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Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?
A person wants to visit some places. He starts from a vertex and then wants to visit every vertex till it finishes from one vertex, backtracks and then explore other vertex from same vertex. What algorithm he should use?
Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is 
Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.
Which of the following equation is true for the hyperbola, where P is on the hyperbola curve, F1, F2 are the two fixed points, the foci, and a is the distance from the vertices of the hyperbola to its center.
Rectangular hyperbola is one of the hyperbola but the asymptotes are perpendicular in case of rectangular hyperbola.
Steps are given to determine the centre of curvature at a given point on a hyperbola. Arrange the steps. Let P be the given point on the conic, V is vertex and F and F1 are the foci. i. Draw a line GO parallel to HF and cutting the axis at O. ii. Draw a line F1G inclined to the axis and equal to FV1. iii. Then O is the centre of curvature at the vertex V. iv. On F1G, mark a point H such that HG = VF. Join H with F.
Superman is flying over the home krypton. Krypton is spherical in shape. It is in Pune city, which is situated on the equator. It is now facing towards the North Pole. He crosses the equator and flies to his left and reaches Mumbai, which is just opposite the equator of Pune city. He decides to fly to the South Pole, but he stops in Delhi on half way. What are the measurements of the following angles, considering the center of the krypton as a reference point? 1. Pune-Center-Delhi 2. Pune-Center-Mumbai 3. Mumbai-Center-Delhi
A hyperbola in which length of transverse and conjugate axis are equal is called _________ hyperbola.
At which point does the normal to the hyperbola xy = 4 at (2, 2) intersects the hyperbola again?