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s(e,t){s.__super__.constructor.call(this)}return n.Extend(s,n.Observable),s.prototype.current=function(e){throw new Error("The `current` method must be defined in child classes.")},s.prototype.query=function(e,t){throw new Error("The `query` method must be defined in child classes.")},s.prototype.bind=function(e,t){},s.prototype.destroy=function(){},s.prototype.generateResultId=function(e,t){e=e.id+"-result-";return e+=n.generateChars(4),null!=t.id?e+="-"+t.id.toString():e+="-"+n.generateChars(4),e},s}),u.define("select2/data/select",["./base","../utils","jquery"],function(e,a,l){function n(e,t){this.$element=e,this.options=t,n.__super__.constructor.call(this)}return a.Extend(n,e),n.prototype.current=function(e){var t=this;e(Array.prototype.map.call(this.$element[0].querySelectorAll(":checked"),function(e){return t.item(l(e))}))},n.prototype.select=function(i){var e,r=this;if(i.selected=!0,null!=i.element&&"option"===i.element.tagName.toLowerCase())return i.element.selected=!0,void this.$element.trigger("input").trigger("change");this.$element.prop("multiple")?this.current(function(e){var t=[];(i=[i]).push.apply(i,e);for(var n=0;n<i.length;n++){var s=i[n].id;-1===t.indexOf(s)&&t.push(s)}r.$element.val(t),r.$element.trigger("input").trigger("change")}):(e=i.id,this.$element.val(e),this.$element.trigger("input").trigger("change"))},n.prototype.unselect=function(i){var r=this;if(this.$element.prop("multiple")){if(i.selected=!1,null!=i.element&&"option"===i.element.tagName.toLowerCase())return i.element.selected=!1,void this.$element.trigger("input").trigger("change");this.current(function(e){for(var t=[],n=0;n<e.length;n++){var s=e[n].id;s!==i.id&&-1===t.indexOf(s)&&t.push(s)}r.$element.val(t),r.$element.trigger("input").trigger("change")})}},n.prototype.bind=function(e,t){var n=this;(this.container=e).on("select",function(e){n.select(e.data)}),e.on("unselect",function(e){n.unselect(e.data)})},n.prototype.destroy=function(){this.$element.find("*").each(function(){a.RemoveData(this)})},n.prototype.query=function(t,e){var n=[],s=this;this.$element.children().each(function(){var e;"option"!==this.tagName.toLowerCase()&&"optgroup"!==this.tagName.toLowerCase()||(e=l(this),e=s.item(e),null!==(e=s.matches(t,e))&&n.push(e))}),e({results:n})},n.prototype.addOptions=function(e){this.$element.append(e)},n.prototype.option=function(e){var t;e.children?(t=document.createElement("optgroup")).label=e.text:void 0!==(t=document.createElement("option")).textContent?t.textContent=e.text:t.innerText=e.text,void 0!==e.id&&(t.value=e.id),e.disabled&&(t.disabled=!0),e.selected&&(t.selected=!0),e.title&&(t.title=e.title);e=this._normalizeItem(e);return e.element=t,a.StoreData(t,"data",e),l(t)},n.prototype.item=function(e){var t={};if(null!=(t=a.GetData(e[0],"data")))return t;var n=e[0];if("option"===n.tagName.toLowerCase())t={id:e.val(),text:e.text(),disabled:e.prop("disabled"),selected:e.prop("selected"),title:e.prop("title")};else if("optgroup"===n.tagName.toLowerCase()){t={text:e.prop("label"),children:[],title:e.prop("title")};for(var s=e.children("option"),i=[],r=0;r<s.length;r++){var o=l(s[r]),o=this.item(o);i.push(o)}t.children=i}return(t=this._normalizeItem(t)).element=e[0],a.StoreData(e[0],"data",t),t},n.prototype._normalizeItem=function(e){e!==Object(e)&&(e={id:e,text:e});return null!=(e=l.extend({},{text:""},e)).id&&(e.id=e.id.toString()),null!=e.text&&(e.text=e.text.toString()),null==e._resultId&&e.id&&null!=this.container&&(e._resultId=this.generateResultId(this.container,e)),l.extend({},{selected:!1,disabled:!1},e)},n.prototype.matches=function(e,t){return this.options.get("matcher")(e,t)},n}),u.define("select2/data/array",["./select","../utils","jquery"],function(e,t,c){function s(e,t){this._dataToConvert=t.get("data")||[],s.__super__.constructor.call(this,e,t)}return t.Extend(s,e),s.prototype.bind=function(e,t){s.__super__.bind.call(this,e,t),this.addOptions(this.convertToOptions(this._dataToConvert))},s.prototype.select=function(n){var e=this.$element.find("option").filter(function(e,t){return t.value==n.id.toString()});0===e.length&&(e=this.option(n),this.addOptions(e)),s.__super__.select.call(this,n)},s.prototype.convertToOptions=function(e){var t=this,n=this.$element.find("option"),s=n.map(function(){return t.item(c(this)).id}).get(),i=[];for(var r=0;r<e.length;r++){var o,a,l=this._normalizeItem(e[r]);0<=s.indexOf(l.id)?(o=n.filter(function(e){return function(){return c(this).val()==e.id}}(l)),a=this.item(o),a=c.extend(!0,{},l,a),a=this.option(a),o.replaceWith(a)):(a=this.option(l),l.children&&(l=this.convertToOptions(l.children),a.append(l)),i.push(a))}return i},s}),u.define("select2/data/ajax",["./array","../utils","jquery"],function(e,t,r){function n(e,t){this.ajaxOptions=this._applyDefaults(t.get("ajax")),null!=this.ajaxOptions.processResults&&(this.processResults=this.ajaxOptions.processResults),n.__super__.constructor.call(this,e,t)}return t.Extend(n,e),n.prototype._applyDefaults=function(e){var t={data:function(e){return r.extend({},e,{q:e.term})},transport:function(e,t,n){e=r.ajax(e);return e.then(t),e.fail(n),e}};return r.extend({},t,e,!0)},n.prototype.processResults=function(e){return e},n.prototype.query=function(t,n){var s=this;null!=this._request&&("function"==typeof this._request.abort&&this._request.abort(),this._request=null);var i=r.extend({type:"GET"},this.ajaxOptions);function e(){var e=i.transport(i,function(e){e=s.processResults(e,t);s.options.get("debug")&&window.console&&console.error&&(e&&e.results&&Array.isArray(e.results)||console.error("Select2: The AJAX results did not return an array in the `results` key of the response.")),n(e)},function(){"status"in e&&(0===e.status||"0"===e.status)||s.trigger("results:message",{message:"errorLoading"})});s._request=e}"function"==typeof i.url&&(i.url=i.url.call(this.$element,t)),"function"==typeof i.data&&(i.data=i.data.call(this.$element,t)),this.ajaxOptions.delay&&null!=t.term?(this._queryTimeout&&window.clearTimeout(this._queryTimeout),this._queryTimeout=window.setTimeout(e,this.ajaxOptions.delay)):e()},n}),u.define("select2/data/tags",["jquery"],function(t){function e(e,t,n){var s=n.get("tags"),i=n.get("createTag");void 0!==i&&(this.createTag=i);i=n.get("insertTag");if(void 0!==i&&(this.insertTag=i),e.call(this,t,n),Array.isArray(s))for(var r=0;r<s.length;r++){var o=s[r],o=this._normalizeItem(o),o=this.option(o);this.$element.append(o)}}return e.prototype.query=function(e,c,u){var d=this;this._removeOldTags(),null!=c.term&&null==c.page?e.call(this,c,function e(t,n){for(var s=t.results,i=0;i<s.length;i++){var r=s[i],o=null!=r.children&&!e({results:r.children},!0);if((r.text||"").toUpperCase()===(c.term||"").toUpperCase()||o)return!n&&(t.data=s,void u(t))}if(n)return!0;var a,l=d.createTag(c);null!=l&&((a=d.option(l)).attr("data-select2-tag","true"),d.addOptions([a]),d.insertTag(s,l)),t.results=s,u(t)}):e.call(this,c,u)},e.prototype.createTag=function(e,t){if(null==t.term)return null;t=t.term.trim();return""===t?null:{id:t,text:t}},e.prototype.insertTag=function(e,t,n){t.unshift(n)},e.prototype._removeOldTags=function(e){this.$element.find("option[data-select2-tag]").each(function(){this.selected||t(this).remove()})},e}),u.define("select2/data/tokenizer",["jquery"],function(c){function e(e,t,n){var s=n.get("tokenizer");void 0!