{"id":89977,"date":"2025-06-01T10:18:26","date_gmt":"2025-06-01T10:18:26","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89977"},"modified":"2025-06-01T10:18:26","modified_gmt":"2025-06-01T10:18:26","slug":"consider-the-following-diagram-not-in-scale-diagram-showing-point","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/","title":{"rendered":"Consider the following diagram (not in scale) :\n[Diagram showing point"},"content":{"rendered":"

Consider the following diagram (not in scale) :
\n[Diagram showing points P, Q, R, S, T, U and V with connecting lines and distances]
\nThere are seven places marked as P, Q, R, S, T, U and V as shown in the diagram. The directly connected paths between two places are indicated by line segments joining the two places along with the length labelled in km. Then, the shortest distance between P and U is:<\/p>\n

[amp_mcq option1=”14 km” option2=”15 km” option3=”12 km” option4=”13 km” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
The shortest distance between P and U is 15 km.<\/section>\n
To find the shortest distance, we can analyze potential paths and sum the lengths of the segments.
\nPaths from P to U:
\n1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km.
\n2. Paths via V: First, find the shortest path from P to V.
\n – P -> Q -> V: 4 km + 8 km = 12 km
\n – P -> R -> V: 5 km + 8 km = 13 km
\n – P -> S -> V: 6 km + 8 km = 14 km
\n – P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km
\n – P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km
\n The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km.
\n So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km.
\nComparing the shortest path via T (15 km) and the shortest path via V (16 km), the minimum distance is 15 km.<\/section>\n
This problem involves finding the shortest path in a graph, which can be systematically solved using algorithms like Dijkstra’s. For a small number of nodes and edges, listing and comparing paths is feasible. The distances are given as edge weights.<\/section>\n","protected":false},"excerpt":{"rendered":"

Consider the following diagram (not in scale) : [Diagram showing points P, Q, R, S, T, U and V with connecting lines and distances] There are seven places marked as P, Q, R, S, T, U and V as shown in the diagram. The directly connected paths between two places are indicated by line segments … <\/p>\n

Detailed SolutionConsider the following diagram (not in scale) :
\n[Diagram showing point<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1098,1102],"class_list":["post-89977","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1098","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nConsider the following diagram (not in scale) : [Diagram showing point<\/title>\n<meta name=\"description\" content=\"The shortest distance between P and U is 15 km. To find the shortest distance, we can analyze potential paths and sum the lengths of the segments. Paths from P to U: 1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km. 2. Paths via V: First, find the shortest path from P to V. - P -> Q -> V: 4 km + 8 km = 12 km - P -> R -> V: 5 km + 8 km = 13 km - P -> S -> V: 6 km + 8 km = 14 km - P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km - P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km. So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km. Comparing the shortest path via T (15 km) and the shortest path via V (16 km), the minimum distance is 15 km.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Consider the following diagram (not in scale) : [Diagram showing point\" \/>\n<meta property=\"og:description\" content=\"The shortest distance between P and U is 15 km. To find the shortest distance, we can analyze potential paths and sum the lengths of the segments. Paths from P to U: 1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km. 2. Paths via V: First, find the shortest path from P to V. - P -> Q -> V: 4 km + 8 km = 12 km - P -> R -> V: 5 km + 8 km = 13 km - P -> S -> V: 6 km + 8 km = 14 km - P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km - P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km. So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km. Comparing the shortest path via T (15 km) and the shortest path via V (16 km), the minimum distance is 15 km.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:18:26+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Consider the following diagram (not in scale) : [Diagram showing point","description":"The shortest distance between P and U is 15 km. To find the shortest distance, we can analyze potential paths and sum the lengths of the segments. Paths from P to U: 1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km. 2. Paths via V: First, find the shortest path from P to V. - P -> Q -> V: 4 km + 8 km = 12 km - P -> R -> V: 5 km + 8 km = 13 km - P -> S -> V: 6 km + 8 km = 14 km - P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km - P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km. So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km. Comparing the shortest path via T (15 km) and the shortest path via V (16 km), the minimum distance is 15 km.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/","og_locale":"en_US","og_type":"article","og_title":"Consider the following diagram (not in scale) : [Diagram showing point","og_description":"The shortest distance between P and U is 15 km. To find the shortest distance, we can analyze potential paths and sum the lengths of the segments. Paths from P to U: 1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km. 2. Paths via V: First, find the shortest path from P to V. - P -> Q -> V: 4 km + 8 km = 12 km - P -> R -> V: 5 km + 8 km = 13 km - P -> S -> V: 6 km + 8 km = 14 km - P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km - P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km. So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km. Comparing the shortest path via T (15 km) and the shortest path via V (16 km), the minimum distance is 15 km.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:18:26+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/","url":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-diagram-not-in-scale-diagram-showing-point\/","name":"Consider the following diagram (not in scale) : [Diagram showing point","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:18:26+00:00","dateModified":"2025-06-01T10:18:26+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The shortest distance between P and U is 15 km. To find the shortest distance, we can analyze potential paths and sum the lengths of the segments. Paths from P to U: 1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km. 2. Paths via V: First, find the shortest path from P to V. - P -> Q -> V: 4 km + 8 km = 12 km - P -> R -> V: 5 km + 8 km = 13 km - P -> S -> V: 6 km + 8 km = 14 km - P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km - P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km. So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km. 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