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I'll be uploading the second video to the channel tomorrow...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3579199/0113cc0d43f38db6df9b6433d7e65643/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/y7xwOQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=videoid:16950019177916090282","teaser":[{"list":{"type":"unordered","items":["Bu video, İbrahim Hoca tarafından sunulan bir matematik eğitim içeriğidir. Hoca, Acil Yayınları'nın fermantasyon, kombinasyon, binom ve olasılık kitabından permütasyon konusunu ele almaktadır.","Videoda permütasyon konusu detaylı olarak anlatılmakta ve çeşitli örnek sorular çözülmektedir. İlk olarak permütasyonun tanımı (n tane elemanın r'li sıralaması) ve faktöriyel kavramı kullanılarak permütasyon formülü (P(n,r) = n! / (n-r)!) açıklanmaktadır. Ardından dört öğrenci yedi koltuğa oturma, çift sayılarla palindron sayı oluşturma, masada kişilerin oturma düzeni ve evli çiftlerin eşler yan yana olmak şartıyla sıralanması gibi çeşitli permütasyon problemleri adım adım çözülmektedir.","Video, AYT sınavına hazırlanan öğrenciler için temel permütasyon sorularının çözüm tekniklerini göstermekte ve günlük hayattan örneklerle konuyu pekiştirmektedir. Hoca, özellikle masanın şekli ve deseni gibi detaylara dikkat edilmesi gerektiğini vurgulamakta ve soru çözüm mantığına odaklanmanın önemini anlatmaktadır."]},"endTime":1439,"title":"Permütasyon Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Soru Çözümü Serisi Tanıtımı","list":{"type":"unordered","items":["Acil Yayınları'nın fermantasyon, kombinasyon, binom ve olasılık kitabından soru çözümleri yapılacak.","Kitap konu anlatımlı olup, test kısmında zorlanılmayacağı belirtiliyor.","Videolar permütasyon, tekrarlı permütasyon, kombinasyon, binom ve olasılık konularını içerecek."]},"beginTime":11,"endTime":106,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=11&ask_summarization=1"},{"index":1,"title":"Permütasyon Kavramı","list":{"type":"unordered","items":["Permütasyon, n ve r doğal sayıları için n ≥ r olmak üzere n elemanın r'li sıralamasıdır.","n'in r'li permütasyonu P(n,r) = n! / (n-r)! formülüyle hesaplanır.","Permütasyon, bir kümeyi belirli bir sırada düzenlemeyi ifade eder."]},"beginTime":106,"endTime":216,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=106&ask_summarization=1"},{"index":2,"title":"Permütasyon Örnekleri","list":{"type":"unordered","items":["Dört öğrenci yan yana duran yedi koltuğa kaç farklı şekilde oturabilir sorusu çözülerek permütasyon kavramı açıklanıyor.","Aynı konsepte sahip elemanlar varsa, bunları bir bütün olarak düşünebiliriz.","Matematik kitapları bir arada olacak şekilde sıralama örneği veriliyor."]},"beginTime":216,"endTime":552,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=216&ask_summarization=1"},{"index":3,"title":"Soru Çözümüne Başlangıç","list":{"type":"unordered","items":["Palindrom sayılar (soldan sağa ve sağdan sola aynı şekilde okunan sayılar) tanıtılıyor.","Beş basamaklı bir palindrom sayı örneği veriliyor.","A kümesindeki elemanlarla kaç tane çift sayı yazılabilmesi sorusu çözülecek."]},"beginTime":552,"endTime":583,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=552&ask_summarization=1"},{"index":4,"title":"Çift ve Palindrom Sayı Sorusu","list":{"type":"unordered","items":["Çift sayı aranan bir soruda, son basamağa 2 veya 4 yazılabilir, bu nedenle 2 farklı seçenek vardır.","Palindrom sayı olması için ortadaki basamak mecburen 1 olmalıdır.","Geriye kalan basamaklara herhangi bir rakam konulabilir, bu durumda 6 farklı seçenek vardır.","Toplam durum sayısı 6 x 6 = 36 olup, çift sayı olma durumu için 2 farklı seçenek olduğu için toplam 72 durum vardır."]