==s&&(this.tokenizer=s),e.call(this,t,n)}return e.prototype.bind=function(e,t,n){e.call(this,t,n),this.$search=t.dropdown.$search||t.selection.$search||n.find(".select2-search__field")},e.prototype.query=function(e,t,n){var s=this;t.term=t.term||"";var i=this.tokenizer(t,this.options,function(e){var t,n=s._normalizeItem(e);s.$element.find("option").filter(function(){return c(this).val()===n.id}).length||((t=s.option(n)).attr("data-select2-tag",!0),s._removeOldTags(),s.addOptions([t])),t=n,s.trigger("select",{data:t})});i.term!==t.term&&(this.$search.length&&(this.$search.val(i.term),this.$search.trigger("focus")),t.term=i.term),e.call(this,t,n)},e.prototype.tokenizer=function(e,t,n,s){for(var i=n.get("tokenSeparators")||[],r=t.term,o=0,a=this.createTag||function(e){return{id:e.term,text:e.term}};o<r.length;){var l=r[o];-1!==i.indexOf(l)?(l=r.substr(0,o),null!=(l=a(c.extend({},t,{term:l})))?(s(l),r=r.substr(o+1)||"",o=0):o++):o++}return{term:r}},e}),u.define("select2/data/minimumInputLength",[],function(){function e(e,t,n){this.minimumInputLength=n.get("minimumInputLength"),e.call(this,t,n)}return e.prototype.query=function(e,t,n){t.term=t.term||"",t.term.length<this.minimumInputLength?this.trigger("results:message",{message:"inputTooShort",args:{minimum:this.minimumInputLength,input:t.term,params:t}}):e.call(this,t,n)},e}),u.define("select2/data/maximumInputLength",[],function(){function e(e,t,n){this.maximumInputLength=n.get("maximumInputLength"),e.call(this,t,n)}return e.prototype.query=function(e,t,n){t.term=t.term||"",0<this.maximumInputLength&&t.term.length>this.maximumInputLength?this.trigger("results:message",{message:"inputTooLong",args:{maximum:this.maximumInputLength,input:t.term,params:t}}):e.call(this,t,n)},e}),u.define("select2/data/maximumSelectionLength",[],function(){function e(e,t,n){this.maximumSelectionLength=n.get("maximumSelectionLength"),e.call(this,t,n)}return e.prototype.bind=function(e,t,n){var s=this;e.call(this,t,n),t.on("select",function(){s._checkIfMaximumSelected()})},e.prototype.query=function(e,t,n){var s=this;this._checkIfMaximumSelected(function(){e.call(s,t,n)})},e.prototype._checkIfMaximumSelected=function(e,t){var n=this;this.current(function(e){e=null!=e?e.length:0;0<n.maximumSelectionLength&&e>=n.maximumSelectionLength?n.trigger("results:message",{message:"maximumSelected",args:{maximum:n.maximumSelectionLength}}):t&&t()})},e}),u.define("select2/dropdown",["jquery","./utils"],function(t,e){function n(e,t){this.$element=e,this.options=t,n.__super__.constructor.call(this)}return e.Extend(n,e.Observable),n.prototype.render=function(){var e=t('<span class="select2-dropdown"><span class="select2-results"></span></span>');return e.attr("dir",this.options.get("dir")),this.$dropdown=e},n.prototype.bind=function(){},n.prototype.position=function(e,t){},n.prototype.destroy=function(){this.$dropdown.remove()},n}),u.define("select2/dropdown/search",["jquery"],function(r){function e(){}return e.prototype.render=function(e){var t=e.call(this),n=this.options.get("translations").get("search"),e=r('<span class="select2-search select2-search--dropdown"><input class="select2-search__field" type="search" tabindex="-1" autocorrect="off" autocapitalize="none" spellcheck="false" role="searchbox" aria-autocomplete="list" /></span>');return this.$searchContainer=e,this.$search=e.find("input"),this.$search.prop("autocomplete",this.options.get("autocomplete")),this.$search.attr("aria-label",n()),t.prepend(e),t},e.prototype.bind=function(e,t,n){var s=this,i=t.id+"-results";e.call(this,t,n),this.$search.on("keydown",function(e){s.trigger("keypress",e),s._keyUpPrevented=e.isDefaultPrevented()}),this.$search.on("input",function(e){r(this).off("keyup")}),this.$search.on("keyup input",function(e){s.handleSearch(e)}),t.on("open",function(){s.$search.attr("tabindex",0),s.$search.attr("aria-controls",i),s.$search.trigger("focus"),window.setTimeout(function(){s.$search.trigger("focus")},0)}),t.on("close",function(){s.$search.attr("tabindex",-1),s.$search.removeAttr("aria-controls"),s.$search.removeAttr("aria-activedescendant"),s.$search.val(""),s.$search.trigger("blur")}),t.on("focus",function(){t.isOpen()||s.$search.trigger("focus")}),t.on("results:all",function(e){null!=e.query.term&&""!==e.query.term||(s.showSearch(e)?s.$searchContainer[0].classList.remove("select2-search--hide"):s.$searchContainer[0].classList.add("select2-search--hide"))}),t.on("results:focus",function(e){e.data._resultId?s.$search.attr("aria-activedescendant",e.data._resultId):s.$search.removeAttr("aria-activedescendant")})},e.prototype.handleSearch=function(e){var t;this._keyUpPrevented||(t=this.$search.val(),this.trigger("query",{term:t})),this._keyUpPrevented=!1},e.prototype.showSearch=function(e,t){return!0},e}),u.define("select2/dropdown/hidePlaceholder",[],function(){function e(e,t,n,s){this.placeholder=this.normalizePlaceholder(n.get("placeholder")),e.call(this,t,n,s)}return e.prototype.append=function(e,t){t.results=this.removePlaceholder(t.results),e.call(this,t)},e.prototype.normalizePlaceholder=function(e,t){return t="string"==typeof t?{id:"",text:t}:t},e.prototype.removePlaceholder=function(e,t){for(var n=t.slice(0),s=t.length-1;0<=s;s--){var i=t[s];this.placeholder.id===i.id&&n.splice(s,1)}return n},e}),u.define("select2/dropdown/infiniteScroll",["jquery"],function(n){function e(e,t,n,s){this.lastParams={},e.call(this,t,n,s),this.$loadingMore=this.createLoadingMore(),this.loading=!1}return e.prototype.append=function(e,t){this.$loadingMore.remove(),this.loading=!1,e.call(this,t),this.showLoadingMore(t)&&(this.$results.append(this.$loadingMore),this.loadMoreIfNeeded())},e.prototype.bind=function(e,t,n){var s=this;e.call(this,t,n),t.on("query",function(e){s.lastParams=e,s.loading=!0}),t.on("query:append",function(e){s.lastParams=e,s.loading=!0}),this.$results.on("scroll",this.loadMoreIfNeeded.bind(this))},e.prototype.loadMoreIfNeeded=function(){var e=n.contains(document.documentElement,this.$loadingMore[0]);!this.loading&&e&&(e=this.$results.offset().top+this.$results.outerHeight(!1),this.$loadingMore.offset().top+this.$loadingMore.outerHeight(!1)<=e+50&&this.loadMore())},e.prototype.loadMore=function(){this.loading=!0;var e=n.extend({},{page:1},this.lastParams);e.page++,this.trigger("query:append",e)},e.prototype.showLoadingMore=function(e,t){return t.pagination&&t.pagination.more},e.prototype.createLoadingMore=function(){var e=n('<li class="select2-results__option select2-results__option--load-more"role="option" aria-disabled="true"></li>'),t=this.options.get("translations").get("loadingMore");return e.html(t(this.lastParams)),e},e}),u.define("select2/dropdown/attachBody",["jquery","../utils"],function(u,o){function e(e,t,n){this.$dropdownParent=u(n.get("dropdownParent")||document.body),e.call(this,t,n)}return e.prototype.bind=function(e,t,n){var s=this;e.call(this,t,n),t.on("open",function(){s._showDropdown(),s._attachPositioningHandler(t),s._bindContainerResultHandlers(t)}),t.on("close",function(){s._hideDropdown(),s._detachPositioningHandler(t)}),this.$dropdownContainer.on("mousedown",function(e){e.stopPropagation()})},e.prototype.destroy=function(e){e.call(this),this.$dropdownContainer.remove()},e.prototype.position=function(e,t,n){t.attr("class",n.attr("class")),t[0].classList.remove("select2"),t[0].classList.add("select2-container--open"),t.css({position:"absolute",top:-999999}),this.