ISRO CS 2009

Question 41

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

• k and n
• k-1 and k+1
• k-1 and n-1
• k+1 and n-k

Question 42

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

• Multigraph
• Non regular graph
• Regular graph
• Complete graph

Question 43

In a graph G there is one and only one path between every pair of vertices then G is a

• Path
• Walk
• Tree
• Circuit

Question 44

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

• n edges
• n-k edges
• (n − k)(n − k + 1) edges
• (n − k)(n − k + 1)/2 edges

Question 45

Consider the polynomial, p(x) = a₀ + a₁x + a₂x² + a₃x³ where a_i ≠ 0, ∀i . The minimum number of multiplications needed to evaluate p on an input x is:

• 3
• 4
• 6
• 9

Question 46

Consider the following code written in a pass-by-reference language like FORTRAN and these statements about the code.

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:

• S1 and S2
• S1 and S4
• S3
• S1 and S5

Question 47

A square matrix A is called orthogonal if A\'A =

• I
• A
• -A
• -I

Question 48

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

• becomes zero
• remains unaltered
• becomes infinitive
• becomes negative of its original value

Question 49

If A, B, C are any three matrices, then A\'+ B\'+ C\' is equal to

• a null matrix
• A+B+C
• (A+B+C)\'
• -(A+B+C)

Question 50

Activities which ensure that the software that has been built, is traceable to customer requirement is covered as part of

• Verification
• Validation
• Maintenance
• Modeling