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A = {x∈N : x2 > 8 এবং x3 < 200}

B = {x ∈ N : x জোড় সংখ্যা এবং x ≤6}

এবং C = {√7}

প্রমাণ করো যে, C এর উপাদানটি একটি অমূলদ সংখ্যা।

Created: 1 year ago | Updated: 1 year ago
Updated: 1 year ago
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f(a)=2a-12a+1 হলে f(-13) এর মান নির্ণয় কর ।
দেখাও যে, P(B∩C) এর উপাদান সংখ্যা 2n কে সমর্থন করে যেখানে, n হচ্ছে (B∩C) এর উপাদান সংখ্যা।
অন্বয় S কে তালিকা পদ্ধতিতে প্রকাশ কর এবং ডোমেন ও রেঞ্জ নির্ণয় কর।
x4-3x2+1 কে উৎপাদকে বিশ্লেষণ কর।
a = 0, m = 4 এবং n = 10 হলে b5+c5 এর মান নির্ণয় কর।
m=0 হলে প্রমাণ কর যে, (b+c)212bc+(c+a)212ca+(a+b)212ab=14
Promotion
MessagesTimelineExceptionsViews31RouteQueries33Models34Livewire0MailsGateSessionRequest
Request history8.2.27PHP Version92.73msRequest Duration9MBMemory UsageGET academy/written-questionRoute
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      App\Http\Controllers\Academy\QuestionController@singleWritten
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        • app/Http/Controllers/Academy/QuestionController.php:154
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        • app/Http/Controllers/Academy/QuestionController.php:154
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        • app/Http/Controllers/Academy/QuestionController.php:323
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        • app/Http/Controllers/Academy/QuestionController.php:323
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        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        • app/Http/Controllers/Academy/QuestionController.php:116
      • QuestionController.php#323debugerror_satt350μsselect `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 (92698) and `subjectables`.`subjectable_type` = 'App\\Models\\WrittenQuestion' and `subjects`.`deleted_at` is null
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        • app/Http/Controllers/Academy/QuestionController.php:323
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        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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      • QuestionController.php#323debugerror_satt150μsselect `id`, `name`, `slug`, `category_id` from `sub_categories` where `sub_categories`.`id` in (4871) and `sub_categories`.`deleted_at` is null
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        • app/Http/Controllers/Academy/QuestionController.php:323
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        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
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        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        • app/Http/Controllers/Academy/QuestionController.php:323
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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      • QuestionController.php#323debugerror_satt100μsselect `id`, `bookmarkable_id`, `bookmarkable_type`, `user_id` from `bookmarks` where `bookmarks`.`bookmarkable_id` in (92698) and `bookmarks`.`bookmarkable_type` = 'App\\Models\\WrittenQuestion' and `user_id` is null
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:323
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:375
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:345
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        Bindings
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:411
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:402
      • QuestionController.php#488debugerror_satt90μsselect `id`, `name` from `boards` where `boards`.`id` in (6) and `boards`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:402
      • QuestionController.php#488debugerror_satt100μsselect `id`, `name`, `slug` from `sub_categories` where `sub_categories`.`id` in (4871) and `sub_categories`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:402
      • QuestionController.php#488debugerror_satt100μsselect `id`, `name`, `slug` from `subjects` where `subjects`.`id` in (1825) and `subjects`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:402
      • QuestionController.php#488debugerror_satt170μsselect `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 (44069, 44070, 44071, 44073, 44074, 44075) and `subjectables`.`subjectable_type` = 'App\\Models\\WrittenQuestion' and `subjects`.`deleted_at` is null
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:402
      • QuestionController.php#488debugerror_satt160μsselect * from `written_metas` where `written_metas`.`written_question_id` in (44069, 44070, 44071, 44073, 44074, 44075) and `written_metas`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:488
        • app/Http/Controllers/Academy/QuestionController.php:414
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Http/Controllers/Academy/QuestionController.php:402
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        Backtrace
        • view::academy.subject.written.single_question:41
        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22
        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
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        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
      • restrict.blade.php#30debugerror_satt160μsselect * from `package_plans` where `status` = 'active' and `package_plans`.`deleted_at` is null
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        Backtrace
        • view::includes.restrict:30
        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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      App\Models\Subject
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      App\Models\SubCategory
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      App\Models\Category
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      App\Models\BoardExam
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      App\Models\Board
      2Board.php#?
      App\Models\MainCategory
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