$container=n},e.prototype.render=function(e){var t=u("<span></span>"),e=e.call(this);return t.append(e),this.$dropdownContainer=t},e.prototype._hideDropdown=function(e){this.$dropdownContainer.detach()},e.prototype._bindContainerResultHandlers=function(e,t){var n;this._containerResultsHandlersBound||(n=this,t.on("results:all",function(){n._positionDropdown(),n._resizeDropdown()}),t.on("results:append",function(){n._positionDropdown(),n._resizeDropdown()}),t.on("results:message",function(){n._positionDropdown(),n._resizeDropdown()}),t.on("select",function(){n._positionDropdown(),n._resizeDropdown()}),t.on("unselect",function(){n._positionDropdown(),n._resizeDropdown()}),this._containerResultsHandlersBound=!0)},e.prototype._attachPositioningHandler=function(e,t){var n=this,s="scroll.select2."+t.id,i="resize.select2."+t.id,r="orientationchange.select2."+t.id,t=this.$container.parents().filter(o.hasScroll);t.each(function(){o.StoreData(this,"select2-scroll-position",{x:u(this).scrollLeft(),y:u(this).scrollTop()})}),t.on(s,function(e){var t=o.GetData(this,"select2-scroll-position");u(this).scrollTop(t.y)}),u(window).on(s+" "+i+" "+r,function(e){n._positionDropdown(),n._resizeDropdown()})},e.prototype._detachPositioningHandler=function(e,t){var n="scroll.select2."+t.id,s="resize.select2."+t.id,t="orientationchange.select2."+t.id;this.$container.parents().filter(o.hasScroll).off(n),u(window).off(n+" "+s+" "+t)},e.prototype._positionDropdown=function(){var e=u(window),t=this.$dropdown[0].classList.contains("select2-dropdown--above"),n=this.$dropdown[0].classList.contains("select2-dropdown--below"),s=null,i=this.$container.offset();i.bottom=i.top+this.$container.outerHeight(!1);var r={height:this.$container.outerHeight(!1)};r.top=i.top,r.bottom=i.top+r.height;var o=this.$dropdown.outerHeight(!1),a=e.scrollTop(),l=e.scrollTop()+e.height(),c=a<i.top-o,e=l>i.bottom+o,a={left:i.left,top:r.bottom},l=this.$dropdownParent;"static"===l.css("position")&&(l=l.offsetParent());i={top:0,left:0};(u.contains(document.body,l[0])||l[0].isConnected)&&(i=l.offset()),a.top-=i.top,a.left-=i.left,t||n||(s="below"),e||!c||t?!c&&e&&t&&(s="below"):s="above",("above"==s||t&&"below"!==s)&&(a.top=r.top-i.top-o),null!=s&&(this.$dropdown[0].classList.remove("select2-dropdown--below"),this.$dropdown[0].classList.remove("select2-dropdown--above"),this.$dropdown[0].classList.add("select2-dropdown--"+s),this.$container[0].classList.remove("select2-container--below"),this.$container[0].classList.remove("select2-container--above"),this.$container[0].classList.add("select2-container--"+s)),this.$dropdownContainer.css(a)},e.prototype._resizeDropdown=function(){var e={width:this.$container.outerWidth(!1)+"px"};this.options.get("dropdownAutoWidth")&&(e.minWidth=e.width,e.position="relative",e.width="auto"),this.$dropdown.css(e)},e.prototype._showDropdown=function(e){this.$dropdownContainer.appendTo(this.$dropdownParent),this._positionDropdown(),this._resizeDropdown()},e}),u.define("select2/dropdown/minimumResultsForSearch",[],function(){function e(e,t,n,s){this.minimumResultsForSearch=n.get("minimumResultsForSearch"),this.minimumResultsForSearch<0&&(this.minimumResultsForSearch=1/0),e.call(this,t,n,s)}return e.prototype.showSearch=function(e,t){return!(function e(t){for(var n=0,s=0;s<t.length;s++){var i=t[s];i.children?n+=e(i.children):n++}return n}(t.data.results)<this.minimumResultsForSearch)&&e.call(this,t)},e}),u.define("select2/dropdown/selectOnClose",["../utils"],function(s){function e(){}return e.prototype.bind=function(e,t,n){var s=this;e.call(this,t,n),t.on("close",function(e){s._handleSelectOnClose(e)})},e.prototype._handleSelectOnClose=function(e,t){if(t&&null!=t.originalSelect2Event){var n=t.originalSelect2Event;if("select"===n._type||"unselect"===n._type)return}n=this.getHighlightedResults();n.length<1||(null!=(n=s.GetData(n[0],"data")).element&&n.element.selected||null==n.element&&n.selected||this.trigger("select",{data:n}))},e}),u.define("select2/dropdown/closeOnSelect",[],function(){function e(){}return e.prototype.bind=function(e,t,n){var s=this;e.call(this,t,n),t.on("select",function(e){s._selectTriggered(e)}),t.on("unselect",function(e){s._selectTriggered(e)})},e.prototype._selectTriggered=function(e,t){var n=t.originalEvent;n&&(n.ctrlKey||n.metaKey)||this.trigger("close",{originalEvent:n,originalSelect2Event:t})},e}),u.define("select2/dropdown/dropdownCss",["../utils"],function(n){function e(){}return e.prototype.render=function(e){var t=e.call(this),e=this.options.get("dropdownCssClass")||"";return-1!==e.indexOf(":all:")&&(e=e.replace(":all:",""),n.copyNonInternalCssClasses(t[0],this.$element[0])),t.addClass(e),t},e}),u.define("select2/dropdown/tagsSearchHighlight",["../utils"],function(s){function e(){}return e.prototype.highlightFirstItem=function(e){var t=this.$results.find(".select2-results__option--selectable:not(.select2-results__option--selected)");if(0<t.length){var n=t.first(),t=s.GetData(n[0],"data").element;if(t&&t.getAttribute&&"true"===t.getAttribute("data-select2-tag"))return void n.trigger("mouseenter")}e.call(this)},e}),u.define("select2/i18n/en",[],function(){return{errorLoading:function(){return"The results could not be loaded."},inputTooLong:function(e){var t=e.input.length-e.maximum,e="Please delete "+t+" character";return 1!=t&&(e+="s"),e},inputTooShort:function(e){return"Please enter "+(e.minimum-e.input.length)+" or more characters"},loadingMore:function(){return"Loading more results…"},maximumSelected:function(e){var t="You can only select "+e.maximum+" item";return 1!=e.maximum&&(t+="s"),t},noResults:function(){return"No results found"},searching:function(){return"Searching…"},removeAllItems:function(){return"Remove all items"},removeItem:function(){return"Remove item"},search:function(){return"Search"}}}),u.define("select2/defaults",["jquery","./results","./selection/single","./selection/multiple","./selection/placeholder","./selection/allowClear","./selection/search","./selection/selectionCss","./selection/eventRelay","./utils","./translation","./diacritics","./data/select","./data/array","./data/ajax","./data/tags","./data/tokenizer","./data/minimumInputLength","./data/maximumInputLength","./data/maximumSelectionLength","./dropdown","./dropdown/search","./dropdown/hidePlaceholder","./dropdown/infiniteScroll","./dropdown/attachBody","./dropdown/minimumResultsForSearch","./dropdown/selectOnClose","./dropdown/closeOnSelect","./dropdown/dropdownCss","./dropdown/tagsSearchHighlight","./i18n/en"],function(l,r,o,a,c,u,d,p,h,f,g,t,m,y,v,_,b,$,w,x,A,D,S,E,O,C,L,T,q,I,e){function n(){this.reset()}return n.prototype.apply=function(e){var t;null==(e=l.extend(!0,{},this.defaults,e)).dataAdapter&&(null!=e.ajax?e.dataAdapter=v:null!=e.data?e.dataAdapter=y:e.dataAdapter=m,0<e.minimumInputLength&&(e.dataAdapter=f.Decorate(e.dataAdapter,$)),0<e.maximumInputLength&&(e.dataAdapter=f.Decorate(e.dataAdapter,w)),0<e.maximumSelectionLength&&(e.dataAdapter=f.Decorate(e.dataAdapter,x)),e.tags&&(e.dataAdapter=f.Decorate(e.dataAdapter,_)),null==e.tokenSeparators&&null==e.tokenizer||(e.dataAdapter=f.Decorate(e.dataAdapter,b))),null==e.resultsAdapter&&(e.resultsAdapter=r,null!=e.ajax&&(e.resultsAdapter=f.Decorate(e.resultsAdapter,E)),null!