},"beginTime":586,"endTime":787,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=586&ask_summarization=1"},{"index":5,"title":"Masa Oturma Sorusu","list":{"type":"unordered","items":["Mert ve Canan'ın karşı karşıya oturacağı şekilde 6 kişinin oturma durumları inceleniyor.","Mert ve Canan'ın oturabileceği 3 farklı yer vardır ve her yerde karşılıklı oturabilirler.","Geriye kalan 4 kişinin oturabileceği 4! = 24 farklı şekilde olabilir.","Toplam durum sayısı 3 x 2 x 24 = 144 olarak hesaplanır."]},"beginTime":787,"endTime":896,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=787&ask_summarization=1"},{"index":6,"title":"Olasılık ve Permütasyon Sorularında Dikkat Edilmesi Gerekenler","list":{"type":"unordered","items":["Masanın şekli veya üzerindeki desen, permütasyon sorularında önemli bir faktör olabilir.","Sorularda görülen gereksiz detaylar atlanmamalı, sonradan onların etkisi değerlendirilmelidir.","Olasılık ve permütasyon sorularında çözüm mantığına odaklanmak, soru kalıplarına değil, daha fazla şey öğrenmeye yardımcı olur."]},"beginTime":896,"endTime":1009,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=896&ask_summarization=1"},{"index":7,"title":"Çocukların Sıralanması Problemi","list":{"type":"unordered","items":["Dokuz çocuğun sıralanma problemi ele alınıyor, bu çocuklardan üçü kardeş.","Satır şeklinde sıralama yaparken, ilk çocuk 9 farklı şekilde, ikinci çocuk 6 farklı şekilde, üçüncü çocuk 3 farklı şekilde yerleştirilebilir.","Satır ve sütun şeklinde yapılan hesaplamalar aynı sonuç verir: 6 üzeri 4."]},"beginTime":1011,"endTime":1193,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1011&ask_summarization=1"},{"index":8,"title":"Evli Çiftlerin Sıralanması Problemi","list":{"type":"unordered","items":["Dört evli çiftin eşlerin yan yana oturması şartıyla sıralanma problemi çözülüyor.","Evli çiftler kutu şeklinde düşünülerek, 4 kutunun sıralanması 4 faktöriyel şeklinde hesaplanır.","Her çift içindeki kişilerin yer değiştirebilmesi durumu, toplam durumda 2 üzeri 4 katı fazlasını oluşturur."]},"beginTime":1193,"endTime":1382,"href":"/video/preview/16950019177916090282?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1193&ask_summarization=1"},{"index":9,"title":"Problem Çözme Stratejisi","list":{"type":"unordered","items":["Problem çözme stratejisi olarak, önce gerçek hayatta nasıl düşünüleceğini düşünmek, 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Eğitmen, olasılık konusunu anlatmaktadır.","Video, binom dağılımının tanımı ve özellikleriyle başlayıp, formülünü detaylı şekilde açıklamaktadır. Ardından para atma, çocuk sayısı gibi örneklerle binom dağılımının nasıl hesaplanacağı gösterilmekte, \"en az\" ve \"en çok\" gibi ifadelerin nasıl işleneceği anlatılmaktadır. Daha sonra Poisson dağılımına geçilerek, bir mağazaya gelen müşteri sayısı gibi pratik örneklerle konu pekiştirilmektedir.","Video, olasılık konusunu öğrenmek isteyenler için temel formülleri ve çözüm yöntemlerini içermekte, özellikle binom dağılımının sayımla belirtilen kesikli değişkenlerin dağılımı olduğunu ve bir olayın oluş olasılığının büyük ve denek sayısının küçük olduğu durumlarda kullanıldığını vurgulamaktadır."]},"endTime":1081,"title":"Olasılık Dersi: Binom ve Poisson Dağılımları","beginTime":0}],"fullResult":[{"index":0,"title":"Binom Dağılımı Tanıtımı","list":{"type":"unordered","items":["Bu videoda binom ve pozisyon dağılımları ele alınacak, önceki videoda normal dağılım ve z tablosu anlatılmıştı.","Binom dağılımı, sayımla belirtilen kesikli değişkenlerin dağılımıdır ve bir olayın oluş olasılığının büyük, denek sayısının küçük olduğu durumlarda kullanılır.","Binom dağılımında incelenen olayın birbirinden bağımsız iki olası sonucu vardır ve denemeler birbirinden bağımsızdır."]},"beginTime":2,"endTime":59,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2&ask_summarization=1"},{"index":1,"title":"Binom Dağılım Formülü","list":{"type":"unordered","items":["Binom dağılım formülü n'in r'li kombinasyonu, istenen olayın oluş sayısı ve olma olasılığı ile hesaplanır.","Olma olasılığı (p) ile olmama olasılığı (q) toplamı 1'e eşittir, yani p+q=1.","Formülde olma olasılığı üzeri istenen olayın oluş sayısı ve olmama olasılığı üzeri toplam olay sayısından istenen olayın oluş sayısını çıkararak bulunur."]