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ByGSpeech

सवालीराम और ज़रा सिर तो खुजलाइए

इस बार के सवाल   
सवालीराम

सवालीराम से इस बार पूछा गया सवाल कुछ इस तरह से है। प्रयोगशाला में जो थर्मामीटर हम इम्तेमाल करते हैं, उसमें पारा या एल्कोहल भरा होता है। यदि हम इस थर्मामीटर को उल्टा या टेढ़ा कर देते हैं तो भी उसमें भरा पारा या एल्कोहल दूसरी ओर नहीं सरकता। ऐसा क्यों होता है?

---चौइथराम कुल इंदौर, कक्षा 8वीं के कई छात्र

ज़रा सिर खुजलाइए     

ऊपर तीन वृत्त बने हैं जिनकी परिधि दुसरे वृत्त के केन्द्र से होकर गुज़र रहीं हैं। इस बार आपको यह बताना है कि ऊपर तीनों वृत्तों द्वारा एक-दुसरे को ढांकने से बना शेडेड भाग किसी भी एक वृत्त के चौथाई हिस्से से बड़ा है या छोटा है। वैसे सवाल का जवाब आप गणितीय विधि से दे सकते हैं या किसी तर्क के आधार पर भी।

इन दोनों सवालों के जवाब में संदर्भ के पते पर भेजिए।

 

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J! InfoRequestSessionProfileQueries143Log
13.954MBMemory Usage222msRequest Duration
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PHP Version8.1.31
Identityguest
Response200
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Conn Collation
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  • beforeRenderModule mod_menu () (696B) (11μs)
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UniquesDuplicates 1
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  • 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)839μs8.63KBParams/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`3.12ms21.19KBParams/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)633μs5.2KBParams/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`4.05ms21.19KBParams/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 ASC1.02ms6.06KBParams/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`3.4ms21.19KBParams/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.ordering1.49ms50.67KB/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` = 1418μs1.75KB/administrator/components/com_conditions/src/Model/ItemModel.php:821Copy
  • SHOW FULL COLUMNS FROM `j4_conditions`1.64ms2.08KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:625Copy
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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 = 14 ORDER BY m.extension,m.item_id1.36ms1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
  • SELECT `id`,`title` AS `value` FROM `j4_modules`298μs3.38KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
  • SHOW FULL COLUMNS FROM `j4_modules`1.74ms2.2KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:625Copy
  • SELECT `id`,`published` AS `value` FROM `j4_modules`849μs14.38KB/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_id208μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
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  • SELECT * FROM j4_conditions_groups as g WHERE g.condition_id = 178μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:1034Copy
  • SELECT * FROM j4_conditions_rules as r WHERE r.group_id = 177μs1.14KB/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_id100μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
  • SELECT * FROM `j4_conditions` WHERE `id` = '2'328μs2.06KB/libraries/src/Table/Table.php:755Copy
  • SELECT * FROM j4_conditions_groups as g WHERE g.condition_id = 2173μs1KB/administrator/components/com_conditions/src/Model/ItemModel.php:1034Copy
  • SELECT * FROM j4_conditions_rules as r WHERE r.group_id = 290μs1.14KB/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 = 2 ORDER BY m.extension,m.item_id124μs17KB/administrator/components/com_conditions/src/Model/ItemModel.php:907Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 19179μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 18992μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 18874μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 18596μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT `metakey` FROM `j4_content` WHERE `id` = :id158μs1.63KBParams/modules/mod_related_items/src/Helper/RelatedItemsHelper.php:88Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 22363μs840B/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 ASC4.25ms425KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:166Copy
  • SELECT a.params FROM j4_advancedmodules AS a WHERE a.module_id = 22484μs840B/plugins/system/advancedmodules/src/Helper.php:151Copy
  • SELECT `name`,`element` FROM `j4_extensions` WHERE `type` = 'plugin' AND `folder` = 'finder' AND `enabled` = 1617μs1KB/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)316μs936B/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 ASC876μs4.52KBParams/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` = 1403μs1.68KBParams/administrator/components/com_scheduler/src/Model/TasksModel.php:466Copy
  • SELECT `session_id` FROM `j4_session` WHERE `session_id` = ?201μs1.63KBParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:291Copy
  • UPDATE `j4_session` SET `data` = ? , `time` = ? WHERE `session_id` = ?213μs912BParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:318Copy