=e.placeholder&&(e.resultsAdapter=f.Decorate(e.resultsAdapter,S)),e.selectOnClose&&(e.resultsAdapter=f.Decorate(e.resultsAdapter,L)),e.tags&&(e.resultsAdapter=f.Decorate(e.resultsAdapter,I))),null==e.dropdownAdapter&&(e.multiple?e.dropdownAdapter=A:(t=f.Decorate(A,D),e.dropdownAdapter=t),0!==e.minimumResultsForSearch&&(e.dropdownAdapter=f.Decorate(e.dropdownAdapter,C)),e.closeOnSelect&&(e.dropdownAdapter=f.Decorate(e.dropdownAdapter,T)),null!=e.dropdownCssClass&&(e.dropdownAdapter=f.Decorate(e.dropdownAdapter,q)),e.dropdownAdapter=f.Decorate(e.dropdownAdapter,O)),null==e.selectionAdapter&&(e.multiple?e.selectionAdapter=a:e.selectionAdapter=o,null!=e.placeholder&&(e.selectionAdapter=f.Decorate(e.selectionAdapter,c)),e.allowClear&&(e.selectionAdapter=f.Decorate(e.selectionAdapter,u)),e.multiple&&(e.selectionAdapter=f.Decorate(e.selectionAdapter,d)),null!=e.selectionCssClass&&(e.selectionAdapter=f.Decorate(e.selectionAdapter,p)),e.selectionAdapter=f.Decorate(e.selectionAdapter,h)),e.language=this._resolveLanguage(e.language),e.language.push("en");for(var n=[],s=0;s<e.language.length;s++){var i=e.language[s];-1===n.indexOf(i)&&n.push(i)}return e.language=n,e.translations=this._processTranslations(e.language,e.debug),e},n.prototype.reset=function(){function a(e){return e.replace(/[^\u0000-\u007E]/g,function(e){return t[e]||e})}this.defaults={amdLanguageBase:"./i18n/",autocomplete:"off",closeOnSelect:!0,debug:!1,dropdownAutoWidth:!1,escapeMarkup:f.escapeMarkup,language:{},matcher:function e(t,n){if(null==t.term||""===t.term.trim())return n;if(n.children&&0<n.children.length){for(var s=l.extend(!0,{},n),i=n.children.length-1;0<=i;i--)null==e(t,n.children[i])&&s.children.splice(i,1);return 0<s.children.length?s:e(t,s)}var r=a(n.text).toUpperCase(),o=a(t.term).toUpperCase();return-1<r.indexOf(o)?n:null},minimumInputLength:0,maximumInputLength:0,maximumSelectionLength:0,minimumResultsForSearch:0,selectOnClose:!1,scrollAfterSelect:!1,sorter:function(e){return e},templateResult:function(e){return e.text},templateSelection:function(e){return 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t=["select2"];null==this.options.multiple&&(this.options.multiple=e.prop("multiple")),null==this.options.disabled&&(this.options.disabled=e.prop("disabled")),null==this.options.autocomplete&&e.prop("autocomplete")&&(this.options.autocomplete=e.prop("autocomplete")),null==this.options.dir&&(e.prop("dir")?this.options.dir=e.prop("dir"):e.closest("[dir]").prop("dir")?this.options.dir=e.closest("[dir]").prop("dir"):this.options.dir="ltr"),e.prop("disabled",this.options.disabled),e.prop("multiple",this.options.multiple),u.GetData(e[0],"select2Tags")&&(this.options.debug&&window.console&&console.warn&&console.warn('Select2: The `data-select2-tags` attribute has been changed to use the `data-data` and `data-tags="true"` attributes and will be removed in future versions of Select2.'),u.StoreData(e[0],"data",u.GetData(e[0],"select2Tags")),u.StoreData(e[0],"tags",!0)),u.GetData(e[0],"ajaxUrl")&&(this.options.debug&&window.console&&console.warn&&console.warn("Select2: The `data-ajax-url` 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o=function(e,t){null!=r.GetData(e[0],"select2")&&r.GetData(e[0],"select2").destroy(),this.$element=e,this.id=this._generateId(e),t=t||{},this.options=new i(t,e),o.__super__.constructor.call(this);var n=e.attr("tabindex")||0;r.StoreData(e[0],"old-tabindex",n),e.attr("tabindex","-1");t=this.options.get("dataAdapter");this.dataAdapter=new t(e,this.options);n=this.render();this._placeContainer(n);t=this.options.get("selectionAdapter");this.selection=new t(e,this.options),this.$selection=this.selection.render(),this.selection.position(this.$selection,n);t=this.options.get("dropdownAdapter");this.dropdown=new t(e,this.options),this.$dropdown=this.dropdown.render(),this.dropdown.position(this.$dropdown,n);n=this.options.get("resultsAdapter");this.results=new n(e,this.options,this.dataAdapter),this.$results=this.results.render(),this.results.position(this.$results,this.$dropdown);var 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<nav><ul class="ez-toc-list ez-toc-list-level-1 "><li class="ez-toc-page-1 ez-toc-heading-level-1"><a class="ez-toc-link ez-toc-heading-1" href="#Bihar_Board_Class_10_Math_Triangle_MCQ_Very_Important_Question" title="Bihar Board Class 10 Math Triangle MCQ Very Important Question">Bihar Board Class 10 Math Triangle MCQ Very Important Question</a><ul class="ez-toc-list-level-3"><li class="ez-toc-heading-level-3"><ul class="ez-toc-list-level-3"><li class="ez-toc-heading-level-3"><a class="ez-toc-link ez-toc-heading-2" href="#Bihar_Board_Class_10_Math_Triangle_Very_Important_Question_2022" title="Bihar Board Class 10 Math Triangle Very Important Question 2022">Bihar Board Class 10 Math Triangle Very Important Question 2022</a></li></ul></li></ul></li></ul></nav></div>
<h1><span class="ez-toc-section" id="Bihar_Board_Class_10_Math_Triangle_MCQ_Very_Important_Question"></span>Bihar Board Class 10 Math Triangle MCQ Very Important Question<span class="ez-toc-section-end"></span></h1>
<p>बिहार बोर्ड इंटर परीक्षा 2022 के सभी विद्यार्थी के सभी विषय की सभी प्रकार के प्रश्न का प्रारूप और PDF वर्ग नोट विषयवार सभी प्रकार के study note ( MCQ , Short question long question )</p><div class="su-divider su-divider-style-default acss5d8b0"><a href="#" class="acssae270">Go to top</a></div> <p><a href="https://examfriends.com/">Bihar Board</a> Class 10 &amp; 12 <a href="https://vidyanjalipoint.com/12th-inter/" target="_blank" rel="noopener">Science</a> all subject Note and PDF</p> <h3><span class="ez-toc-section" id="Bihar_Board_Class_10_Math_Triangle_Very_Important_Question_2022"></span>Bihar Board Class 10 Math Triangle Very Important Question 2022<span class="ez-toc-section-end"></span></h3> <ol> <li><strong>यदि किसी समद्विबाहु त्रिभुज का आधार </strong><strong>b </strong><strong>और बराबर भुजा </strong><strong>a </strong><strong>हो</strong><strong>, </strong><strong>तो उसका क्षेत्रफल होगा-</strong><strong>अथवा</strong><strong>, </strong><strong>समद्विबाहु </strong><strong>Δ </strong><strong>का क्षेत्रफल यदि आधार </strong><strong>b </strong><strong>और बराबर भुजा </strong><strong>b </strong><strong>हो –</strong></li> </ol> <p><amp-img data-hero class="alignnone size-medium wp-image-13733 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q1-300x95.jpg" alt="Bihar Board Class 10 Math Triangle Very Important Question" width="300" height="95" srcset="https://examfriends.com/wp-content/uploads/2021/10/Q1-300x95.jpg 300w, https://examfriends.com/wp-content/uploads/2021/10/Q1-360x113.jpg 360w, https://examfriends.com/wp-content/uploads/2021/10/Q1.jpg 768w" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-medium wp-image-13733 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Bihar Board Class 10 Math Triangle Very Important Question" width="300" height="95"  layout="intrinsic"></amp-img></amp-img></p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="2"> <li><strong>यदि दो समरूप त्रिभुजों की संगत भुजाओं में </strong><strong>3 : 4 </strong><strong>का अनुपात है</strong><strong>, </strong><strong>तो उनके परिमापों का अनुपात है –</strong></li> </ol> <p>(A) 3 : 4<br>
(B) 4 : 3<br>
(C) 9 : 16<br>
