{"id":292,"date":"2023-06-09T11:08:50","date_gmt":"2023-06-09T11:08:50","guid":{"rendered":"https:\/\/ilm.com.pk\/online-test\/?p=292"},"modified":"2023-06-09T15:17:46","modified_gmt":"2023-06-09T10:17:46","slug":"1st-year-math-chapter-8-mathematical-induction-and-binomial-theorem-mcqs-with-answers","status":"publish","type":"post","link":"https:\/\/ilm.com.pk\/online-test\/1st-year-math-chapter-8-mathematical-induction-and-binomial-theorem-mcqs-with-answers\/","title":{"rendered":"1st Year Math Chapter 8 Mathematical Induction and Binomial Theorem MCQs With Answers"},"content":{"rendered":"<p style=\"text-align: justify;\">This is the place where you are getting the 1st Year Math Chapter 8 Mathematical Induction and Binomial Theorem MCQs With Answers. If you are studying for the Entry Test, then this is the place where you will get the MCQs of this chapter. Through these MCQs, you will be able to build concepts on the topics including the Principle of mathematical induction and the principle of extended mathematical induction. After this, the Binomial theorem is very important and there is the concept of the binomial expansion. These MCQs will help you in the topics including the middle term in expansion, deductions from binomial expansion, and applications of the binomial theorem. So, the 1st Year Mathematics MCQs chapter 8 will help you to prepare well for the entry test. A quiz is given below. So, solve this quiz and check the answers.<\/p>\n<h2 style=\"text-align: center;\">1st Year Math Chapter 8 Mathematical Induction and Binomial Theorem MCQs With Answers<\/h2>\n<div class='ays-quiz-wrap'>\n            <div class='ays-quiz-container ays_quiz_elegant_light  '\n                 data-quest-effect='shake' \n                 data-hide-bg-image='false'\n                 id='ays-quiz-container-66'>\n                <div class='ays-live-bar-wrap '><div class='ays-live-bar-fill ' style='width: 0%;'><span><span class='ays-live-bar-percent'>0<\/span>%<\/span><\/div><\/div>\n                \n                <div class='ays-questions-container'>\n                    <div class='ays-quiz-some-items-icons-wrap'><\/div>\n                    <span class='ays_quizn_ancnoxneri_qanak'><i class='ays_fa ays_fa_users'><\/i> 312<\/span>\n                    <div id='ays-quiz-questions-nav-wrap-66' class='ays-quiz-questions-nav-wrap'><div class='ays-quiz-questions-nav-go-left'>\n                    <i class='ays_fa ays_fa_angle_left'><\/i>\n                <\/div><div class='ays-quiz-questions-nav-go-right'>\n                    <i class='ays_fa ays_fa_angle_right'><\/i>\n                <\/div><div class='ays-quiz-questions-nav-content'><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1374' class='ays_questions_nav_question'>1<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1381' class='ays_questions_nav_question'>2<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1369' class='ays_questions_nav_question'>3<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1380' class='ays_questions_nav_question'>4<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1375' class='ays_questions_nav_question'>5<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1367' class='ays_questions_nav_question'>6<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1378' class='ays_questions_nav_question'>7<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1370' class='ays_questions_nav_question'>8<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1382' class='ays_questions_nav_question'>9<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1368' class='ays_questions_nav_question'>10<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1383' class='ays_questions_nav_question'>11<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1371' class='ays_questions_nav_question'>12<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1377' class='ays_questions_nav_question'>13<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1379' class='ays_questions_nav_question'>14<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1373' class='ays_questions_nav_question'>15<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1376' class='ays_questions_nav_question'>16<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1372' class='ays_questions_nav_question'>17<\/a><\/div><\/div><\/div>\n                    <form \n                        action='' \n                        method='post' \n                        autocomplete='off'\n                        id='ays_finish_quiz_66' \n                        class=' enable_questions_result '\n                    >\n            <input type='hidden' value='list' class='answer_view_class'>\n            <input type='hidden' value='' class='ays_qm_enable_arrows'><section  style='display:none;'  class='ays_quiz_timer_container'>\n                <div class='ays-quiz-timer ' data-timer='100'><\/div>\n                <div class='ays-quiz-after-timer  empty_after_timer_text '><\/div>\n                <hr style='height:1px;'>\n            <\/section>\n            \n            <div class='step active-step'>\n                <div class='ays-abs-fs ays-start-page'>\n                    \n                    \n                    <p class='ays-fs-title'>Math Chapter 8<\/p>\n                    \n                    <input type='hidden' name='ays_quiz_id' value='66'\/>\n                    <input type='hidden' name='ays_quiz_questions' value='1383,1382,1381,1380,1379,1378,1377,1376,1375,1374,1373,1372,1371,1370,1369,1368,1367'>\n                    \n                    <div class='ays_buttons_div'>\n                        <input type='button'   name='next' class='ays_next start_button action-button' value='Start' data-enable-leave-page=\"false\" \/>\n                    <\/div>\n                    \n                    \n                <\/div>\n            <\/div><div class='step  '\n                        data-question-id='1374'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>1 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>1. 4th term from the end in the expansion of (a + b)<sup>9<\/sup> is<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1374]' id='ays-answer-5287-66' value='5287'\/>\n\n                    <label for='ays-answer-5287-66' class='  ays_position_initial '>\n                        A) T6\n                    <\/label>\n                    <label for='ays-answer-5287-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1374]' id='ays-answer-5288-66' value='5288'\/>\n\n                    <label for='ays-answer-5288-66' class='  ays_position_initial '>\n                        B) T4\n                    <\/label>\n                    <label for='ays-answer-5288-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1374]' id='ays-answer-5290-66' value='5290'\/>\n\n                    <label for='ays-answer-5290-66' class='  ays_position_initial '>\n                        C) none of these\n                    <\/label>\n                    <label for='ays-answer-5290-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1374]' id='ays-answer-5289-66' value='5289'\/>\n\n                    <label for='ays-answer-5289-66' class='  ays_position_initial '>\n                        D) T7\n                    <\/label>\n                    <label for='ays-answer-5289-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1381'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>2 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">2. The\u00a0 series (l+x)<sup>n<\/sup> is valid if<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1381]' id='ays-answer-5318-66' value='5318'\/>\n\n                    <label for='ays-answer-5318-66' class='  ays_position_initial '>\n                        A) x=1\n                    <\/label>\n                    <label for='ays-answer-5318-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1381]' id='ays-answer-5317-66' value='5317'\/>\n\n                    <label for='ays-answer-5317-66' class='  ays_position_initial '>\n                        B) x > 1\n                    <\/label>\n                    <label for='ays-answer-5317-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1381]' id='ays-answer-5315-66' value='5315'\/>\n\n                    <label for='ays-answer-5315-66' class='  ays_position_initial '>\n                        C) x < 1\n                    <\/label>\n                    <label for='ays-answer-5315-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1381]' id='ays-answer-5316-66' value='5316'\/>\n\n                    <label for='ays-answer-5316-66' class='  ays_position_initial '>\n                        D) - 1< x < 1\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5316-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1369'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>3 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">3. In the expansion (a + x)^n, the<span>\u00a0\u00a0\u00a0 <\/span>sum of exponents of a and x is<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1369]' id='ays-answer-5267-66' value='5267'\/>\n\n                    <label for='ays-answer-5267-66' class='  ays_position_initial '>\n                        A) n\n                    <\/label>\n                    <label for='ays-answer-5267-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1369]' id='ays-answer-5270-66' value='5270'\/>\n\n                    <label for='ays-answer-5270-66' class='  ays_position_initial '>\n                        B) 2n\n                    <\/label>\n                    <label for='ays-answer-5270-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1369]' id='ays-answer-5269-66' value='5269'\/>\n\n                    <label