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যোগজীকরণ

একাদশ- দ্বাদশ শ্রেণি - উচ্চতর গণিত উচ্চতর গণিত – ১ম পত্র | - | NCTB BOOK
common.please_contribute_to_add_content_into যোগজীকরণ.
Content

# বহুনির্বাচনী প্রশ্ন

- 1b  ln(ay - bx)
 1b  ln(ay - bx)
 ln(ay - bx)
 1a  ln(ay - bx)
14(1-6x)23
-14(1-6x)23
-14(1-6x)32
14(1-6x)32
12
23
25
কোনটিই নয়

অনির্দিষ্ট যোগজ

common.please_contribute_to_add_content_into অনির্দিষ্ট যোগজ.
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# বহুনির্বাচনী প্রশ্ন

sec-1x+c
cosec-1x+c
-x2x2-1+c
None of these
11-x2
1-2xx2
x-2x
1-2x2

নির্দিষ্ট যোগজ

common.please_contribute_to_add_content_into নির্দিষ্ট যোগজ.
Content

নির্দিষ্ট যোগজ ব্যবহার করে ক্ষেত্রফল

common.please_contribute_to_add_content_into নির্দিষ্ট যোগজ ব্যবহার করে ক্ষেত্রফল.
Content
টপ রেটেড অ্যাপ

