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G = (V, E) is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE? I. If e is the lightest edge of some cycle in G, then every MST of G includes e II. If e is the heaviest edge of some cycle in G, then every MST of G excludes e 
Let G be a simple undirected graph. Let TD be a depth first search tree of G. Let TB be a breadth first search tree of G. Consider the following statements. (I) No edge of G is a cross edge with respect to TD. (A cross edge in G is between two nodes neither of which is an ancestor of the other in TD .) (II) For every edge (u, v) of if u is at depth i and v is at depth j in TB , then |? − ?| = 1. Which of the statements above must necessarily be true?
Which of the following statements are true about edge dislocations?
P. Edge dislocations do not have an extra half plane associated with them.
Q. The Burger vectors is perpendicular to the direction.
R. Edge dislocations can avoid obstacles by cross-slip.
S. Depending on geometry, parallel edge dislocations of opposite signs can attract or repel one another.
In a solid cubical wooden piece, a cavity is made in the shape of an inverted square pyramid, such that the depth of the cavity is 2 times the base edge of the square pyramid. If the lengths of the base edge of the pyramid and the edge of the cubical piece are in the ratio 2 ∶ 5, then the volume of the cavity is what percentage of the volume of the cubical piece.
Let G be an undirected connected graph with distinct edge weights . Let emax be the edge with maximum weight and emin be the edge with minimum weight. Which of the following statements is false.
Let G be an undirected connected graph with distinct edge weight. Let emax be the edge maximum weight and emin the edge with minimum weight. Which of the following statements are false?
A rectangular lamina of sides 20 mm X 25mm has an edge in HP and adjoining edge in VP, is tilted such that the front view appears as a rectangle of 20 mm X 15 mm. The edge which is in VP is 30 mm from the right profile plane. Find its inclinations with the corresponding principal planes.
Which of the following are correct regarding the effects of National Emergency? (1) Effect on fundamental rights.  (2) Effect on Centre-State relations. (3) Effect on the life of Lok Sabha and State Assembly. (4) Effect on Right to Life and Personal Liberty.
If the length of a edge of cube X is thrice the length of an edge of cube Y, What is the ration of the volume of cube Y to the volume of cube X?
In order to avoid tearing of the plate at edge, the distance from the center line of the rivet hole to the nearest edge of the plate in terms of dia. of rivet d should be equal to