for='ays-answer-5269-66' class='  ays_position_initial '>\n                        C) n + 1\n                    <\/label>\n                    <label for='ays-answer-5269-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1369]' id='ays-answer-5268-66' value='5268'\/>\n\n                    <label for='ays-answer-5268-66' class='  ays_position_initial '>\n                        D) n-1\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5268-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1380'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>4 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>4. Which term of (x + 2)<sup>8<\/sup> is independent of x<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1380]' id='ays-answer-5311-66' value='5311'\/>\n\n                    <label for='ays-answer-5311-66' class='  ays_position_initial '>\n                        A) First\n                    <\/label>\n                    <label for='ays-answer-5311-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1380]' id='ays-answer-5312-66' value='5312'\/>\n\n                    <label for='ays-answer-5312-66' class='  ays_position_initial '>\n                        B) Second\n                    <\/label>\n                    <label for='ays-answer-5312-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1380]' id='ays-answer-5313-66' value='5313'\/>\n\n                    <label for='ays-answer-5313-66' class='  ays_position_initial '>\n                        C) Middle\n                    <\/label>\n                    <label for='ays-answer-5313-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1380]' id='ays-answer-5314-66' value='5314'\/>\n\n                    <label for='ays-answer-5314-66' class='  ays_position_initial '>\n                        D) Last\n                    <\/label>\n                    <label for='ays-answer-5314-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1375'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>5 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>5. The term independent of x in the expansion of (a +2x)<sup>n<\/sup> is<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1375]' id='ays-answer-5293-66' value='5293'\/>\n\n                    <label for='ays-answer-5293-66' class='  ays_position_initial '>\n                        A) last term\n                    <\/label>\n                    <label for='ays-answer-5293-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1375]' id='ays-answer-5294-66' value='5294'\/>\n\n                    <label for='ays-answer-5294-66' class='  ays_position_initial '>\n                        B) 2nd last term\n                    <\/label>\n                    <label for='ays-answer-5294-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1375]' id='ays-answer-5292-66' value='5292'\/>\n\n                    <label for='ays-answer-5292-66' class='  ays_position_initial '>\n                        C) Middle term\n                    <\/label>\n                    <label for='ays-answer-5292-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1375]' id='ays-answer-5291-66' value='5291'\/>\n\n                    <label for='ays-answer-5291-66' class='  ays_position_initial '>\n                        D) first term\n                    <\/label>\n                    <label for='ays-answer-5291-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1367'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>6 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>6. The statement 4n> 3n-+ 4 is true when<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1367]' id='ays-answer-5262-66' value='5262'\/>\n\n                    <label for='ays-answer-5262-66' class='  ays_position_initial '>\n                        A) n is any positive integer\n                    <\/label>\n                    <label for='ays-answer-5262-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1367]' id='ays-answer-5259-66' value='5259'\/>\n\n                    <label for='ays-answer-5259-66' class='  ays_position_initial '>\n                        B) n = 0\n                    <\/label>\n                    <label for='ays-answer-5259-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1367]' id='ays-answer-5260-66' value='5260'\/>\n\n                    <label for='ays-answer-5260-66' class='  ays_position_initial '>\n                        C) n = 1\n                    <\/label>\n                    <label for='ays-answer-5260-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1367]' id='ays-answer-5261-66' value='5261'\/>\n\n                    <label for='ays-answer-5261-66' class='  ays_position_initial '>\n                        D) n>= 2\n                    <\/label>\n                    <label for='ays-answer-5261-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1378'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>7 