DSM 105 Quiz

If A be a finite set of size n, then number of elements in the power set of A×A.

• 2^2n

• 2^(n2)

• (2n)2

• None of these

If the constraints of an Linear Programming Problem has an in equation of ≥ type, the variable to be added to are

• Slack

• Surplus

• Artificial

• Decision

If in a graph multiple edges between the same set of vertices are allowed, it is called?

• a. Hamiltonian Graphs

• b. Simple graph

• c. Multi graph

• d. Euler Graphs

If 𝑎=𝑞𝑏 for some integers q and 𝑎,𝑏≠0 then we say that

• b divides a

• b is a factor of a

• a is a multiple of b

• All of the above

A feasible solution to a linear programming problem

• Must satisfy all the constraints of the problem simultaneously

• Need not satisfy all of the constraints, only some of them

• Must be a corner point of the feasible region

• Must optimize the value of the objective function

The cost of a slack variable is

• 1

• 1

• 0

• M

What are the gradient and the determinant of the Hessian of the function f(x,y)=x^2y^2 at its global optimum?

• ∇f = 0i + 0j and H > 0

• ∇f = 0i + 0j and H = 0

• ∇f = 1i +1j and H < 0

• ∇f = 1i +1j and H = 0

If the kth constraint of the primal problem is equality, then the corresponding dual variable yk is _______.

• Unrestricted in sign

• Restricted in sign

• Nothing can be said

• None of the above.

Every LPP is associated with another LPP is called

• a)Primal

• b)Dual

• c)Non‐linear programming

• d)None of the above

Determine the gradient of the function x^2-2y^2-4y+6 at point (0, 0)?

• ∇f = 2i − 4j

• ∇f = 0i − 4j

• ∇f = 0i + 0j

• ∇f = −4i − 4j