codeigniter : getting ajax result issues

i have this simple exams system and i want to use ajax when a user answer

this is my form :

when i use action="<*?=site_url("exams/check_answer")?>" it gives 302 error

<form action="<?=site_url('exams/'.$result->id.'/check_answer');?>" method="post" id="answer-exam-frm">
   <div>
        <p><input type="radio"  name="response"  value="first"><span class="choice-exam"><?php echo $result->choice1;?></span></p>
          <p><input type="radio"  name="response"  value="second"><span class="choice-exam"><?php echo $result->choice2;?></span></p>
            <p><input type="radio"  name="response"  value="third"><span class="choice-exam"><?php echo $result->choice3;?></span></p>
       <input type="hidden"  name="examid" value="<?php echo $result->id;?>">

       <input type="submit"  class="btn btn-default" value="اجابة">
      </div>

</form>

this is my controller :

public  function check_answer(){
        $user_answer = $this->input->post('response') ;
        $exam_id = $this->input->post('examid') ;
        $result = $this->style_model->check_answer($user_answer,$exam_id) ;
        $this->output->set_content_type('application/json') ;
        if($result){
            $this->output->set_output(json_encode(['result' => 1 ])) ;
            return false;
        }
            $this->output->set_output(json_encode(['result' => 0 ])) ;



    }

And this is my model :

public  function check_answer($user_answer,$exam_id)
{
    $this->db->where('response' , $user_answer);
    $this->db->where('id' , $exam_id);
    $get = $this->db->get('exam') ;
    return $get->result() ;

}