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">7. The Sum of odd binomial coefficients in the expansion of (a + x)<sup>n<\/sup> is<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1378]' id='ays-answer-5303-66' value='5303'\/>\n\n                    <label for='ays-answer-5303-66' class='  ays_position_initial '>\n                        A) 2n\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5303-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1378]' id='ays-answer-5306-66' value='5306'\/>\n\n                    <label for='ays-answer-5306-66' class='  ays_position_initial '>\n                        B) n+1\n                    <\/label>\n                    <label for='ays-answer-5306-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1378]' id='ays-answer-5305-66' value='5305'\/>\n\n                    <label for='ays-answer-5305-66' class='  ays_position_initial '>\n                        C) 2^n+1\n                    <\/label>\n                    <label for='ays-answer-5305-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1378]' id='ays-answer-5304-66' value='5304'\/>\n\n                    <label for='ays-answer-5304-66' class='  ays_position_initial '>\n                        D) 2^n-1\n                    <\/label>\n                    <label for='ays-answer-5304-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1370'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>8 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>8. In the expansion (q +x)<sup>n<\/sup> the exponent of 'a'<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1370]' id='ays-answer-5272-66' value='5272'\/>\n\n                    <label for='ays-answer-5272-66' class='  ays_position_initial '>\n                        A) Increases from 0 to n\n                    <\/label>\n                    <label for='ays-answer-5272-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1370]' id='ays-answer-5271-66' value='5271'\/>\n\n                    <label for='ays-answer-5271-66' class='  ays_position_initial '>\n                        B) decreases from n to 0\n                    <\/label>\n                    <label for='ays-answer-5271-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1370]' id='ays-answer-5273-66' value='5273'\/>\n\n                    <label for='ays-answer-5273-66' class='  ays_position_initial '>\n                        C) remains n everywhere\n                    <\/label>\n                    <label for='ays-answer-5273-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1370]' id='ays-answer-5274-66' value='5274'\/>\n\n                    <label for='ays-answer-5274-66' class='  ays_position_initial '>\n                        D) becomes n at the end\n                    <\/label>\n                    <label for='ays-answer-5274-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1382'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>9 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>9. Number of terms in the expansion of (1 + X)<sup>n <\/sup>is:<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1382]' id='ays-answer-5320-66' value='5320'\/>\n\n                    <label for='ays-answer-5320-66' class='  ays_position_initial '>\n                        A) n\/2\u00a0\n                    <\/label>\n                    <label for='ays-answer-5320-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1382]' id='ays-answer-5319-66' value='5319'\/>\n\n                    <label for='ays-answer-5319-66' class='  ays_position_initial '>\n                        B) n\u00a0\n                    <\/label>\n                    <label for='ays-answer-5319-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1382]' id='ays-answer-5321-66' value='5321'\/>\n\n                    <label for='ays-answer-5321-66' class='  ays_position_initial '>\n                        C) n^n -1\n                    <\/label>\n                    <label for='ays-answer-5321-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1382]' id='ays-answer-5322-66' value='5322'\/>\n\n                    <label for='ays-answer-5322-66' class='  ays_position_initial '>\n                        D) n + l\n                    <\/label>\n                    <label for='ays-answer-5322-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1368'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>10 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                10. <p>The statement 3n< n! is true, when\n<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1368]' id='ays-answer-5263-66' value='5263'\/>\n\n                    <label for='ays-answer-5263-66' class='  ays_position_initial '>\n                        A) n=2\n                    <\/label>\n                    <label for='ays-answer-5263-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1368]' id='ays-answer-5266-66' value='5266'\/>\n\n                    <label for='ays-answer-5266-66' class='  ays_position_initial '>\n                        B) n>6\n                    <\/label>\n                    <label for='ays-answer-5266-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1368]' id='ays-answer-5265-66' value='5265'\/>\n\n                    <label for='ays-answer-5265-66' class='  ays_position_initial '>\n                        C) n=6\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5265-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1368]' id='ays-answer-5264-66' value='5264'\/>\n\n                    <label for='ays-answer-5264-66' class='  ays_position_initial '>\n                        D) n = 4\n                    <\/label>\n                    <label for='ays-answer-5264-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1383'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>11 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>11. The number of terms in the expansion of (a+ b)<sup>20<\/sup> is:<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1383]' id='ays-answer-5326-66' value='5326'\/>\n\n                    <label for='ays-answer-5326-66' class='  ays_position_initial '>\n                        A) 19\n                    <\/label>\n                    <label for='ays-answer-5326-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1383]' id='ays-answer-5325-66' value='5325'\/>\n\n                    <label for='ays-answer-5325-66' class='  ays_position_initial '>\n                        B) 21\n                    <\/label>\n                    <label for='ays-answer-5325-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1383]' id='ays-answer-5323-66' value='5323'\/>\n\n                    <label for='ays-answer-5323-66' class='  ays_position_initial '>\n                        C) 18\u00a0\n                    <\/label>\n                    <label for='ays-answer-5323-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1383]' id='ays-answer-5324-66' value='5324'\/>\n\n                    <label for='ays-answer-5324-66' class='  ays_position_initial '>\n                        D) 20\u00a0\n                    <\/label>\n                    <label for='ays-answer-5324-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1371'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>12 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">12. In the expansion (a + x)<sup>n<\/sup> the\u00a0 exponent of 'x'<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1371]' id='ays-answer-5278-66' value='5278'\/>\n\n                    <label for='ays-answer-5278-66' class='  ays_position_initial '>\n                        A) becomes 0 at the end\n                    <\/label>\n                    <label for='ays-answer-5278-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1371]' id='ays-answer-5275-66' value='5275'\/>\n\n                    <label for='ays-answer-5275-66' class='  ays_position_initial '>\n                        B) Decreases from\u00a0 n to 0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5275-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1371]' id='ays-answer-5277-66' value='5277'\/>\n\n                    <label for='ays-answer-5277-66' class='  ays_position_initial '>\n                        C) Remains n everywhere\n                    <\/label>\n                    <label for='ays-answer-5277-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1371]' id='ays-answer-5276-66' value='5276'\/>\n\n                    <label for='ays-answer-5276-66' class='  ays_position_initial '>\n                        D) Increases from 0 to n\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5276-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1377'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>13 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>13. The Sum of all binomial coefficients in the expansion of (a + x)<sup>n<\/sup> is.<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1377]' id='ays-answer-5302-66' value='5302'\/>\n\n                    <label for='ays-answer-5302-66' class='  ays_position_initial '>\n                        A) n+1\n                    <\/label>\n                    <label for='ays-answer-5302-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1377]' id='ays-answer-5299-66' value='5299'\/>\n\n                    <label for='ays-answer-5299-66' class='  ays_position_initial '>\n                        B) 2n\n                    <\/label>\n                    <label for='ays-answer-5299-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1377]' id='ays-answer-5300-66' value='5300'\/>\n\n                    <label for='ays-answer-5300-66' class='  ays_position_initial '>\n                        C) 2^n-1\u00a0\n                    <\/label>\n                    <label