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ByGSpeech

ज़रा सिर तो खुजलाइए

चार एक समान त्रिकोण बनाना

पिछले अंक में हमने आप से एक सवाल पूछा था कि 16 भुजाओं से बनी आकृति में से 4 भुजाएं इस तरह मिटानी हैं कि चार एक समान त्रिकोण ही बचने चाहिए और कुछ नहीं।
शायद इस सवाल के और भी हल हो फिलहाल हम इस सवाल का एक हल यहां दे रहे हैं।

इस बार का सवाल : फर्ज कीजिए आप किसी कार में सफर की तैयारी कर रहे हैं। कार के सभी दरवाजे, खिड़कियां और हवा आने के सभी छेड बंद हैं। पिछली सीट पर एक बच्चा हया से हल्की गैस से भरा एक गुब्बारा लिए बैठा है। गुब्बारा हवा में तैर रहा है। अचानक कार स्टार्ट होती है और आगे की और चल पड़ती है। अब आपको यह बताना है कि कार के आगे चल पड़ने से क्या गुब्बारा अपनी जगह वना रहेगा, या यह आगे की ओर जाएगा, या पीछे की ओर जाएगा?
आपके कारण समझाते हुए जवाब संदर्भ के पत्ते पर भेजिए।

 

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J! InfoRequestSessionProfileQueries144Log
13.958MBMemory Usage327msRequest Duration
Joomla! Version4.4.5
PHP Version8.1.31
Identityguest
Response200
Templatej51_maya
Database
Server
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Version
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Collation
utf8mb4_0900_ai_ci
Conn Collation
utf8mb4_0900_ai_ci
$_GET
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$_SERVER
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  • After Access::preloadComponents (all components) (119.27KB) (5.44ms)
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  • After Access::preloadPermissions (com_content) (3.54MB) (14.76ms)
  • Before Access::getAssetRules (id:2822 name:com_content.article.2220) (258.8KB) (1.22ms)
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  • beforeRenderModule mod_menu () (696B) (14μs)
  • afterRenderModule mod_menu () (26.88KB) (180μs)
  • beforeRenderRawModule mod_menu () (24.38KB) (56μs)
  • afterRenderRawModule mod_menu () (26.45KB) (3.38ms)
  • beforeRenderModule mod_menu () (696B) (15μs)
  • afterRenderModule mod_menu () (26.27KB) (182μs)
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  • afterRenderRawModule mod_menu () (65.22KB) (245μs)
  • beforeRenderModule mod_menu () (696B) (8μs)
  • afterRenderModule mod_menu () (1.64KB) (107μs)
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144 statements were executed, 3 of which were duplicates, 141 unique116ms3.46MB
UniquesDuplicates 1
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  • UPDATE `j4_content` SET `hits` = (`hits` + 1) WHERE `id` = '2220'2.88ms2.55KB/libraries/src/Table/Table.php:1325Copy
  • SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `j4_content` AS `a` INNER JOIN `j4_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `j4_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `j4_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `j4_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `j4_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray1,:preparedArray2)926μs8.63KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `j4_categories` AS `s` INNER JOIN `j4_categories` AS `c` ON (`s`.`lft` <= `c`.`lft` AND `c`.`lft` < `s`.`rgt`) OR (`c`.`lft` < `s`.`lft` AND `s`.`rgt` < `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`4.35ms21.19KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `m`.`tag_id`,`t`.* FROM `j4_contentitem_tag_map` AS `m` INNER JOIN `j4_tags` AS `t` ON `m`.`tag_id` = `t`.`id` WHERE `m`.`type_alias` = :contentType AND `m`.`content_item_id` = :id AND `t`.`published` = 1 AND `t`.`access` IN (:preparedArray1)445μs5.2KBParams/libraries/src/Helper/TagsHelper.php:388Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `j4_categories` AS `s` INNER JOIN `j4_categories` AS `c` ON (`s`.`lft` <= `c`.`lft` AND `c`.`lft` < `s`.`rgt`) OR (`c`.`lft` < `s`.`lft` AND `s`.