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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.
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?
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?
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
Which of the following statements is/are correct about Municipalities? 1. "Metropolitan area" means an area having a population of ten lakhs or more, comprised in one or more districts and consisting of two or more Municipalities or Panchayats or other contiguous areas, specified by the State Legislature by public notification to be a Metropolitan area for the purposes. 2. A Nagar Panchayat (by whatever name called) for a transitional area, that is to say, an area in transition from a rural area to an urban area;
Which of the following changes occurred in cropping pattern of Rajasthan since First Plan Period till 2012-13 is/are correct? i) Area under cereals has increased from 42.5 to 56.0 percent.  ii) Area under pulses has declined from 21.0 to 13.5 percent. iii) Area under oilseeds has increased from 6.2 to 20.5 percent. iv) Area under cotton, sugarcane, guar, fruits, vegetables, spices and fodder crops has increased ' from 16.8 to 23.5 percent. Select the correct answer using the following codes -
With reference to the cultivation of Kharif crops in India in the last five years, consider the following statements: 1. Area under rice cultivation is the highest. 2. Area under the cultivation of jowar is more than that of oilseeds. 3. Area of cotton cultivation is more than that of sugarcane. 4. Area under sugarcane cultivation has steadily decreased. Which of the statements given above are correct?
The average area of 2 rooms I and II are 400 square meters. If one rectangular room(III) area is added then the average area becomes 500 square meters. If another room IV, whose area is 600 square meters more than the III room, replaces room I, then the average area of II, III and IV room becomes 900 square meters. Find the area of I room.
The average area of 3 square rooms I, II, and III are 1600 square meters. If one rectangular room(IV) area is added then the average area becomes 1400 square meters. If another room V, whose area is 400 square meters more than the IV room, replaces room I, then the average area of II, III, IV, and V room becomes 1350 square meters. Find the area of I room.
ABCD is a rectangle and O is point inside the rectangle. Point O joins all four vertices of the rectangle. Which statement(s) is/are wrong? A) Sum of area of △AOB and △DOC is equal to sum of area of △BOC and △AOD B) Sum of area of △AOB and △DOC is half the area of rectangle. C) Sum of area of △BOC and △AOD is half the area of rectangle.