(D) 16 : 9</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="3"> <li><strong>त्रिभुज </strong><strong>ΔDEF </strong><strong>तथा </strong><strong>∆</strong><strong>PQR </strong><strong>में दिया है कि </strong><strong>∠</strong><strong>D= </strong><strong>∠</strong><strong>Q </strong><strong>तथा </strong><strong>∠</strong><strong>R = </strong><strong>∠</strong><strong>E </strong><strong>तो निम्नलिखित में से कौन-सा सही है –</strong></li> </ol> <p>(A) ∠F = ∠P<br>
(B) ∠F = ∠Q<br>
(C) ∠D = ∠P<br>
(D) ∠E = ∠P</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="4"> <li><strong> ∆ABC </strong><strong>तथा </strong><strong>∆</strong><strong>DEF </strong><strong>में </strong><strong>AB/DE =BC/DF </strong><strong>ये दोनों त्रिभुज समरूप होंगे</strong><strong>, </strong><strong>यदि –</strong></li> </ol> <p>(A) ∠B = ∠E<br>
(B) ∠A = ∠D<br>
(C) ∠B = ∠D<br>
(D) ∠A = ∠F</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="5"> <li><strong>एक समबाहु त्रिभुज </strong><strong>ABC </strong><strong>की एक भुजा </strong><strong>12 cm </strong><strong>हो</strong><strong>, </strong><strong>तो इसकी ऊँचाई होगी –</strong></li> </ol> <p>(A) 6√2 cm<br>
(B) 6√3 cm<br>
(C) 3√6 cm<br>
(D) 6√6 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="6"> <li><strong>चित्र में </strong><strong>BC || DE, AD : AB = AE :x, </strong><strong>तो </strong><strong>x </strong><strong>बराबर है –</strong></li> </ol> <p> </p> <p>(A) BD<br>
(B) BC<br>
(C) AC<br>
(D) EC</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="7"> <li><strong>दो समरूप त्रिभुजों की भुजाएँ </strong><strong>3 : 5 </strong><strong>के अनुपात में हैं इन त्रिभुजों के क्षेत्रफलों का अनुपात है –</strong></li> </ol> <p>(A) 3 : 5<br>
(B) 5 : 3<br>
(C) 9 : 25<br>
(D) 25 : 9</p> <table width="413"> <tbody> <tr> <td width="412"><strong>Answer⇒C</strong> <p> </p></td> </tr> </tbody> </table> <ol start="8"> <li><strong> ∆ABC </strong><strong>में </strong><strong>BC </strong><strong>को </strong><strong>D </strong><strong>बिन्दु तक बढ़ाया गया है जिससे </strong><strong>∠</strong><strong>ABC = 110° </strong><strong>तथा </strong><strong>∠</strong><strong>BAC = 57°, </strong><strong>तो </strong><strong>∠</strong><strong>ABC </strong><strong>का मान होगा –</strong></li> </ol> <p>(A) 53°<br>
(B) 57°<br>
(C) 33°<br>
(D) 123</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="9"> <li><strong> ∆ABC </strong><strong>में</strong><strong>, DE || BC </strong><strong>एवं </strong><strong>AD/DB = 3/5, </strong><strong>यदि </strong><strong>AC = 5.6 cm, </strong><strong>तो </strong><strong>AE =</strong></li> </ol> <p>(A) 4.2 cm<br>
(B) 3.1 cm<br>
(C) 2.8 cm<br>
(D) 2.1 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="10"> <li><strong> ∆ABC </strong><strong>में </strong><strong>DE || BC </strong><strong>और </strong><strong>AD/DB = 3/5 </strong><strong>यदि </strong><strong>AE = 1.8 cm, </strong><strong>तो </strong><strong>AC </strong><strong>बराबर है –</strong></li> </ol> <p>(A) 2 cm<br>
(B) 2.5 cm<br>
(C) 4.8 cm<br>
(D) 3 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="11"> <li><strong>किसी त्रिभुज में दो कोणों का योग</strong><strong>, </strong><strong>तीसरे कोण के बराबर है। यदि दो कोणों का अन्तर </strong><strong>30° </strong><strong>है</strong><strong>, </strong><strong>तब त्रिभुज के कोण हैं –</strong></li> </ol> <p>(A) 30°, 60°, 90°<br>
(B) 45°, 45, 90°<br>
(C) 60°, 60°, 60°<br>
(D) 30°, 75,75°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="12"> <li><strong>यदि दो समरूप त्रिभुजों के क्षेत्रफलों का अनुपात </strong><strong>64 : 121 </strong><strong>है</strong><strong>, </strong><strong>तो इनके संगत भुजाओं का अनुपात होगा –</strong></li> </ol> <p>(A) 8 : 11<br>
(B) 8 : 12<br>
(C) 12 :14<br>
(D) 11 : 8</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="13"> <li><strong>किसी समचतुर्भुज के विकर्णों की लम्बाई </strong><strong>30 cm </strong><strong>तथा </strong><strong>40 cm </strong><strong>है</strong><strong>, </strong><strong>तो इसकी एक भुजा की लम्बाई है –</strong></li> </ol> <p>(A) 15 cm<br>
(B) 26 cm<br>
(C) 25 cm<br>
(D) 20 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="14"> <li><strong>किसी त्रिभुज </strong><strong>ABC </strong><strong>के दो शीर्ष </strong><strong>A(2, 3) </strong><strong>तथा </strong><strong>B(1, -3) </strong><strong>हैं एवं केन्द्रक</strong><strong>, (3, 0) </strong><strong>है</strong><strong>, </strong><strong>तो तीसरे शीर्ष </strong><strong>C </strong><strong>का नियामक है –</strong></li> </ol> <p>(A) ( 5, 2 )<br>
(B) ( 1, 3 )<br>
(C) ( 6, 0 )<br>
(D) ( 2, -3)</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="15"> <li><strong>बिन्दुओं (-</strong><strong>2, 3) </strong><strong>और (</strong><strong>4, 1) </strong><strong>को मिलाने वाली रेखाखण्ड के मध्य बिन्दु का नियामक है –</strong></li> </ol> <p>(A) ( 1, 2 )<br>
(B) (-1, 2 )<br>
(C) (1,-2 )<br>
(D) (2, 2 )</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="16"> <li><strong>किसी त्रिभुज </strong><strong>ABC </strong><strong>में </strong><strong>∠</strong><strong>A = 90°, BC = 13 cm,  AB = 12 cm, </strong><strong>तो </strong><strong>AC </strong><strong>का मान है –</strong></li> </ol> <p>(A) 3 cm<br>
(B) 4 cm<br>
(C) 5 cm<br>
(D) 6 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="17"> <li><strong> ∆ABC </strong><strong>में </strong><strong>DE || BC </strong><strong>एवं </strong><strong>AD/DB = 3/5 </strong><strong>यदि </strong><strong>AE = 4.8 cm, </strong><strong>तो </strong><strong>EC </strong><strong>का मान है –</strong></li> </ol> <p>(A) 2 cm<br>
(B) 2.5 cm<br>
(C) 8 cm<br>
(D) 32 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="18"> <li><strong>एक समबाहु त्रिभुज </strong><strong>ABC </strong><strong>की एक भुजा </strong><strong>2a </strong><strong>है</strong><strong>, </strong><strong>तो इसकी ऊँचाई होगी –</strong></li> </ol> <p>(A) 3a<br>
(B) √3a<br>
(C) √3a<sup>2</sup><br>
(D) √3/2a<br>
उत्तर – (B)</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="19"> <li><strong>दो समरूप त्रिभुजों की भुजाएँ </strong><strong>3 : 5 </strong><strong>के अनुपात में हैं</strong><strong>, </strong><strong>तब इन त्रिभुजों के क्षेत्रफलों का अनुपात है-</strong></li> </ol> <p>(A) √81:√625<br>
(B) √9 : √25<br>
(C) √3 : √5<br>
(D) √9 : √50</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="20"> <li><strong>किसी </strong><strong>∆</strong><strong>ABC </strong><strong>में</strong><strong>, </strong><strong>∠</strong><strong>A = 90°, BC = 13 cm, AB = 12 cm, </strong><strong>तो निम्न में से </strong><strong>AC </strong><strong>का मान है –</strong></li> </ol> <p>(A) 3 cm<br>
(B) 4 cm<br>
(C) 5 cm<br>
(D) 6 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="21"> <li><strong>समद्विबाहु </strong><strong>∆</strong><strong>ABC </strong><strong>में</strong><strong>, </strong><strong>यदि </strong><strong>AC = BC </strong><strong>और </strong><strong>AB</strong><strong><sup>2</sup></strong><strong>= 2AC</strong><strong><sup>2</sup></strong><strong>तब </strong><strong>∠</strong><strong>C = ?</strong></li> </ol> <p>(A) 30°<br>
(B) 45°<br>
(C) 60°<br>
(D) 90°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="22"> <li><strong>समबाहु </strong><strong>∆</strong><strong>ABC </strong><strong>में यदि </strong><strong>AD </strong><strong>⊥</strong><strong> BC, </strong><strong>तब </strong><strong>AB</strong><strong><sup>2</sup></strong><strong>/AD</strong><strong><sup>2</sup></strong><strong>=</strong></li> </ol> <p>(A) 3/4<br>
(B) 4/3<br>
(C) 1/2<br>