for='ays-answer-5300-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1377]' id='ays-answer-5301-66' value='5301'\/>\n\n                    <label for='ays-answer-5301-66' class='  ays_position_initial '>\n                        D) 2^n+1\u00a0\n                    <\/label>\n                    <label for='ays-answer-5301-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1379'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>14 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>14. The Sum of even binomial coefficient in the expansion of (a + x)<sup>n<\/sup> is<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1379]' id='ays-answer-5310-66' value='5310'\/>\n\n                    <label for='ays-answer-5310-66' class='  ays_position_initial '>\n                        A) n+l\n                    <\/label>\n                    <label for='ays-answer-5310-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1379]' id='ays-answer-5309-66' value='5309'\/>\n\n                    <label for='ays-answer-5309-66' class='  ays_position_initial '>\n                        B) 2^n+1\u00a0\n                    <\/label>\n                    <label for='ays-answer-5309-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1379]' id='ays-answer-5308-66' value='5308'\/>\n\n                    <label for='ays-answer-5308-66' class='  ays_position_initial '>\n                        C) 2^n-1\n                    <\/label>\n                    <label for='ays-answer-5308-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1379]' id='ays-answer-5307-66' value='5307'\/>\n\n                    <label for='ays-answer-5307-66' class='  ays_position_initial '>\n                        D) 2n\n                    <\/label>\n                    <label for='ays-answer-5307-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1373'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>15 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>15. Middle term\/s in the expansion of (a - 3x)<sup> 14<\/sup>\u00a0 is\/are.<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1373]' id='ays-answer-5286-66' value='5286'\/>\n\n                    <label for='ays-answer-5286-66' class='  ays_position_initial '>\n                        A) T7 & T8\n                    <\/label>\n                    <label for='ays-answer-5286-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1373]' id='ays-answer-5284-66' value='5284'\/>\n\n                    <label for='ays-answer-5284-66' class='  ays_position_initial '>\n                        B) T8\u00a0\n                    <\/label>\n                    <label for='ays-answer-5284-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1373]' id='ays-answer-5285-66' value='5285'\/>\n\n                    <label for='ays-answer-5285-66' class='  ays_position_initial '>\n                        C) T6 & T7\n                    <\/label>\n                    <label for='ays-answer-5285-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1373]' id='ays-answer-5283-66' value='5283'\/>\n\n                    <label for='ays-answer-5283-66' class='  ays_position_initial '>\n                        D) T7\n                    <\/label>\n                    <label for='ays-answer-5283-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1376'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>16 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>16. The coefficient of the last term in the expansion of (2- x)<sup>7<\/sup> is<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1376]' id='ays-answer-5296-66' value='5296'\/>\n\n                    <label for='ays-answer-5296-66' class='  ays_position_initial '>\n                        A) 1\n                    <\/label>\n                    <label for='ays-answer-5296-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1376]' id='ays-answer-5297-66' value='5297'\/>\n\n                    <label for='ays-answer-5297-66' class='  ays_position_initial '>\n                        B) 7\n                    <\/label>\n                    <label for='ays-answer-5297-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1376]' id='ays-answer-5298-66' value='5298'\/>\n\n                    <label for='ays-answer-5298-66' class='  ays_position_initial '>\n                        C) - 7\n                    <\/label>\n                    <label for='ays-answer-5298-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1376]' id='ays-answer-5295-66' value='5295'\/>\n\n                    <label for='ays-answer-5295-66' class='  ays_position_initial '>\n                        D) 1\n                    <\/label>\n                    <label for='ays-answer-5295-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1372'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>17 \/ 17<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">17. Middle