{
int i, inp;
float x, term=1, sum=0;
scanf(“%d %f”,&inp, &x);
for(i=1;i<=inp;i++)
{
term=term*x/i;
sum=sum+term;
}
printf(“Result=%f\n”,sum);
}
The program computes the sum of which of the following series?
Consider the following two statements:
(a) A publicly derived class is a subtype of its base class.
(b) Inheritance provides for code reuse.
Which of the following statements is correct?
Consider a “CUSTOMERS” database table having a column “CITY” filled with all the names of Indian cities (in capital letters). The SQL statement that finds all cities that have “GAR” somewhere in its name, is:
Match the following database terms to their functions:
List-I List-II
(a) Normalization (i) Enforces match of primary key to foreign key
(b) Data Dictionary (ii) Reduces data redundancy in a database
(c) Referential Integrity (iii) Define view(s) of the database for particular user(s).
(d) External Schema (iv) Contains metadata describing database structure.
In general, in a recursive and non-recursive implementation of a problem (program):
A three dimensional array in ‘C’ is declared as int A[x][y][z]. Here, the address of an item at the location A[p][q][r] can be computed as follows (where w is the word length of an integer):
In C++, which system-provided function is called when no handler is provided to deal with an exception?
Which of the following provides the best description of an entity type?
Data which improves the performance and accessibility of the database are called:
A relation R={A,B,C,D,E,F,G} is given with following set of functional dependencies:
F={AD→E, BE→F, B→C, AF→G}
Which of the following is a candidate key?
Which of the following services is not provided by wireless access point in 802.11 WLAN?
Which of the following fields in IPv4 datagram is not related to fragmentation?
Four channels are multiplexed using TDM. If each channel sends 100 bytes/second and we multiplex 1 byte per channel, then the bit rate for the link is ……………
In a typical mobile phone system with hexagonal cells, it is forbidden to reuse a frequency band in adjacent cells. If 840 frequencies are available, how many can be used in a given cell?
Using p=3, q=13, d=7 and e=3 in the RSA algorithm, what is the value of ciphertext for a plain text 5?
A virtual memory has a page size of 1K words. There are eight pages and four blocks. The associative memory page table contains the following entries:
Which of the following list of virtual addresses (in decimal) will not cause any page fault if referenced by the CPU?
Page | Block |
---|---|
0 | 3 |
2 | 1 |
5 | 2 |
7 | 0 |
Suppose that the number of instructions executed between page faults is directly proportional to the number of page frames allocated to a program. If the available memory is doubled, the mean interval between page faults is also doubled. Further, consider that a normal instruction takes one micro second, but if a page fault occurs, it takes 2001 micro seconds. If a program takes 60 sec to run, during which time it gets 15000 page faults, how long would it take to run if twice as much memory were available?
Consider a disk with 16384 bytes per track having a rotation time of 16 msec and average seek time of 40 msec. What is the time in msec to read a block of 1024 bytes from this disk?
A system has four processes and five relocatable resources. The current allocation and maximum needs are as follows:
The smallest value of x for which the above system in safe state is ………….999
In Unix, the login prompt can be changed by changing the contents of the file ……………
A data cube C, has n dimensions, and each dimensions has exactly p distinct values in the base cuboid. Assume that there are no concept hierarchies associated with the dimensions. What is the maximum number of cells possible in the data cube, C?
Suppose that from given statistics, it is known that meningitis causes stiff neck 50% of the time, that the proportion of persons having meningitis is 1/50000, and that the proportion of people having stiff neck is 1/20. Then the percentage of people who had meningitis and complain about stiff neck is:
…………….. system is market oriented and is used for data analysis by knowledge workers including Managers, Executives and Analysts.
……………… allows selection of the relevant information necessary for the data warehouse.
The hash function used in double hashing is of the form:
In the following graph, discovery time stamps and finishing time stamps of Depth First Search (DFS) are shown as x/y where x is discovery time stamp and y is finishing time stamp
It shows which of the following depth first forest?
The number of disk pages access in B-tree search, where h is height, n is the number of keys, and t is the minimum degree, is:
The inorder traversal of the following tree is
tree figure
An ideal sort is an in-place-sort whose additional space requirement is ……………
Which of the following is not a congestion policy at network layer?
Loop unrolling is a code optimization technique:
What will be the hexadecimal value in the register ax (32-bit) after executing the following instructions?
Mov al, 15
Mov ah, 15
Xor al, al
Mov cl, 3
Shr ax, cl
Which of the following statements is false?
System calls are usually invoked by using:
The …………… transfers the executable image of a C++ program from hard disk to main memory.
In software testing, how the error, fault and failure are related to each other?
Which of the following is not a software process model.
How many solutions are there for the equation x+y+z+u=29 subject to the constraints that x≥1, y≥2, z≥3 and u≥0?
A unix file system has 1-KB blocks and 4-byte disk addresses. What is the maximum file size if i-nodes contain 10 direct entries and one single, double and triple indirect entry each?
…………….. uses electronic means to transfer funds directly from one account to another rather than by cheque or cash?