স্যাট অ্যাকাডেমী অ্যাপ

আমাদের অল-ইন-ওয়ান মোবাইল অ্যাপের মাধ্যমে সীমাহীন শেখার সুযোগ উপভোগ করুন।

ভিডিও
লাইভ ক্লাস
এক্সাম
ডাউনলোড করুন
Promotion
Request history8.2.27PHP Version104msRequest Duration11MBMemory UsageGET academy/{slug}Route
    • Booting (32.3ms)time
    • Application (71.64ms)time
    • 1 x Application (68.92%)
      71.64ms
      1 x Booting (31.07%)
      32.30ms
      67 templates were rendered
      • 1x academy.subject.read_chapterread_chapter.blade.php#?blade
      • 1x academy.include.sidebarListsidebarList.blade.php#?blade
      • 1x academy.include.left_sidebar_menuleft_sidebar_menu.blade.php#?blade
      • 21x academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • 8x academy.include.question_cardquestion_card.blade.php#?blade
      • 1x common.modal.self_test_modalself_test_modal.blade.php#?blade
      • 1x common.modal.bookmark_modalbookmark_modal.blade.php#?blade
      • 1x common.modal.error_report_modalerror_report_modal.blade.php#?blade
      • 1x common.modal.video_modalvideo_modal.blade.php#?blade
      • 1x common.script.page_type_scriptpage_type_script.blade.php#?blade
      • 1x job.job_include.job_scriptjob_script.blade.php#?blade
      • 1x common.script.activity_scriptactivity_script.blade.php#?blade
      • 1x common.script.test_scripttest_script.blade.php#?blade
      • 1x common.script.custom_dropdowncustom_dropdown.blade.php#?blade
      • 1x common.script.follow_unfollow_scriptfollow_unfollow_script.blade.php#?blade
      • 1x common.script.short_statistics_scriptshort_statistics_script.blade.php#?blade
      • 1x common.script.navigator_sharenavigator_share.blade.php#?blade
      • 1x layouts.satt-appsatt-app.blade.php#?blade
      • 1x includes.header_link2header_link2.blade.php#?blade
      • 1x laravelpwa::metameta.blade.php#?blade
      • 1x layouts.headerheader.blade.php#?blade
      • 1x layouts.toolbartoolbar.blade.php#?blade
      • 1x frontend.downloadourappdownloadourapp.blade.php#?blade
      • 1x frontend.referralreferral.blade.php#?blade
      • 1x auth.user_type_modaluser_type_modal.blade.php#?blade
      • 1x layouts.footerfooter.blade.php#?blade
      • 1x common.login_modallogin_modal.blade.php#?blade
      • 1x components.authentication-card-logoauthentication-card-logo.blade.php#?blade
      • 1x common.includes.promotion_modalpromotion_modal.blade.php#?blade
      • 1x common.includes.notification_item_modalnotification_item_modal.blade.php#?blade
      • 1x common.includes.notification_item_list_modalnotification_item_list_modal.blade.php#?blade
      • 1x common.includes.promotion_offcanvaspromotion_offcanvas.blade.php#?blade
      • 1x includes.footer_link2footer_link2.blade.php#?blade
      • 1x includes.restrictrestrict.blade.php#?blade
      • 1x livewire-alert::components.scriptsscripts.blade.php#?blade
      • 1x livewire-alert::components.flashflash.blade.php#?blade
      • 1x admin.include.toastrtoastr.blade.php#?blade
      • 1x common.search.search_scriptsearch_script.blade.php#?blade
      • 1x common.script.promotion_scriptpromotion_script.blade.php#?blade
      • 1x common.script.promotion_functionspromotion_functions.blade.php#?blade
      uri
      GET academy/{slug}
      middleware
      web, throttle:global
      controller
      App\Http\Controllers\Academy\SubjectController@chapter
      namespace
      prefix
      where
      as
      academy.subject.chapter
      file
      app/Http/Controllers/Academy/SubjectController.php:102-110
      21 statements were executed (2 duplicates)Show only duplicates35.05ms
      • SubjectRepository.php#89debugerror_satt170μsselect `id`, `main_category_id`, `parent_id`, `show_content` from `subjects` where `slug` = 'যোগজীকরণ' and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: যোগজীকরণ
        Backtrace
        • app/Repositories/SubjectRepository.php:89
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:86
        • app/Services/SubjectService.php:23
      • SubjectService.php#34debugerror_satt520μsupdate `subjects` set `view_count` = `view_count` + 1, `subjects`.`updated_at` = '2025-03-12 02:24:33' where `id` = 2128
        Bindings
        • 0: 2025-03-12 02:24:33
        • 1: 2128
        Backtrace
        • app/Services/SubjectService.php:34
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • QueryBuilder.php#38debugerror_satt120μsselect `_lft`, `_rgt` from `subjects` where `id` = 2128 limit 1
        Bindings
        • 0: 2128
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:235
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:227
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
      • QueryBuilder.php#305debugerror_satt170μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `show_content`, `num_of_mcq`, `num_of_written`, `des_added_by`, `des_updated_by`, `author_name`, `link_subject_id`, `sub_category_id`, `main_category_id`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description`, `vote`, `view_count`, `icon`, `page_type`, `chapter_name` from `subjects` where (`subjects`.`_lft` between 14455 and 14462) and `subjects`.`deleted_at` is null
        Bindings
        • 0: 14455
        • 1: 14462
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt160μsselect `id`, `description`, `short_description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (2128, 2194, 2195, 2196) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt110μsselect `id`, `name`, `slug` from `sub_categories` where `sub_categories`.`id` in (4878) and `sub_categories`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt140μsselect `id`, `user_id`, `completeable_type`, `completeable_id`, `complete_progress`, `is_complete` from `completes` where `completes`.`completeable_id` in (2128, 2194, 2195, 2196) and `completes`.`completeable_type` = 'App\\Models\\Subject'
        Bindings
        • 0: App\Models\Subject
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt8.89msselect * from (select `questions`.`id`, `questions`.`subject_id`, `questions`.`category_id`, `questions`.`sub_category_id`, `questions`.`board_exam_id`, `questions`.`passage_id`, `questions`.`question_type`, `questions`.`question`, `questions`.`is_duplicate`, `questions`.`status`, `questions`.`image`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, row_number() over (partition by `subjectables`.`subject_id` order by `questions`.`created_at` desc) as `laravel_row` from `questions` inner join `subjectables` on `questions`.`id` = `subjectables`.`subjectable_id` where `subjectables`.`subject_id` in (2128, 2194, 2195, 2196) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `questions`.`status` = 'active' and `questions`.`deleted_at` is null) as `laravel_table` where `laravel_row` <= 5 order by `laravel_row`