(D) 2/1</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="23"> <li><strong> ∆ABC = ∆DEF </strong><strong>समरूप है</strong><strong>, </strong><strong>दोनों का क्षेत्रफल क्रमश: </strong><strong>9 </strong><strong>तथा </strong><strong>16 </strong><strong>वर्ग सेमी है। यदि </strong><strong>EF = 4.2 cm, </strong><strong>तो </strong><strong>BC (cm </strong><strong>में) =</strong></li> </ol> <p>(A) 4. 2<br>
(B) 3.15<br>
(C) 4. 7<br>
(D) 5.15</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="24"> <li><strong>दो समद्विबाहु त्रिभुज के कोण बराबर हैं तथा उनके क्षेत्रफलों का अनुपात </strong><strong>16 : 25 </strong><strong>है। उनके ऊँचाई का अनुपात क्रमशः है –</strong></li> </ol> <p>(A) 4 : 5<br>
(B) 5 : 4<br>
(C) 3 : 2<br>
(D) 1 : 4</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="25"> <li><strong>एक सरल रेखा को खींचने (निर्धारित करने) में </strong><strong>K </strong><strong>बिन्दु आवश्यक है</strong><strong>, </strong><strong>तो </strong><strong>K </strong><strong>का मान है –</strong></li> </ol> <p>(A) 4<br>
(B) 3<br>
(C) 2<br>
(D) 1</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="26"> <li><strong>यदि किसी </strong><strong>∆</strong><strong>ABC </strong><strong>में</strong><strong>, BD = 5 cm, BC = 7.5 cm </strong><strong>तथा </strong><strong>∠</strong><strong>A </strong><strong>का समविभाजक </strong><strong>AD </strong><strong>है तो </strong><strong>AB/AC =</strong></li> </ol> <p>(A) 1<br>
(B) 2<br>
(C) 0.8<br>
(D) 0.6</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="27"> <li><strong>किसी त्रिभुज के तीनों लम्ब (ऊँचाई) के मिलान बिन्दु को कहा जाता हैं –</strong></li> </ol> <p>(A) अंत: केन्द्र<br>
(B) बाह्य केन्द्र<br>
(C) मध्य केन्द्र<br>
(D) लम्ब केन्द्र</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="28"> <li><strong>दिये गए चित्र में </strong><strong>DE || BC, AD = 2 cm, DB = 3 cm </strong><strong>और </strong><strong>AE = 1.6 cm, </strong><strong>तब </strong><strong>EC (cm </strong><strong>में) =</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13737 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q28-1.jpg" alt="Q28 1" width="300" height="267" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13737 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q28 1" width="300" height="267" layout="intrinsic"></amp-img></amp-img></p> <p>(A) 1. 2<br>
(B) 2. 4<br>
(C) 2. 5<br>
(D) 4. 8</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="29"> <li><strong>दिए गये चित्र में बिन्दु </strong><strong>P, </strong><strong>रेखा </strong><strong>AB </strong><strong>को आंतरिक रूप में किस अनुपात में बाँटती है –</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13738 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q29.jpg" alt="Q29" width="270" height="300" srcset="https://examfriends.com/wp-content/uploads/2021/10/Q29.jpg 270w, https://examfriends.com/wp-content/uploads/2021/10/Q29-243x270.jpg 243w" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13738 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q29" width="270" height="300"  layout="intrinsic"></amp-img></amp-img></p> <p>(A) 3 : 4<br>
(B) 3 : 7<br>
(C) 4 .3<br>
(D) कोई नही</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="30"> <li><strong>दिये गए चित्र में </strong><strong>PQ|| BC, AP = 2 cm, PB = 6 cm, PQ = 3 cm, </strong><strong>तो </strong><strong>BC (cm </strong><strong>में) =</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13739 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q30.jpg" alt="Q30" width="293" height="300" srcset="https://examfriends.com/wp-content/uploads/2021/10/Q30.jpg 293w, https://examfriends.com/wp-content/uploads/2021/10/Q30-264x270.jpg 264w" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13739 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q30" width="293" height="300"  layout="intrinsic"></amp-img></amp-img></p> <p>(A) 8<br>
(B) 9<br>
(C) 10<br>
(D) 12</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="31"> <li><strong>किसी रेखाखण्ड </strong><strong>AB </strong><strong>को </strong><strong>2 : 3 </strong><strong>के अनुपात में बाँटना है। एक किरण </strong><strong>AX </strong><strong>खींचा गया तथा </strong><strong>∠</strong><strong>BAX </strong><strong>एक न्यून कोण बनाया गया। अब बराबर दूरी परबिन्द </strong><strong>A</strong><strong><sub>1</sub></strong><strong>, A</strong><strong><sub>2</sub></strong><strong>, ………….. </strong><strong>बिन्दु निर्धारित किये गये। इस अनुपात हेतु कम – से – कम कितने बिन्दु </strong><strong>A</strong><strong><sub>1</sub></strong><strong>, A</strong><strong><sub>2</sub></strong><strong>, ……………. </strong><strong>चुने जाने हैं </strong><strong>?</strong></li> </ol> <p>(A) 3<br>
(B) 5<br>
(C) 8<br>
(D) 6</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="32"> <li><strong>दिए गए </strong><strong>∆</strong><strong>POR </strong><strong>में </strong><strong>AB </strong><strong>समानान्तर है </strong><strong>QR </strong><strong>के</strong><strong>, </strong><strong>दो समरूप </strong><strong>∆</strong><strong>PAB </strong><strong>और </strong><strong>PQ ∆POR </strong><strong>के क्षेत्रफलों का अनुपात </strong><strong>1 : 2 </strong><strong>है</strong><strong>, </strong><strong>तो </strong><strong>PQ/AQ =</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13741 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q32.jpg" alt="Q32" width="300" height="257" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13741 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q32" width="300" height="257" layout="intrinsic"></amp-img></amp-img></p> <p>(A) √2 : 1<br>
(B) 1 : (√2 – 1)<br>
(C) 1 : (√2 + 1)<br>
(D) इनमे से कोई नही</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="33"> <li><strong>चित्र में यदि </strong><strong>BD = CD,CE = AE, </strong><strong>∠</strong><strong>BAD = </strong><strong>∠</strong><strong>CAD; </strong><strong>∠</strong><strong>EBC = </strong><strong>∠</strong><strong>EBA </strong><strong>तो निम्नलिखित में कौन सत्य है </strong><strong>?</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13742 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q33.jpg" alt="Q33" width="300" height="199" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13742 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q33" width="300" height="199" layout="intrinsic"></amp-img></amp-img></p> <p>(A) AB = BC ≠ AC<br>
(B) AB ≠ BC<br>
(C) AB ≠ AC<br>
(D) BC ≠ AC</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="34"> <li><strong>चक्रीय चतुर्भुज के सम्मुख कोणों का योग होता है –</strong></li> </ol> <p>(A) 360°<br>
(B) 90°<br>
(C) 180°<br>
(D) 120°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="35"> <li><strong>दो समानकोणिक त्रिभुजों में उनकी संगत भुजाओं का अनुपात सदैव समान रहता है। किसने कहा </strong><strong>?</strong></li> </ol> <p>(A) यूक्लिड<br>
(B) आर्यभट्ट<br>
(C) थेल्स<br>
(D) पाइथागोरस</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="36"> <li><strong>यदि दो समरूप त्रिभुज </strong><strong>∆</strong><strong>ABC </strong><strong>और </strong><strong>∆</strong><strong>DEF </strong><strong>इस प्रकार है कि </strong><strong>2AB = DE </strong><strong>और </strong><strong>BC = 8 cm </strong><strong>तो </strong><strong>EF = ?</strong></li> </ol> <p>(A) 16 cm<br>
(B) 12 cm<br>
(C) 14 cm<br>
(D) 8 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="37"> <li><strong> ∆ABC </strong><strong>तथा </strong><strong>∆</strong><strong>PQR </strong><strong>में दिया गया है कि </strong><strong>AB/PQ = BC/RP </strong><strong>तो –</strong></li> </ol> <p>(A) ∠B = ∠ Q<br>
