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The line graph L(G) of a simple graph G is defined as follows: There is exactly one vertex v(e) in L(G) for each edge e in G. For any two edges e and e' in G, L(G) has an edge between v(e) and v(e'), if and only if e and e' are incident with the same vertex in G. Which of the following statements is/are TRUE? (P) The line graph of a cycle is a cycle. (Q) The line graph of a clique is a clique. (R) The line graph of a planar graph is planar. (S) The line graph of a tree is a tree.
In the following figure, square represents the people who use the product of Colorbar, the triangle represents the people who use products of NYX, the circle represents people who use products of M.A.C., the rectangle represents people who use products of Maybelline and semi-circle represents the people who use the products of Lakme. Which set of letter(s) represents people who use more than one product?
In the following figure, square represents the people who use the product of Colorbar, the triangle represents the people who use products of NYX, the circle represents people who use products of M.A.C., the rectangle represents people who use products of Maybelline and semi-circle represents the people who use the products of Lakme. Which set of letter(s) represents people who use products of M.A.C. and NYX only?
In the following figure, square represents the people who use the product of Colorbar, the triangle represents the people who use products of NYX, the circle represents people who use products of M.A.C., the rectangle represents people who use products of Maybelline and semi-circle represents the people who use the products of Lakme. Which set of letters represents people who use only products of Colorbar?
Study the line graph and answer the question that follows. The line graph represents the number of vehicles (in thousands) manufactured by two automobile companies A and B over the years from 2010 to 2015. The X-axis represents the years and the Y-axis represents number of vehicles in thousands. (The data shown here is only for mathematical exercise. They do not represent the actual figures of the country.) Company B is projecting an increase in the number of vehicles to be manufactured in 2016 by 70% with respect to its average number of vehicles from 2010 to 2015. What should be the approximate percentage increase in the number of vehicles (in thousands) to be manufactured by Company A in 2016 with respect to the number of vehicles in 2015, so that it is at par with Company B?
Study the line graph and answer the question that follows. The line graph represents the number of vehicles (in thousands) manufactured by two automobile companies A and B over the years from 2010 to 2015. The X-axis represents the years and the Y-axis represents number of vehicles in thousands. (The data shown here is only for mathematical exercise. They do not represent the actual figures of the country.) The average value of the vehicles manufactured by Company A is what per cent of the average value of the vehicles manufactured by Company B during 2010 to 2015?
Study the line graph and answer the question that follows The line graph represents the number of vehicles (in thousands) manufactured by two automobile companies A and B over the years from 2010 to 2015. The X-axis represents the years and the Y-axis represents the number of vehicles in thousands. (The data shown here is only for mathematical exercise. They do not represent the actual figures  of the country) What is the difference between the average number of vehicles (in thousands) of companies A and B for the years 2010, 2012,2014, and 2015?
There are four students in a class namely A, B, C and D. A tells that a triangle is a bipartite graph. B tells pentagon is a bipartite graph. C tells square is a bipartite graph. D tells heptagon is a bipartite graph. Who among the following is correct?
1. A student drew a neat and error-free graph on a graph paper basing on the given data relating to physics. 2. The student answered the questions based on the graph correctly. 3. The student predicted the trend of the graph correctly by studying its nature. Out of the knowledge, understanding, application and skill based educational objectives, the above mentioned facts are based altogether on how many objectives?
In the following diagram, rectangle represents men, triangle represents educated, circle represents urban and square represents government employees. Which one of the following represents educated men who are not urban?