},"beginTime":59,"endTime":139,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=59&ask_summarization=1"},{"index":2,"title":"Para Atma Örneği","list":{"type":"unordered","items":["Metal ve hilesiz bir para on kez atıldığında, yazı gelme olasılığı 0,5'tir ve gelmeme olasılığı da 0,5'tir.","Bir kez yazı gelme olasılığı 10'un 1'li kombinasyonu çarpı 0,5 üzeri 1 çarpı 0,5 üzeri 9 olarak hesaplanır.","En az iki kez yazı gelme olasılığı, toplamda bir kez veya hiç gelmeme olasılığını çıkararak bulunabilir."]},"beginTime":139,"endTime":404,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=139&ask_summarization=1"},{"index":3,"title":"Çocuk Sayısı Örneği","list":{"type":"unordered","items":["Dört çocuklu bir ailede en az bir erkek olması durumu, 1'den 4'e kadar erkek olma olasılıklarının toplamı olarak hesaplanabilir.","En az bir erkek ve bir kız olması durumu, 1'den 4'e kadar erkek ve kız olma olasılıklarının toplamı olarak hesaplanabilir.","İki yoldan da hesaplanabilir: her bir durumu ayrı ayrı hesaplayıp toplamak veya hiç gelmeme olasılığını çıkarıp toplam ihtimalden bulmak."]},"beginTime":404,"endTime":596,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=404&ask_summarization=1"},{"index":4,"title":"Aile Sayısı Örneği","list":{"type":"unordered","items":["Her biri dört çocuklu 2000 aileden kaçının en az bir erkek çocuğu vardır, bu 15/16 bulunur.","İki erkek olma ihtimali 3/8 olarak hesaplanır.","2000 ailenin içerisinde iki erkek çocuğu olma ihtimali olan aile sayısı 750 olarak bulunur."]},"beginTime":596,"endTime":699,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=596&ask_summarization=1"},{"index":5,"title":"Binom Dağılımı Örnekleri","list":{"type":"unordered","items":["Bir ve iki kız olma ihtimali hesaplanırken, bir kız olma ihtimali 1/2, iki kız olma ihtimali 3/8 olarak bulunur ve toplam 5/8 ihtimal elde edilir.","2000 ailenin bir veya iki kız çocuğu olma ihtimali 1250'dir.","Tüm çocuklarının erkek olma ihtimali 125'tir."]},"beginTime":705,"endTime":809,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=705&ask_summarization=1"},{"index":6,"title":"Pozisyon Dağılımı","list":{"type":"unordered","items":["Pozisyon dağılımı, sayımla belirten değişkenlerin dağılımını ifade eder ve olay sayısı büyük olduğunda olasılık hesaplamak için kullanılır.","Pozisyon dağılımında kullanılan formül: P(X=x) = (e^(-λ)) * (λ^x) / x! şeklindedir.","λ, belirlenen periyotta ortaya çıkan olay sayısıdır ve x ise ortaya çıkma olasılığı araştırılan olaydır."]},"beginTime":809,"endTime":873,"href":"/video/preview/4766786262018287166?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=809&ask_summarization=1"},{"index":7,"title":"Pozisyon Dağılımı 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this video, we solved the 8th video on our KPSS Mathematics list, which is about prime numbers. You can follow our Telegram channel to access clear and solved PDFs and stay informed about the...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3284897/4df103d6ab6cdae64b1a3560eaf0cdb3/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/irYjPgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"12","reqid":"1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=videoid:17965567997694286089","teaser":[{"list":{"type":"unordered","items":["Bu video, Tunç Kurt tarafından sunulan bir matematik eğitim içeriğidir. Eğitmen, Elif adında bir ekip arkadaşıyla birlikte hazırladığı dosyaları kullanarak konuyu anlatmaktadır.","Video, asal sayılar ve bölenler konusunu kapsamlı şekilde ele almaktadır. İçerikte asal sayıların tanımı ve özellikleri, aralarında asallık kavramı, asal çarpanlar, tam bölenler ve bunların sayıları gibi konular örneklerle açıklanmaktadır. Video, KPSS sınavına hazırlanan öğrenciler için hazırlanmış sorular üzerinden ilerlemekte ve her soru için detaylı çözüm yöntemleri sunulmaktadır.","Videoda ayrıca x+y=5 ve 2x-y=5 gibi denklemlerin çözümü, faktöriyel içindeki asal çarpanları tespit etme, pozitif tam bölen sayısı belirli olan sayıları bulma ve asal olmayan tam bölenlerin toplamı gibi konular da ele alınmaktadır. Video, sayı basamakları konusunun bir sonraki videoda ele alınacağı bilgisiyle sonlanmaktadır."]