term\/s in the expansion of (a+b)<sup>11<\/sup> is\/ are<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1372]' id='ays-answer-5280-66' value='5280'\/>\n\n                    <label for='ays-answer-5280-66' class='  ays_position_initial '>\n                        A) T5 & T6\u00a0\n                    <\/label>\n                    <label for='ays-answer-5280-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1372]' id='ays-answer-5282-66' value='5282'\/>\n\n                    <label for='ays-answer-5282-66' class='  ays_position_initial '>\n                        B) T5\n                    <\/label>\n                    <label for='ays-answer-5282-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1372]' id='ays-answer-5279-66' value='5279'\/>\n\n                    <label for='ays-answer-5279-66' class='  ays_position_initial '>\n                        C) T6\n                    <\/label>\n                    <label for='ays-answer-5279-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1372]' id='ays-answer-5281-66' value='5281'\/>\n\n                    <label for='ays-answer-5281-66' class='  ays_position_initial '>\n                        D) T6 & T7\n                    <\/label>\n                    <label for='ays-answer-5281-66' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                            \n                            <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                            <input type='button' name='next' class='ays_previous action-button '  value='Prev' \/>\n                            <i class='ays_display_none ays_fa ays_fa_arrow_right ays_finish action-button ays_arrow ays_next_arrow'><\/i><input type='button' name='next' class='  ays_next action-button' value='Finish' \/>\n                        <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step'>\n                    <div class='ays-abs-fs ays-end-page information_form'>\n                    <div class='ays-form-title'><\/div>\n                        <input id='ays_form_field_ays_user_name_66' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_name' placeholder='Name' \/><input id='ays_form_field_ays_user_email_66' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_email' placeholder='Email' \/><input id='ays_form_field_ays_user_phone_66' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_phone' placeholder='Phone Number' \/>\n                        <div class='ays_buttons_div'>\n                            <i class='ays_display_none ays_fa ays_fa_flag_checkered ays_finish action-button ays_arrow ays_next_arrow'><\/i>\n                            <input type='submit' name='ays_finish_quiz' class=' ays_next ays_finish action-button' value='See Result'\/>\n                        <\/div>\n                    <\/div>\n                  <\/div><div class='step ays_thank_you_fs'>\n            <div class='ays-abs-fs ays-end-page'>\n            <div style='text-align:center;'><div data-class='lds-ellipsis' data-role='loader' class='ays-loader'><div><\/div><div><\/div><div><\/div><div><\/div><\/div><\/div><div class='ays_quiz_results_page'><div class='ays_score_message'><\/div><div class='ays_message'><\/div><p class='ays_score ays_score_display_none animated'>Your score is <\/p><div class='ays-progress first'>\n                <span class='ays-progress-value first'>0%<\/span>\n                <div class='ays-progress-bg first'>\n                    <div class='ays-progress-bar first' style='width:0%;'><\/div>\n                <\/div>\n            <\/div><p class='ays_restart_button_p'><button type='button' class='action-button ays_restart_button'>\n                    <i class='ays_fa ays_fa_undo'><\/i>\n                    <span>Restart quiz<\/span>\n                <\/button><\/p><\/div><\/div><\/div><style> div#ays-quiz-container-66 * { box-sizing: border-box; } \/* Styles for Internet Explorer start *\/ #ays-quiz-container-66 #ays_finish_quiz_66 { } \/* Styles for Quiz container *\/ #ays-quiz-container-66{ min-height: 350px; width:100%; background-color:#f2f2f2; background-position:center center;border-radius:0px 0px 0px 0px;box-shadow: 0px 0px 15px 1px rgba(0,0,0,0.4);border-width: 1px;border-style: solid;border-color: #2fa0ca;} \/* Styles for Navigation bar *\/ #ays-quiz-questions-nav-wrap-66 { width: 100%;border-radius:0px 0px 0px 0px;box-shadow: 0px 0px 15px 1px rgba(0,0,0,0.4);border-width: 1px;border-style: solid;border-color: #2fa0ca;} #ays-quiz-questions-nav-wrap-66 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question { color: #000000; border-color: #000000; background-color: #f2f2f2; } #ays-quiz-questions-nav-wrap-66 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item.ays-quiz-questions-nav-item-active a.ays_questions_nav_question { box-shadow: inset 0 0 5px #000000, 0 0 5px #000000; } #ays-quiz-questions-nav-wrap-66 