`rgt` < `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`3.43ms21.19KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT DISTINCT a.id, a.title, a.name, a.checked_out, a.checked_out_time, a.note, a.state, a.access, a.created_time, a.created_user_id, a.ordering, a.language, a.fieldparams, a.params, a.type, a.default_value, a.context, a.group_id, a.label, a.description, a.required, a.only_use_in_subform,l.title AS language_title, l.image AS language_image,uc.name AS editor,ag.title AS access_level,ua.name AS author_name,g.title AS group_title, g.access as group_access, g.state AS group_state, g.note as group_note FROM j4_fields AS a LEFT JOIN `j4_languages` AS l ON l.lang_code = a.language LEFT JOIN j4_users AS uc ON uc.id=a.checked_out LEFT JOIN j4_viewlevels AS ag ON ag.id = a.access LEFT JOIN j4_users AS ua ON ua.id = a.created_user_id LEFT JOIN j4_fields_groups AS g ON g.id = a.group_id LEFT JOIN `j4_fields_categories` AS fc ON fc.field_id = a.id WHERE ( (`a`.`context` = :context AND (`fc`.`category_id` IS NULL OR `fc`.`category_id` IN (:preparedArray1,:preparedArray2,:preparedArray3,:preparedArray4,:preparedArray5)) AND `a`.`access` IN (:preparedArray6)) AND (`a`.`group_id` = 0 OR `g`.`access` IN (:preparedArray7)) AND `a`.`state` = :state) AND (`a`.`group_id` = 0 OR `g`.`state` = :gstate) AND `a`.`only_use_in_subform` = :only_use_in_subform ORDER BY a.ordering ASC1.21ms6.06KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:166Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `j4_categories` AS `s` INNER JOIN `j4_categories` AS `c` ON (`s`.`lft` <= `c`.`lft` AND `c`.`lft` < `s`.`rgt`) OR (`c`.`lft` < `s`.`lft` AND `s`.`rgt` < `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`5.21ms21.19KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT m.id, m.title, m.module, m.position, m.content, m.showtitle, m.params,am.params AS extra, 0 AS menuid, m.publish_up, m.publish_down FROM j4_modules AS m LEFT JOIN j4_extensions AS e ON e.element = m.module AND e.client_id = m.client_id LEFT JOIN j4_advancedmodules as am ON am.module_id = m.id WHERE m.published = 1 AND e.enabled = 1 AND m.client_id = 0 ORDER BY m.position, m.ordering1.54ms50.67KB/plugins/system/advancedmodules/src/Helper.php:191Copy
  • SELECT m.condition_id,m.item_id FROM j4_conditions_map as m LEFT JOIN j4_conditions as c ON c.id = m.condition_id WHERE `m`.`extension` = 'com_advancedmodules' AND `c`.`published` = 1607μs1.75KB/administrator/components/com_conditions/src/Model/ItemModel.php:821Copy
  • SHOW FULL COLUMNS FROM `j4_conditions`1.68ms2.08KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:625Copy
  • SELECT * FROM `j4_conditions` WHERE `id` = '14'214μs2.06KB/libraries/src/Table/Table.php:755Copy
  • SELECT * FROM j4_conditions_groups as g WHERE g.condition_id = 14343μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:1034Copy
  • SELECT * FROM j4_conditions_rules as r WHERE r.group_id = 14421μs1.13KB/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM j4_conditions_map as m WHERE m.condition_id = 14 ORDER BY m.extension,m.item_id393μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
  • SELECT `id`,`title` AS `value` FROM `j4_modules`477μs3.38KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
  • SHOW FULL COLUMNS FROM `j4_modules`2.06ms2.2KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:625Copy
  • SELECT `id`,`published` AS `value` FROM `j4_modules`377μs14.38KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
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  • SELECT m.extension,m.item_id,m.table,m.name_column FROM j4_conditions_map as m WHERE m.condition_id = 15 ORDER BY m.extension,m.item_id231μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
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  • SELECT m.extension,m.item_id,m.table,m.name_column FROM j4_conditions_map as m WHERE m.condition_id = 18 ORDER BY m.extension,m.item_id127μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
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  • SELECT * FROM j4_conditions_rules as r WHERE r.group_id = 1188μs1.14KB/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM j4_conditions_map as m WHERE m.condition_id = 1 ORDER BY m.extension,m.item_id136μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
  • SELECT * FROM `j4_conditions` WHERE `id` = '2'198μs2.06KB/libraries/src/Table/Table.php:755Copy
  • SELECT * FROM j4_conditions_groups as g WHERE g.condition_id = 2130μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:1034Copy