},"endTime":2554,"title":"KPSS Matematik: Asal Sayılar ve Bölenler Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Asal Sayılar Konusuna Giriş","list":{"type":"unordered","items":["Asal sayılar testi sekiz ile devam ediliyor ve bu konu çözdüğünüz tüm matematik konularıyla ilgilidir.","Asal sayılar, matematikte yapı taşı niteliğindedir ve tüm pozitif tam sayılar asal sayıların çarpımları şeklinde ifade edilebilir.","En küçük asal sayı iki'dir ve çift tek asal sayıdır; diğer asal sayılar üç, beş, yedi, onbir, onüç gibi tek sayılardır."]},"beginTime":0,"endTime":121,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=0&ask_summarization=1"},{"index":1,"title":"Pozitif Tam Bölen Sayısı","list":{"type":"unordered","items":["Bir sayının pozitif tam bölenlerinin sayısını bulmak için, sayının asal çarpanları üsleri bir arttırılıp çarpılır.","Tam bölen sayısı, pozitif tam bölen sayısının iki katıdır çünkü her pozitif bölenin negatif karşılığı da bölen olur.","Asal olmayan pozitif tam bölenlerinin sayısı, toplam pozitif tam bölen sayısından asal bölenlerin sayısı çıkarılarak bulunur."]},"beginTime":121,"endTime":283,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=121&ask_summarization=1"},{"index":2,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["\"4b+3b ifadesi asal sayı yapan b tam sayı değeri kaç tanedir?\" sorusunda, b yerine eksi üç, bir ve üç değerleri konulabilir.","Bu değerler sırasıyla 3, 7 ve 5 asal sayılarını verir, dolayısıyla b için üç farklı değer bulunabilir."]},"beginTime":283,"endTime":355,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=283&ask_summarization=1"},{"index":3,"title":"Asal Sayılar ve Doğal Sayılar","list":{"type":"unordered","items":["Asal sayılar, iki sayının çarpımı şeklinde sadece kendisi çarpı bir veya eksi bir çarpı eksi asal sayı şeklinde yazılabilir.","İki doğal sayının çarpımı bir asal sayı olabilmesi için mutlaka bir çarpanının bir olması gerekir.","Soruda x ve y doğal sayıları için x+y=5 ve 2x-y=1 denklemleri çözülerek x=2 ve y=3 bulunur, çarpımları 6'dır."]},"beginTime":357,"endTime":508,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=357&ask_summarization=1"},{"index":4,"title":"Aralarında Asal Sayılar","list":{"type":"unordered","items":["Aralarında asal sayılar, en büyük ortak bölenlerinin (EBOB) 1 olduğu sayılardır.","İki sayı aralarında asal olmak için ortak bölenleri olmamalıdır, örneğin 7 ve 15 aralarında asaldır çünkü ortak bölenleri yoktur."]},"beginTime":508,"endTime":590,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=508&ask_summarization=1"},{"index":5,"title":"Asal Sayılar ve Özellikleri","list":{"type":"unordered","items":["Asal sayılar konusunda pozitiflik ve çiftlik teknikleri kullanılır.","Bir sayının basamaklarının toplamı 3'ün bir katıysa, o sayı 3'e bölünür ve asal değildir.","Tek bir sayının karesi tektir, çift bir sayının asal olması sadece 2 olduğu durumda mümkündür."]},"beginTime":597,"endTime":652,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=597&ask_summarization=1"},{"index":6,"title":"Asal Sayı Problemleri","list":{"type":"unordered","items":["Çift sayılar (2 hariç) asal değildir çünkü mutlaka 2'ye bölünür.","83 sayısı asal sayıdır çünkü 3 üzeri 4 ile 2'nin toplamı 83'tür.","91 sayısı asal değildir çünkü 7 ile 13'ün çarpımıdır."]