ISRO Scientist or Engineer Computer Science 2009

The formula $$ P_k = y_0 + k\triangledown y_o + \frac{k(k+1)}{2} \triangledown^2 y_0 + ......+\frac{k...(k + n - 1)}{n!} \triangledown^n y_0 is $$

If G is a graph with e edges and n vertices the sum of the degrees of all vertices in G is

Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of componentsin the resultant graph must necessarily lie between.

A graph in which all nodes are of equal degree, is known as

If in a graph G there is one and only one path between everypair of vertices then G is a

A simple graph (a graph without parallel edge or loops) with n vertices and k components can have at most

Consider the polynomial $$ p(X) = a_0 + a_1 X + a_2 X^2 + a_3 X^3 $$, where $$ a_i \neq 0, \forall i $$. The minimum numberof multiplications needed to evaluate p on an input is

Consider the following code written in a pass-by-reference language like FORTRAN.
                          Subroutine swap (ix,iy)
                                     it = ix
                           L1:     ix = iy
                           L2:     iy = it
                              end
                              ia = 3
                              ib = 8
                              call swap (ia, ib + 5)
                              print*, ia, ib
                              end
S1: The compiler will generate code to allocate a temporary nameless cell, initialize it to 13, and pass the address of the cell to swap
S2: On execution the code will generate a runtime error on line L1
S3: On execution the code will generate a runtime error on line L2
S4: The program will print 13 and 8
S5: The program will print 13 and -2
         Exactly the following set of statement(s) is correct:

A square matrix A is called orthogonal if A’A =

If two adjacent rows of a determinantare interchanged, the value of the determinant