Let G = ( V , E) be a graph. Define $\xi\left(G\right)=\sum_di_d\times d,\;\mathrm{where}\;i_G$ is the number of vertices of degree d in G. If S and T are two different trees with ξ ( S ) = ξ (T), then
Newton-Raphson method is used to compute a root of the equation x^{2} − 13 = 0 with 3.5 as the initial value. The approximation after one iteration is
What is the possible number of reflexive relations on a set of 5 elements?
Consider the set S = {1, ω, ω^{2}}, where ω and ω^{2} are cube roots of unity. If * denotes the multiplication operation, the structure {S, *} forms
What is the value of $\underset{n\to \infty}{\mathrm{lim}}{\left(1-\frac{1}{n}\right)}^{2n}?$
The minterm expansion of $f\left(P,Q,R\right)=PQ+Q\overline{)R}+P\overline{)R}$ is
A main memory unit with a capacity of 4 megabytes is built using 1M×1-bit DRAM chips.Each DRAM chip has 1K rows of cells with 1K cells in each row. The time taken for a single refresh operation is 100 nanoseconds. The time required to perform one refresh operation on all the cells in the memory unit is
P is a 16-bit signed integer. The 2’s complement representation of P is (F87B)_{16}. The 2’s complement representation of 8*P is
The Boolean expression for the output f of the multiplexer shown below is
In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?
What does the following program print?
#include <stdio.h> void f (int *p, int *q) { p = q; *p = 2; } int i=0, j=1; int main ( ){ f(&i, &j); printf("%d %d\n", i, j ; return 0;
Two alternative packages A and B are available for processing a database having 10^{k} records. Package A requires 0.0001n^{2} time units and package B requires ${10}_{n}{\mathrm{log}}_{10}n$ time units to process n records. What is the smallest value of k for which package B will be preferred over A?
Which data structure in a compiler is used for managing information about variables and their attributes?
Which languages necessarily need heap allocation in the runtime environment?
One of the header fields in an IP datagram is the Time to Live (TTL) field. Which of the following statements best explains the need for this field?
Which one of the following is not a client server application?
Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?
Consider a B^{+}-tree in which the maximum number of keys in a node is 5. What is the minimum number of keys in any non-root node?
A relational schema for a train reservation database is given below
Passenger (pid, pname, age) Reservation (pid, cass, tid)
What pids are returned by the following SQL query for the above instance of the tables?
SELECT pid FROM Reservation WHERE class = 'AC' AND EXISTS (SELECT * FROM Passenger WHERE age 65 AND Passenger.pid Reservation.pid)
Which of the following concurrency control protocols ensure both conflict serializability and freedom from deadlock?
I. 2-phase locking II. Time-stamp ordering