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  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 191326μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 189227μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 188404μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 1855.95ms840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT `metakey` FROM `j4_content` WHERE `id` = :id526μs1.63KBParams/modules/mod_related_items/src/Helper/RelatedItemsHelper.php:88Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 223198μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT `a`.`id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,CASE WHEN `a`.`publish_up` IS NULL THEN `a`.`created` ELSE `a`.`publish_up` END AS `publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`metadata`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`featured`,`a`.`language`,LENGTH(`a`.`fulltext`) AS `readmore`,`a`.`ordering`,`fp`.`featured_up`,`fp`.`featured_down`,CASE WHEN `c`.`published` = 2 AND `a`.`state` > 0 THEN 2 WHEN `c`.`published` != 1 THEN 0 ELSE `a`.`state` END AS `state`,`c`.`title` AS `category_title`,`c`.`path` AS `category_route`,`c`.`access` AS `category_access`,`c`.`alias` AS `category_alias`,`c`.`language` AS `category_language`,`c`.`published`,`c`.`published` AS `parents_published`,`c`.`lft`,CASE WHEN `a`.`created_by_alias` > ' ' THEN `a`.`created_by_alias` ELSE `ua`.`name` END AS `author`,`ua`.`email` AS `author_email`,`uam`.`name` AS `modified_by_name`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,COALESCE(NULLIF(ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1), 0), 0) AS `rating`,COALESCE(NULLIF(`v`.`rating_count`, 0), 0) AS `rating_count` FROM `j4_content` AS `a` LEFT JOIN `j4_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `j4_users` AS `ua` ON `ua`.`id` = `a`.`created_by` LEFT JOIN `j4_users` AS `uam` ON `uam`.`id` = `a`.`modified_by` LEFT JOIN `j4_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `j4_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `j4_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE `a`.`access` IN (:preparedArray1) AND `c`.`access` IN (:preparedArray2) AND `c`.`published` = 1 AND `a`.`state` = :condition AND `a`.`catid` IN (:preparedArray3) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) ORDER BY a.ordering ASC9.25ms464.97KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:166Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 224275μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT `name`,`element` FROM `j4_extensions` WHERE `type` = 'plugin' AND `folder` = 'finder' AND `enabled` = 1460μs1KB/administrator/components/com_finder/src/Helper/LanguageHelper.php:135Copy
  • SELECT `title` FROM `j4_finder_taxonomy` WHERE `parent_id` = 1 AND `state` = 1 AND `access` IN (1)469μs936B/administrator/components/com_finder/src/Indexer/Taxonomy.php:314Copy
  • SELECT a.id, a.parent_id, a.config_name, a.name, a.context, a.label, a.alias, a.display, a.state, a.access, a.root, a.ordering, a.checked_out, a.checked_out_time, a.created_time, a.updated_time, a.language,`a`.`attribs` AS `attributes` FROM `j4_jfilters_filters` AS `a` WHERE `a`.`access` IN (:preparedArray1) AND `a`.`state` IN (:preparedArray2,:preparedArray3) ORDER BY a.ordering ASC905μs4.52KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:166Copy
  • SELECT SUM(CASE WHEN `a`.`next_execution` <= :now THEN 1 ELSE 0 END) AS due_count,SUM(CASE WHEN `a`.`locked` IS NULL THEN 0 ELSE 1 END) AS locked_count FROM `j4_scheduler_tasks` AS `a` WHERE `a`.`state` = 1285μs1.68KBParams/administrator/components/com_scheduler/src/Model/TasksModel.php:466Copy
  • SELECT `session_id` FROM `j4_session` WHERE `session_id` = ?305μs1.63KBParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:291Copy
  • UPDATE `j4_session` SET `data` = ? , `time` = ? WHERE `session_id` = ?211μs912BParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:318Copy
  • DELETE FROM `j4_session` WHERE `time` < ?580μs760BParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:80Copy