        Bindings
        • 0: App\Models\Question
        • 1: active
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt300μsselect `id`, `question_id`, `option_1`, `option_2`, `option_3`, `option_4`, `option_5`, `image_option`, `image_question`, `answer` from `question_options` where `question_options`.`question_id` in (120906, 180117, 198742, 448206, 448207, 448208, 448209, 448210) and `question_options`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt110μsselect `id`, `name`, `slug` from `subjects` where `subjects`.`id` in (74) and `subjects`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt240μsselect `subjects`.`id`, `subjects`.`name`, `subjects`.`slug`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, `subjectables`.`created_user_id` as `pivot_created_user_id`, `subjectables`.`deleted_at` as `pivot_deleted_at`, `subjectables`.`status` as `pivot_status`, `subjectables`.`created_at` as `pivot_created_at`, `subjectables`.`updated_at` as `pivot_updated_at` from `subjects` inner join `subjectables` on `subjects`.`id` = `subjectables`.`subject_id` where `subjectables`.`subjectable_id` in (120906, 180117, 198742, 448206, 448207, 448208, 448209, 448210) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `subjects`.`deleted_at` is null
        Bindings
        • 0: App\Models\Question
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt100μsselect `id`, `title`, `passage` from `passages` where `passages`.`id` in (0) and `passages`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • SubjectRepository.php#117debugerror_satt150μsselect * from `subjects` where `subjects`.`id` = 2128 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 2128
        Backtrace
        • app/Repositories/SubjectRepository.php:117
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:116
        • app/Services/SubjectService.php:51
      • SubjectRepository.php#120debugerror_satt7.97msselect `id`, `name`, `slug`, `parent_id`, `_lft`, `_rgt` from `subjects` where (14462 between `subjects`.`_lft` and `subjects`.`_rgt` and `subjects`.`id` <> 2128) and `subjects`.`deleted_at` is null order by `_lft` asc
        Bindings
        • 0: 14462
        • 1: 2128
        Backtrace
        • app/Repositories/SubjectRepository.php:120
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:116
        • app/Services/SubjectService.php:51
      • SubjectRepository.php#132debugerror_satt170μsselect * from `subjects` where `subjects`.`id` = 2128 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 2128
        Backtrace
        • app/Repositories/SubjectRepository.php:132
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#135debugerror_satt120μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description` from `subjects` where `subjects`.`id` = 2117 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 2117
        Backtrace
        • app/Repositories/SubjectRepository.php:135
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#135debugerror_satt110μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (2117) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • app/Repositories/SubjectRepository.php:135
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#320debugerror_satt160μsselect * from `mediables` where `mediable_type` = 'App\\Models\\Subject' and `mediable_id` in (2128, 2194, 2195, 2196)
        Bindings
        • 0: App\Models\Subject
        • 1: 2128
        • 2: 2194
        • 3: 2195
        • 4: 2196
        Backtrace
        • app/Repositories/SubjectRepository.php:320
        • app/Services/SubjectService.php:67
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectRepository.php#335debugerror_satt140μsselect `videos`.`video_src_url`, `mediables`.`mediable_id` as `chapter_id` from `videos` inner join `mediables` on `mediables`.`mediable_id` = `videos`.`id` where `videos`.`id` = 0 and `videos`.`video_src` = 'youtube' and `videos`.`deleted_at` is null
        Bindings
        • 0: 0
        • 1: youtube
        Backtrace
        • app/Repositories/SubjectRepository.php:335
        • app/Services/SubjectService.php:68
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectService.php#73debugerror_satt15.02msselect `id`, `name`, `main_category_id`, `slug` from `subjects` where `id` <> 2128 and `parent_id` = 2117 and `main_category_id` = 2 and `subjects`.`deleted_at` is null limit 5
        Bindings
        • 0: 2128
        • 1: 2117
        • 2: 2
        Backtrace
        • app/Services/SubjectService.php:73
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • restrict.blade.php#30debugerror_satt180μsselect * from `package_plans` where `status` = 'active' and `package_plans`.`deleted_at` is null
        Bindings
        • 0: active
        Backtrace
        • view::includes.restrict:30
        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22
        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
      App\Models\Subject
      24Subject.php#?
      App\Models\Question
      8Question.php#?
      App\Models\QuestionOption
      8QuestionOption.php#?
      App\Models\SubjectDescription
      5SubjectDescription.php#?
      App\Models\PackagePlan
      4PackagePlan.php#?
      App\Models\SubCategory
      1SubCategory.php#?
          _token
          eCoa6pzXfPnuRuu5t37m2PSb9aeJRrqhum6iymEb
          _previous
          array:1 [ "url" => "https://debugerror.xyz/academy/%E0%A6%AF%E0%A7%8B%E0%A6%97%E0%A6%9C%E0%A7%80%E...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          path_info
          /academy/%E0%A6%AF%E0%A7%8B%E0%A6%97%E0%A6%9C%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:20 [ "x-https" => array:1 [ 0 => "1" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-real-ip" => array:1 [ 0 => "18.191.148.200" ] "x-forwarded-server" => array:1 [ 0 => "debugerror.xyz" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-host" => array:1 [ 0 => "debugerror.xyz" ] "x-forwarded-for" => array:1 [ 0 => "18.191.148.200" ] "host" => array:1 [ 0 => "debugerror.xyz" ] ]
          request_cookies
          []
          
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