(B) ∠A = ∠P<br>
(C) ∠A = ∠R<br>
(D) ∠B = ∠P</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="38"> <li><strong>दो समरूप त्रिभुजों की भुजाएँ </strong><strong>4 : 9 </strong><strong>के अनुपात में है। इनके क्षेत्रफलों का अनुपात क्या होगा </strong><strong>?</strong></li> </ol> <p>(A) 4 : 9<br>
(B) 16 : 81<br>
(C) 3 : 2<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="39"> <li><strong>चित्र में यदि </strong><strong>∆</strong><strong>ODC ~ ∆OBA, </strong><strong>∠</strong><strong>CDO = 70° </strong><strong>तथा </strong><strong>∠</strong><strong>BOC = 115° </strong><strong>तो </strong><strong>∠</strong><strong>DOC </strong><strong>का मान होगा –</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13743 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q39.jpg" alt="Q39" width="300" height="243" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13743 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q39" width="300" height="243" layout="intrinsic"></amp-img></amp-img></p> <p>(A) 30°<br>
(B) 180°<br>
(C) 65°<br>
(D) 70°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="40"> <li><strong>अगर दो त्रिभुज समानकोणिक है तो वे ………. भी होंगे –</strong></li> </ol> <p>(A) समरूप<br>
(B) सर्वांगसम<br>
(C) समानुपाती<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="41"> <li><strong>यदि </strong><strong>l||m </strong><strong>हो</strong><strong>, </strong><strong>तब </strong><strong>d </strong><strong>का मान होगा</strong></li> </ol> <p><amp-img data-hero class="alignnone size-full wp-image-13744 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/uploads/2021/10/Q41.jpg" alt="Q41" width="300" height="130" layout="intrinsic"><amp-img fallback data-hero class="alignnone size-full wp-image-13744 amp-wp-enforced-sizes" src="https://examfriends.com/wp-content/plugins/accelerated-mobile-pages/images/SD-default-image.png" alt="Q41" width="300" height="130" layout="intrinsic"></amp-img></amp-img></p> <p>(A) 22°<br>
(B) 30°<br>
(C) 45°<br>
(D) 80°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="42"> <li><strong> ∆ABC </strong><strong>में </strong><strong>AB </strong><strong>एवं </strong><strong>AC </strong><strong>के मध्य बिन्दु </strong><strong>D </strong><strong>एवं </strong><strong>E </strong><strong>इस प्रकार है कि </strong><strong>DE || BC </strong><strong>तथा </strong><strong>BC = 8 cm, </strong><strong>तब </strong><strong>DE </strong><strong>का मान होगा –</strong></li> </ol> <p>(A) 5 cm<br>
(B) 3 cm<br>
(C) 4cm<br>
(D) 2 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="43"> <li><strong>दो समरूप त्रिभुज की संगत भुजाओं का अनुपात </strong><strong>4 : 9 </strong><strong>है</strong><strong>, </strong><strong>तब उनके क्षेत्रफलों का अनुपात होगा –</strong></li> </ol> <p>(A) 16 / 27<br>
(B) 16 / 81<br>
(C) 9 / 25<br>
(D) 4 / 9</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="44"> <li><strong>समचतुर्भुज के विकर्ण </strong><strong>6 cm </strong><strong>और </strong><strong>8 cm </strong><strong>है। इसकी प्रत्येक भुजा की लम्बाई होगी –</strong></li> </ol> <p>(A) 9 cm<br>
(B) 4cm<br>
(C) 5 cm<br>
(D) 7 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="45"> <li><strong> ∆ABC </strong><strong>में </strong><strong>DE || BC </strong><strong>और (\frac{AD}{DB}=\frac{3}{5})\ और </strong></li> </ol> <p>(A) 1/3<br>
(B) 2/3<br>
(C) 5/3<br>
(D) 4/3</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="46"> <li><strong>किसी त्रिभुज में दो कोणों का योग</strong><strong>, </strong><strong>तीसरे कोण के बराबर है</strong><strong>, </strong><strong>यदि दो कोणों का अन्तर </strong><strong>30° </strong><strong>हो तब त्रिभुज के कोण हैं –</strong></li> </ol> <p>(A) 30°, 60°, 90°<br>
(B) 45°, 45 , 90°<br>
(C) 60°, 60°, 60°<br>
(D) 30°, 75°, 75°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="47"> <li><strong> ∆ABC </strong><strong>में और </strong><strong>AB = 6√3,AC = 12 </strong><strong>और </strong><strong>BC = 6 cm </strong><strong>तो </strong><strong>∠</strong><strong>B </strong><strong>बराबर होगा </strong><strong>?</strong></li> </ol> <p>(A) 120°<br>
(B) 60°<br>
(C) 90°<br>
(D) 45°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="48"> <li><strong>सभी वर्ग होते हैं –</strong></li> </ol> <p>(A) समरूप<br>
(B) सर्वांगसम<br>
(C) समानुपाती<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="49"> <li><strong> x. </strong><strong>के ……………. मान के लिए </strong><strong>l||m </strong><strong>होगा।</strong></li> </ol> <p> </p> <p>(A) 140°<br>
(B) 150°<br>
(C) 30°<br>
(D) 180°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="50"> <li><strong>दिए गये चित्र में </strong><strong>∆</strong><strong>ABC </strong><strong>में </strong><strong>LA = 90° </strong><strong>और </strong><strong>AD </strong><strong>⊥</strong><strong> BC </strong><strong>यदि </strong><strong>BD = 9 cm </strong><strong>तथा </strong><strong>CD = 4cm, </strong><strong>तो </strong><strong>AD = …………….</strong></li> </ol> <p> </p> <p>(A) 80 cm<br>
(B) 90 cm<br>
(C) 60 cm<br>
(D)100 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="51"> <li><strong>दो समान भुजाओं वाले बहुभुज समरूप होते हैं यदि उनकी संगत भुजाएँ ……………… है।</strong></li> </ol> <p>(A) समरूप<br>
(B) सर्वांगसम<br>
(C) समानुपाती<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <p><strong>52.</strong><strong>त्रिभुज </strong><strong>ABC </strong><strong>में </strong><strong>BE || BC </strong><strong>और </strong><strong>AD/DB = 5/3 </strong><strong>तो </strong><strong>AE/AC =</strong></p> <p>(A) 5/2<br>
(B) 3/5<br>
(C) 5/8<br>
(D) 8/5</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="53"> <li><strong>समबाहु </strong><strong>∆</strong><strong>ABC </strong><strong>और </strong><strong>∆</strong><strong>DEF </strong><strong>की एक भुजा क्रमश: </strong><strong>6 cm </strong><strong>और </strong><strong>3 cm </strong><strong>हो तो</strong><strong>?</strong></li> </ol> <p>(A) 2 :1<br>
(B) 1 : 2<br>
(C) 2 : 3<br>
(D) 4 : 1</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="54"> <li><strong>दो बहुभुज समरूप होंगे यदि उनके …………… बराबर हो।</strong></li> </ol> <p>(A) भुजा<br>
(B) माध्यिका<br>
(C) कोण<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="55"> <li><strong> ∆ABC </strong><strong>में</strong><strong>, AD </strong><strong>⊥</strong><strong> BC </strong><strong>और </strong><strong>AD = BD = 8 cm, BC = 23 cm </strong><strong>तो </strong><strong>AC </strong><strong>होगा –</strong></li> </ol> <p>(A) 15 cm<br>
(B) 17 cm<br>
(C) 8 cm<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <p><strong>56.</strong><strong>दो समरूप त्रिभुज के क्षेत्रफलों का अनुपात उनकी संगत भुजाओं के ……………. के अनुपात के बराबर होते हैं।</strong></p> <p>(A) अनुपाती<br>
(B) वर्ग<br>
(C) बराबर<br>
(D) समानुपाती</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="57"> <li><strong>सभी समबाहु त्रिभुज होते हैं –</strong></li> </ol> <p>(A) समरूप<br>
(B) सर्वांगसम<br>
(C) समानुपाती<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="58"> <li><strong>दिये गये चित्र में </strong><strong>x </strong><strong>का मान ……………. होगा।</strong></li> </ol> <p> </p> <p>(A) 140°<br>
(B) 150°<br>
(C) 90°<br>
(D) 180°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="59"> <li><strong>चित्र से</strong><strong>, y </strong><strong>का मान …………….होगा –</strong></li> </ol> <p>(A) 65°<br>
(B) 75°<br>
(C) 550<br>