},"beginTime":652,"endTime":753,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=652&ask_summarization=1"},{"index":7,"title":"Asal Sayılarla İlgili Bir Problemin Çözümü","list":{"type":"unordered","items":["x, y, z asal sayılar ve x=7y şeklinde verilmişse, y'nin 1 olması gerekir.","x=7, y=1 ve z=1 olarak bulunur.","a+b+c=7 olarak hesaplanır."]},"beginTime":753,"endTime":842,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=753&ask_summarization=1"},{"index":8,"title":"Aralarında Asal Sayılar","list":{"type":"unordered","items":["Aralarında asal sayılarla ilgili problemlerde, verilen terimler üzerine oynamak gerekir.","Aralarında asal sayılarla ilgili problemlerde katlarla uğraşmamak ve bunları sindirmeye çalışmak önemlidir.","Aralarında asal sayılarla ilgili problemlerde, verilen sayıların katları olabilir ve bunları bulmak çözümü kolaylaştırır."]},"beginTime":842,"endTime":1065,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=842&ask_summarization=1"},{"index":9,"title":"Sayıların Asal Çarpanlarına Ayrılması ve Tam Kare Yapılması","list":{"type":"unordered","items":["Sayıları asal çarpanlarına ayırarak sürekli yapı taşlarını indirerek yazabiliriz.","Bir sayıyı tam kare yapmak için, asal çarpanlarının kuvvetleri iki'nin katı olmalıdır.","Örneğin, 12 sayısını tam kare yapmak için 3 ile çarpabiliriz çünkü 2²×3×3=36, 6²'nin tam karesidir."]},"beginTime":1066,"endTime":1265,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1066&ask_summarization=1"},{"index":10,"title":"Sayıların Küp Olarak Yazılması","list":{"type":"unordered","items":["Bir sayının küpü olabilmesi için asal çarpanlarının kuvvetleri 3 ve 3'ün katı olmalıdır.","160 sayısını asal çarpanlarına ayırarak 2⁶×5³ şeklinde yazabiliriz ve bunu (2²×5)³ şeklinde yazarak b'nin küpüne eşitleyebiliriz.","a=50 ve b=20 olduğunda, a+b toplamı 70'dir."]},"beginTime":1265,"endTime":1416,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1265&ask_summarization=1"},{"index":11,"title":"Tam Bölen Sayıları Hesaplama","list":{"type":"unordered","items":["Bir sayının asal olmayan tam bölenlerinin sayısını hesaplamak için, önce tüm bölenlerin sayısını bulmak gerekir.","5ˣ×80 sayısının asal olmayan tam bölenleri 118 ise, tüm bölenlerin sayısı 120'dir ve pozitif tam bölen sayısı 60'dır.","Pozitif tam bölen sayısı formülü kullanılarak x=9 olarak bulunur."]},"beginTime":1416,"endTime":1577,"href":"/video/preview/17965567997694286089?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1416&ask_summarization=1"},{"index":12,"title":"Sayıların Pozitif Tam Bölenleri","list":{"type":"unordered","items":["Bin sayısını 2³ × 5³ şeklinde yazabiliriz.","Bir sayının pozitif tam bölen sayısını bulmak için, sayının asal çarpanlarının üslerine 1 ekleyip bunları çarparız.","2ⁿ⁻¹ × 5ⁿ⁻¹ şeklindeki bir sayının pozitif tam bölen sayısı 132 ise, n=11 olarak 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kümedir."]},"beginTime":462,"endTime":533,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=462&ask_summarization=1"},{"index":5,"title":"Rakamlarla İlgili Örnek Sorular","list":{"type":"unordered","items":["\"a ve b rakamdır, 2a+3b toplamının en büyük değeri kaçtır?\" sorusunda, a ve b'nin birbirinden farklı olup olmadığına bağlı olarak farklı sonuçlar elde edilir.","Rakamlar 0'dan 9'a kadar olduğundan, en büyük değer için her iki bilinmeyene de 9 yazılabilir (45).","Birbirinden farklı rakamlar isteniyorsa, en büyük değer için 1 ve 9 kullanılır (43)."]},"beginTime":533,"endTime":723,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=533&ask_summarization=1"},{"index":6,"title":"En Küçük Değer Problemleri","list":{"type":"unordered","items":["\"2a+3b toplamının en küçük değeri kaçtır?\" sorusunda, en küçük değer için her iki bilinmeyene de 0 şeklinde yazılır (0) veya birbirinden farklı rakamlar isteniyorsa, 0, 1 ve 9 kullanılır (2).","\"2a-3b farkının en büyük değeri kaçtır?\" sorusunda, en büyük değer için büyük sayıdan küçük sayı çıkarılır (18).","Birbirinden farklı rakamlar isteniyorsa bile, en büyük değer için 1 ve 9 kullanılır (18)."]