12th Math Online - The College Study

Exercise 7.5 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

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            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.5-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.7: VectorsExercise: 7.5Type: Solution NotesAuthor: Prof. Ahmad AliPages: 13PDF Size: 6.02 MB In this exercise we will read these topics: Scalar triple product of vectors. Define the scalar triple product of three vectors. Define parallelepiped. Define tetrahedron. Give the geometrical interpretation of the scalar triple product. … Read more

Exercise 7.4 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

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Code Context

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            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.4-1-20x11.jpg 20w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.7: VectorsExercise: 7.4Type: Solution NotesAuthor: Prof. Ahmad AliPages: 16PDF Size: 7.55 MB In this exercise we will read these topics: Cross product or vector product. Define the cross product of two vectors. Define the right-hand rule. Important results of the cross product. The analytical expression of … Read more

Exercise 7.3 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

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Code Context

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            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.3-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.3-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.7: VectorsExercise: 7.3Type: Solution NotesAuthor: Prof. Ahmad AliPages: 13PDF Size: 6.27 MB In this exercise we will read these topics: Scalar product of two vectors. Define scalar and dot product. Define the scalar product of vectors in a plane. Define the scalar product of vectors in … Read more

Exercise 7.2 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]

Code Context

        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.2-1.jpg" class="attachment-full size-full wp-post-image" alt="Exercise-7.2" decoding="async" loading="lazy" itemprop="image" srcset="https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.2-1.jpg 1300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.2-1-300x169.jpg 300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.2-1-1024x576.jpg 1024w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.2-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.2-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.7: VectorsExercise: 7.2Type: Solution NotesAuthor: Prof. Ahmad AliPages: 12PDF Size: 5.88 MB In this exercise we will read these topics: Introduction of a vector in space. Discuss the addition and subtraction of two vectors in space. Find the magnitude, length, a norm of a vector in … Read more

Exercise 7.1 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]

Code Context

        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.1-1.jpg" class="attachment-full size-full wp-post-image" alt="Exercise-7.1" decoding="async" loading="lazy" itemprop="image" srcset="https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.1-1.jpg 1300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.1-1-300x169.jpg 300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.1-1-1024x576.jpg 1024w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.1-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-7.1-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.7: VectorsExercise: 7.1Type: Solution NotesAuthor: Prof. Ahmad AliPages: 12PDF Size: 5.86 MB In this exercise we will read these topics: Define scalar quantity. Define the vector quantity. Give the geometrical interpretation of a vector quantity. Define the magnitude of a vector. Define unit vector. Define null … Read more

Exercise 6.9 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]

Code Context

        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.9-1.jpg" class="attachment-full size-full wp-post-image" alt="Exercise-6.9" decoding="async" loading="lazy" itemprop="image" srcset="https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.9-1.jpg 1300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.9-1-300x169.jpg 300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.9-1-1024x576.jpg 1024w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.9-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.9-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.6: Conic SectionExercise: 6.9Type: Solution NotesAuthor: Prof. Ahmad AliPages: 24PDF Size: 11.8 MB In this exercise we will read these topics: Define the general equation of second degree. When the general equation of second degree represents a circle. When the general equation of second degree represents … Read more

Exercise 6.8 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]

Code Context

        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1.jpg" class="attachment-full size-full wp-post-image" alt="Exercise-6.8" decoding="async" loading="lazy" itemprop="image" srcset="https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1.jpg 1300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1-300x169.jpg 300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1-1024x576.jpg 1024w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1-390x220.jpg 390w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.8-1-20x11.jpg 20w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.6: Conic SectionExercise: 6.8Type: Solution NotesAuthor: Prof. Ahmad AliPages: 9PDF Size: 5.71 MB In this exercise we will read these topics: Define the translation of axes. Write the equation of the translation of axes. Define the rotation of axes. Write the equation of rotation of axes. … Read more

Exercise 6.7 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]

Code Context

        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1.jpg" class="attachment-full size-full wp-post-image" alt="Exercise-6.7" decoding="async" loading="lazy" itemprop="image" srcset="https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1.jpg 1300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1-300x169.jpg 300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1-1024x576.jpg 1024w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1-390x220.jpg 390w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.7-1-20x11.jpg 20w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.6: Conic SectionExercise: 6.7Type: Solution NotesAuthor: Prof. Ahmad AliPages: 16PDF Size: 7.64 MB In this exercise we will read these topics: Tangents and normals. Condition of tangency. Find the point of intersection ellipse and hyperbola. Find the point of intersection of conics. [PDF Download]

Exercise 6.6 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]

Code Context

        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.6-1.jpg" class="attachment-full size-full wp-post-image" alt="Exercise-6.6" decoding="async" loading="lazy" itemprop="image" srcset="https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.6-1.jpg 1300w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.6-1-300x169.jpg 300w, https://

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.6-1-1024x576.jpg 1024w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
        {         
            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.6-1-768x432.jpg 768w, https://

Notice (8): Undefined index: api_key [APP/Controller/PageprocessController.php, line 111]Code Context        if ($this->request->is('post'))
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PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.6-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.6: Conic SectionExercise: 6.6Type: Solution NotesAuthor: Prof. Ahmad AliPages: 17PDF Size: 8.61 MB In this exercise we will read these topics: Define hyperbola. Define center of Hyperbola. Define focal axis or transvers axis of Hyperbola. Define the conjugate axis of Hyperbola. Define the vertices of Hyperbola. … Read more

Exercise 6.5 Solution FSc 2nd Year Math

January 25, 2020January 24, 2020 by Ahmad Ali

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Code Context

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PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.5-1.jpg 1300w, https://

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.5-1-300x169.jpg 300w, https://

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            $apikey = $this->request->data['api_key'];
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.5-1-1024x576.jpg 1024w, https://

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PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]Code Context        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 111
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

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            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];
$apikey = null
PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

/wp-content/uploads/2020/01/Exercise-6.5-1-624x351.jpg 624w" sizes="(max-width: 1300px) 100vw, 1300px" />

Level: F.Sc (Pre-Engg)Class: 2nd YearBoard: Punjab Textbook BoardSubject: MathematicsChapter No.6: Conic SectionExercise: 6.5Type: Solution NotesAuthor: Prof. Ahmad AliPages: 18PDF Size: 9.33 MB In this exercise we will read these topics: Define ellipse. The fixed point is called the focus. Define the diameters of an ellipse. Define major axis of an ellipse and length of major … Read more