(D) 90°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="60"> <li><strong>चित्र में </strong><strong>BC || DE, </strong><strong>तो </strong><strong>AD : AB = AE : …..</strong></li> </ol> <p> </p> <p>(A) AC<br>
(B) BC<br>
(C) CD<br>
(D) ED</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="61"> <li><strong>सभी सर्वांगसम आकृतियाँ …………. होती हैं।</strong></li> </ol> <p>(A) समरूप<br>
(B) सर्वांगसम<br>
(C) समानुपाती<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="62"> <li><strong>यदि एक त्रिभुज के एक कोण की समद्विभाजक रेखा त्रिभुज की माध्यिका हो</strong><strong>, </strong><strong>तो वह त्रिभुज ……………. होगा।</strong></li> </ol> <p>(A) विषमबाहु<br>
(B) समबाहु<br>
(C) समद्विबाहु<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="63"> <li><strong>यदि दो त्रिभुजों के क्षेत्रफलों का अनुपात </strong><strong>16 : 9 </strong><strong>हो</strong><strong>, </strong><strong>तो उनकी संगतं भुजाओं का अनुपात ……………. होगा।</strong></li> </ol> <p>(A) 4 : 3<br>
(B) 5 : 3<br>
(C) 2 : 3<br>
(D) 6 : 3</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="64"> <li><strong>यदि एक सरल रेखा किसी त्रिभुज की. किन्हीं दो भुजाओं को एक ही अनुपात में विभाजित करे तो वह रेखा तीसरी भुजा के ……………. होगी।</strong></li> </ol> <p>(A) असमानान्तर<br>
(B) आनत<br>
(C) समानान्तर<br>
(D) इनमें से कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="65"> <li><strong>यदि </strong><strong>∆</strong><strong>ABC ~ ∆LMN </strong><strong>तथा </strong><strong>∠</strong><strong>A = 68°, </strong><strong>∠</strong><strong>B = 45°, </strong><strong>तो </strong><strong>∠</strong><strong>N =</strong></li> </ol> <p>(A) 68°<br>
(B) 72°<br>
(C) 67°<br>
(D) 45°</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="66"> <li><strong> ∆ABC </strong><strong>में </strong><strong>∠</strong><strong>C = 90°, AB = 10 cm, BC = 8 cm, </strong><strong>तो </strong><strong>AC =</strong></li> </ol> <p>(A) 6 cm<br>
(B) 8 cm<br>
(C) 10 cm<br>
(D) 12 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="67"> <li><strong> ∆PQR </strong><strong>में </strong><strong>∠</strong><strong>P = 90°, QR = 17 cm, PQ = 15 cm, PR =</strong></li> </ol> <p>(A) 32 cm<br>
(B) 18 cm<br>
(C) 16 cm<br>
(D) 8 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <p><strong>68.</strong><strong>एक समबाहु त्रिभुज </strong><strong>ABC </strong><strong>में</strong><strong>, AD + BC </strong><strong>तो </strong><strong>AD</strong><strong><sup>2</sup></strong><strong> = ?</strong></p> <p>(A) 2CD<sup>2</sup><br>
(B) 3CD<sup>2</sup><br>
(C) 4CD<sup>2</sup><br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="69"> <li><strong>सभी समबाहु त्रिभुज होते हैं –</strong></li> </ol> <p>(A) समरूप<br>
(B) सर्वांगसम<br>
(C) समानुपाती<br>
(D) कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> A</strong></td> </tr> </tbody> </table> <ol start="70"> <li><strong>यदि </strong><strong>ar (∆ABC) : ar (∆XYZ) = 4 </strong><strong>हों</strong><strong>, </strong><strong>तो </strong><strong>XY =</strong></li> </ol> <p>(A) AB<br>
(B) 1/2AB<br>
(C) 2AB<br>
(D) 4AB</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="71"> <li><strong>यदि </strong><strong>∆</strong><strong>XYZ </strong><strong>में </strong><strong>∠</strong><strong>X = 90°, XY = 60 cm </strong><strong>तथा </strong><strong>XZ = 11 cm, </strong><strong>तो </strong><strong>YZ=</strong></li> </ol> <p>(A) 60 cm<br>
(B) 11 cm<br>
(C) 61 cm<br>
(D) 71 cm</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="72"> <li><strong>केशव </strong><strong>12 m </strong><strong>पश्चिम आकर </strong><strong>5 m </strong><strong>उत्तर जाता है। वह प्रारंभिक बिन्दु से कितनी दूर है </strong><strong>?</strong></li> </ol> <p>(A) 17 m<br>
(B) 13 m<br>
(C) 12 m<br>
(D) 5 m</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="73"> <li><strong>कृष्णा </strong><strong>15 m </strong><strong>पूरब जाकर </strong><strong>8 cm </strong><strong>दक्षिण जाता है । वह प्रारंभिक बिन्द से कितनी दूर है </strong><strong>?</strong></li> </ol> <p>(A) 15 m<br>
(B) 8 m<br>
(C) 23 m<br>
(D) 17 m</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="74"> <li><strong>सभी वृत्त ……………. होते हैं।</strong></li> </ol> <p>(A) सर्वांगसम<br>
(B) समरूप<br>
(C) समानुपाती<br>
(D) इनमें से कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="75"> <li><strong>सभी समचतुर्भुज ……………. होते हैं।</strong></li> </ol> <p>(A) सर्वांगसम<br>
(B) समानुपाती<br>
(C) समरूप<br>
(D) इनमें से कोई नहीं</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="76"> <li><strong>यदि </strong><strong>∆</strong><strong>ABC </strong><strong>में </strong><strong>∠</strong><strong>B = 90° </strong><strong>हो</strong><strong>, </strong><strong>तो –</strong></li> </ol> <p>(A) AB<sup>2</sup> = AC<sup>2</sup> + BC<sup>2</sup><br>
(B) AC<sup>2</sup> = AB<sup>2</sup> + BC<sup>2</sup><br>
(C) BC<sup>2</sup> = AC<sup>2</sup> + AB<sup>2</sup><br>
(D) AC<sup>2</sup> = 2AB<sup>2</sup> + BC<sup>2</sup></p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <ol start="77"> <li><strong>यदि </strong><strong>∠</strong><strong>A = </strong><strong>∠</strong><strong>R, </strong><strong>∠</strong><strong>C = </strong><strong>∠</strong><strong>P </strong><strong>तथा </strong><strong>∠</strong><strong>B = </strong><strong>∠</strong><strong>O, </strong><strong>तो </strong><strong>∆</strong><strong>ABC </strong><strong>समरूप है –</strong></li> </ol> <p>(A) ∆PQR के<br>
(B) ∆QPR के<br>
(C) ∆ROP के<br>
(D) ∆RPQ के</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> C</strong></td> </tr> </tbody> </table> <ol start="78"> <li><strong>यदि </strong><strong>∆</strong><strong>ABC ~ ∆DEF, </strong><strong>तो</strong></li> </ol> <p>(A) ∠A = ∠E<br>
(B) ∠B = ∠F<br>
(C) ∠C = ∠E<br>
(D) ∠D = ∠A</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="79"> <li><strong>एक समकोण त्रिभुज की दो छोटी भुजाएँ </strong><strong>a cm </strong><strong>तथा </strong><strong>b cm </strong><strong>लम्बी है</strong><strong>, </strong><strong>तो तीसरी भुजा की लम्बाई =</strong></li> </ol> <p> </p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> D</strong></td> </tr> </tbody> </table> <ol start="80"> <li><strong> ∆PQR </strong><strong>में </strong><strong>PQ </strong><strong>तथा </strong><strong>PR </strong><strong>पर क्रमशः बिन्दु </strong><strong>S </strong><strong>और </strong><strong>T </strong><strong>है। </strong><strong>PS = 3 cm, SQ = 7 cm, PT = 6 cm, TR = 14 cm </strong><strong>हो तो </strong><strong>∠</strong><strong>PST =</strong></li> </ol> <p>(A) 1/2 ∠ PQR<br>
(B) ∠ PQR<br>
(C) 1/3 PQR<br>
(D) 1/4 PQR</p> <table width="413"> <tbody> <tr> <td width="412"><strong> Answer </strong><strong>⇒</strong><strong> B</strong></td> </tr> </tbody> </table> <pre><span class="acss19431">Bihar Board Class 10 Math Triangle Bihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math Triangle</span>
<span class="acss19431">Bihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math TriangleBihar Board Class 10 Math Triangle</span></pre> </div> <div class="amp-wp-content"><amp-addthis width="320" height="92" data-pub-id="ra-5cc8551aa4f16f5c" data-widget-id="cwgj"></amp-addthis></div> <div class="amp-author "> <div class="amp-author-image "> <amp-img src="https://secure.gravatar.com/avatar/4cc408f9cbcf1b6858bcfbfab9e353ac?s=60&#038;d=mm&#038;r=g" width="60" height="60" layout="fixed"></amp-img> </div> <div class="author-details "><span class="author-name">bihaarboard</span><p></p> </div> </div> <div id="pagination"> <div class="next"> <a 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