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item.ays-quiz-questions-nav-item-answered a.ays_questions_nav_question { color: #f2f2f2; border-color: #f2f2f2; background-color: #000000; } #ays-quiz-questions-nav-wrap-66 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question.ays_quiz_correct_answer { color: rgba(39, 174, 96, 1); border-color: rgba(39, 174, 96, 1); background-color: rgba(39, 174, 96, 0.4); } #ays-quiz-questions-nav-wrap-66 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question.ays_quiz_wrong_answer { color: rgba(243, 134, 129, 1); border-color: rgba(243, 134, 129, 1); background-color: rgba(243, 134, 129, 0.4); } \/* Styles for questions *\/ #ays-quiz-container-66 #ays_finish_quiz_66 div.step { min-height: 350px; } \/* Styles for text inside quiz container *\/ #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays-start-page *:not(input), #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays_question_hint, #ays-quiz-container-66.ays-quiz-container .ays-questions-container label[for^=\"ays-answer-\"], #ays-quiz-container-66.ays-quiz-container .ays-questions-container p, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays-fs-title, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays-fs-subtitle, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .logged_in_message, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays-quiz-limitation-count-of-takers, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays-quiz-limitation-count-of-takers *, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays_score_message, #ays-quiz-container-66.ays-quiz-container .ays-questions-container .ays_message{ color: #000000; outline: none; } \/* Quiz title \/ transformation *\/ #ays-quiz-container-66 .ays-fs-title{ text-transform: uppercase; text-align: center; text-shadow: none; } #ays-quiz-container-66 .ays-quiz-password-message-box, #ays-quiz-container-66 .ays-quiz-question-note-message-box, #ays-quiz-container-66 .ays_quiz_question, #ays-quiz-container-66 .ays_quiz_question *:not([class^='enlighter']) { color: #000000; } #ays-quiz-container-66 textarea, #ays-quiz-container-66 input::first-letter, #ays-quiz-container-66 select::first-letter, #ays-quiz-container-66 option::first-letter { color: initial !important; } #ays-quiz-container-66 p::first-letter:not(.ays_no_questions_message) { color: #000000 !important; background-color: transparent !important; font-size: inherit !important; font-weight: inherit !important; float: none !important; line-height: inherit !important; margin: 0 !important; padding: 0 !important; } #ays-quiz-container-66 .select2-container, #ays-quiz-container-66 .ays-field * { font-size: 16px !important; } #ays-quiz-container-66 .ays-fs-subtitle p { text-align: center ; } #ays-quiz-container-66 .ays_quiz_question p { font-size: 17px; text-align: center; } #ays-quiz-container-66 .ays_quiz_question { text-align: center ; margin-bottom: 10px; } #ays-quiz-container-66 .ays_quiz_question pre { max-width: 100%; white-space: break-spaces; } div#ays-quiz-container-66 .ays-questions-container .ays-field, div#ays-quiz-container-66 .ays-questions-container .ays-field input~label[for^='ays-answer-'], div#ays-quiz-container-66 .ays-questions-container .ays-modern-dark-question *, div#ays-quiz-container-66 .ays-questions-container .ays_quiz_question, div#ays-quiz-container-66 .ays-questions-container .ays_quiz_question *{ word-break: break-word; } #ays-quiz-container-66 .ays-quiz-timer p { font-size: 16px; } #ays-quiz-container-66 section.ays_quiz_redirection_timer_container hr, #ays-quiz-container-66 section.ays_quiz_timer_container hr { margin: 0; } #ays-quiz-container-66 section.ays_quiz_timer_container.ays_quiz_timer_red_warning .ays-quiz-timer { color: red; } #ays-quiz-container-66 .ays_thank_you_fs p { text-align: center; } #ays-quiz-container-66 .information_form input[type='text'], #ays-quiz-container-66 .information_form input[type='url'], #ays-quiz-container-66 .information_form input[type='number'], #ays-quiz-container-66 .information_form input[type='email'], #ays-quiz-container-66 .information_form input[type='tel'], #ays-quiz-container-66 .information_form textarea, #ays-quiz-container-66 .information_form select, #ays-quiz-container-66 .information_form option { color: initial !important; outline: none; margin-left: 0; background-image: unset; } #ays-quiz-container-66 .information_form input[type='checkbox'] { margin: 0 10px; outline: initial; -webkit-appearance: auto; -moz-appearance: auto; position: initial; width: initial; height: initial; border: initial; background: initial; } #ays-quiz-container-66 .information_form input[type='checkbox']::after { content: none; } #ays-quiz-container-66 .wrong_answer_text{ color:#ff4d4d; } #ays-quiz-container-66 .right_answer_text{ color:#33cc33; } 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