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(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed graph with L2 edges. If G has 6 vertices every of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can have? (c) Explain the truth value for each of the following statements: (i) 4 + 3 = 6 AND 3 + 3 = 6(ii) 5 + 3 = 8 OR 3 + 1 = 5(d) Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k is a positive integer. Also estimate f(n) if f is an increasing function. (e) Show the sufficient conditions of Dirac and Ore for a graph to be Hamiltonian. Give an instance of a graph that does not satisfy Dirac's condition, but satisfies Ore's condition. (f) Measure -25 + 75 using 2's complement.
Determine Rank Correlation Coefficient A group of 8 accountancy students are tested in Quantitative Techniques and Law II. Their rankings in the two tests were as:
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When 6 boys were admitted & 6 girls left the percentage of boys increased from 60% to 75%. Find the original no. of boys and girls in the class. Ans: Let the no. of Boys be x
How do you calculate for the distance between two co-ordinates?
why minimum three coplanar vectors are required to give zero resultant and not two?
the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. H v (~T > R) 2. Hv (E > F) 3. ~T v E 4. ~H & D / R v F INSTRUCTIONS: Con
PROOF OF VARIOUS INTEGRAL FACTS/FORMULAS/PROPERTIES In this section we've found the proof of several of the properties we saw in the Integrals section and also a couple from t
If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value(s) of k..
If a differential equation does have a solution how many solutions are there? As we will see ultimately, this is possible for a differential equation to contain more than one s
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