},"beginTime":723,"endTime":974,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=723&ask_summarization=1"},{"index":7,"title":"En Küçük Değer Problemleri (Devam)","list":{"type":"unordered","items":["\"2a-3b farkının en küçük değeri kaçtır?\" sorusunda, en küçük değer için küçük sayıdan büyük sayı çıkarılır (−27).","Birbirinden farklı rakamlar isteniyorsa bile, en küçük değer için 0, 7 ve 9 kullanılır (−27)."]},"beginTime":974,"endTime":1049,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=974&ask_summarization=1"},{"index":8,"title":"Rakamlarla İfadelerin En Büyük ve En Küçük Değerleri","list":{"type":"unordered","items":["a, b ve c birbirinden farklı rakamlar olmak üzere 3a + 2b - c ifadesinin en büyük değeri için pozitif katsayılara büyük sayılar, negatif katsayılara küçük sayılar verilir.","3a + 2b - c ifadesinin en küçük değeri için pozitif katsayılara küçük sayılar, negatif katsayılara büyük sayılar verilir.","Birbirinden farklı rakamlar kullanıldığında, en büyük değer için pozitif katsayılara en büyük sayılar, negatif katsayılara en küçük sayılar verilir."]},"beginTime":1051,"endTime":1311,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1051&ask_summarization=1"},{"index":9,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["İki basamaklı üç doğal sayının toplamı en çok 297 olabilir (99 + 99 + 99).","İki basamaklı üç doğal sayının toplamı en az 33 olabilir (10 + 11 + 12).","Soruları dikkatli okumak ve altını çizmek önemlidir, aksi takdirde hata yapılabilir."]},"beginTime":1311,"endTime":1484,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1311&ask_summarization=1"},{"index":10,"title":"Negatif Tam Sayılarla İşlemler","list":{"type":"unordered","items":["İki basamaklı üç negatif tam sayının toplamı en çok olduğunda, sıfıra yakın olan negatif sayılar seçilir.","İki basamaklı birbirinden farklı iki tam sayının toplamı en az olduğunda, en büyük negatif sayı (eksi doksandokuz) ve en küçük negatif sayı (eksi doksansekiz) seçilir."]},"beginTime":1485,"endTime":1608,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1485&ask_summarization=1"},{"index":11,"title":"Rakamları Toplamı Belirli Sayılar","list":{"type":"unordered","items":["Rakamları toplamı oniki olan üç basamaklı en büyük doğal sayı 930'dur.","Rakamları toplamı oniki olan üç basamaklı en küçük doğal sayı 129'dur.","Bu iki sayının toplamı 1059'dur."]},"beginTime":1608,"endTime":1718,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1608&ask_summarization=1"},{"index":12,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["İki basamaklı üç doğal sayının toplamı doksanbeş ise, bu sayıların en büyüğü 75'tir.","En büyük sayıyı bulmak için, diğer iki sayının toplamı (10+10=20) çıkarılır."]},"beginTime":1718,"endTime":1778,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1718&ask_summarization=1"},{"index":13,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["İki basamaklı üç farklı doğal sayının toplamı 95 ise, bu sayıların en büyüğü en çok 74 olabilir.","Toplamları verip çarpımının en büyük veya en küçük değerini isteyen sorular standart soru tarzıdır."]},"beginTime":1779,"endTime":1853,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1779&ask_summarization=1"},{"index":14,"title":"Toplamları Verilip Çarpımlarının En Büyük Değeri","list":{"type":"unordered","items":["Toplamları 20 olan iki doğal sayının çarpımının en büyük değerini bulmak için sayılar birbirine yakın olmalıdır.","Toplamları verilip çarpımları en küçük değerini bulmak için sayılar birbirine uzak olmalıdır.","Birbirinden farklı doğal sayılar için çarpımların en büyük değerini bulmak için sayılar birbirine yakın olmalıdır."]},"beginTime":1853,"endTime":2069,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=1853&ask_summarization=1"},{"index":15,"title":"Çarpımları Verilip Toplamlarının En Büyük ve En Küçük Değeri","list":{"type":"unordered","items":["Çarpımları 12 olan iki doğal sayının toplamının en büyük değeri 13, en küçük değeri 7'dir.","Çarpımları verip toplamlarının en büyük değerini bulmak için sayılar birbirine uzak olmalıdır.","Çarpımları verip toplamlarının en küçük değerini bulmak için sayılar birbirine yakın olmalıdır."]},"beginTime":2069,"endTime":2153,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2069&ask_summarization=1"},{"index":16,"title":"Tam Sayılar İçin Çarpımlar ve Toplamlar","list":{"type":"unordered","items":["Tam sayılar için çarpımları 12 olan iki sayının toplamının en küçük değeri -13, en büyük değeri 13'tür.","Tam sayılar için çarpımları 12 olan iki sayının toplamının en küçük değeri negatif tam sayılar olmak üzere -13'tür.","Tam sayılar için çarpımları 12 olan iki sayının toplamının en büyük değeri pozitif tam sayılar olmak üzere 13'tür."]},"beginTime":2153,"endTime":2279,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2153&ask_summarization=1"},{"index":17,"title":"Birden Fazla Çarpım ve Toplam","list":{"type":"unordered","items":["a×b=12 ve b×c=16 olan üç doğal sayının toplamının en küçük değeri 11'dir.","a×b=12 ve b×c=16 olan üç doğal sayının toplamının en büyük değeri 29'dur.","a×b=12 ve b×c=16 olan üç doğal sayının toplamının en küçük değerini bulmak için sayılar birbirine yakın olmalıdır."]},"beginTime":2279,"endTime":2379,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2279&ask_summarization=1"},{"index":18,"title":"Çarpanlar ve Denklemler","list":{"type":"unordered","items":["a çarpı b 12, b çarpı c 16 denklemi için a, b ve c'nin birbirinden farklı olması durumunda a=6, b=2, c=8 alınabilir ve toplamları 16 olur.","Konu zor değil ancak çok farklı soru tarzları var ve çok fazla soru çözülmesi gerekiyor.","Negatiflikler sıfırdan farklı olduğu için dikkat edilmeli."]},"beginTime":2390,"endTime":2467,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2390&ask_summarization=1"},{"index":19,"title":"Ortak Kat Problemi","list":{"type":"unordered","items":["2a=3b ve 4b=5c eşitlikleri için b sayısı 2'nin katı ve 5'in katı olmak zorunda, bu nedenle en küçük ortak kat olan 10 bulunur.","b=10 alındığında, 2a=30 denkleminden a=15, 4b=5c denkleminden c=8 bulunur.","a+b+c'nin en küçük değeri 15+10+8=33'tür."]},"beginTime":2467,"endTime":2588,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2467&ask_summarization=1"},{"index":20,"title":"Pozitif Tam Sayılar Problemi","list":{"type":"unordered","items":["a+2b=15 koşulunu sağlayan pozitif tam sayılar için, 15 sayısının 2'nin tam katı olan en büyük değeri 14'tür.","İlk çözüm (a=1, b=14) bulunduktan sonra, küçük sayıyı diğer sayının katına ekleyip, büyük sayıyı diğer sayının katından çıkararak diğer çözümler bulunur.","Pozitif tam sayılar için b sayısı 1, 2, 3, 4, 5, 6, 7 olmak üzere toplam 7 farklı değer alabilir."]},"beginTime":2588,"endTime":2756,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2588&ask_summarization=1"},{"index":21,"title":"Son Örnek","list":{"type":"unordered","items":["3x+5y=25 denklemi için, 5'in katı olan 5 değeri bulunur.","5×5=25 olduğundan, x=0 ve y=5 olarak alınabilir."]},"beginTime":2756,"endTime":2770,"href":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=2756&ask_summarization=1"}],"linkTemplate":"/video/preview/356677748255401539?parent-reqid=1767108431988577-911635978932594470-balancer-l7leveler-kubr-yp-vla-223-BAL&text=The+Solution+-+Topics&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"3) kpss, tyt, ales, dgs - basic concepts part 1 - lots of questions with solutions - topic test","related_orig_text":"The Solution - Topics","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"The Solution - 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Solution 02 By : K.K.... 3. Class-12th Chemistry (Topic-Solution-03) ➡️ • Class 12th Chemistry Solution 03 By : K.K.... 4. 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