新高考數(shù)學(xué)二輪復(fù)習(xí)分層訓(xùn)練專題25 二項(xiàng)式定理（原卷版）

答案第=page11頁，共=sectionpages22頁專題25二項(xiàng)式定理【練基礎(chǔ)】單選題1．（2020·全國·統(tǒng)考高考真題）SKIPIF1<0的展開式中x3y3的系數(shù)為（

）A．5 B．10C．15 D．202．（2022·北京·統(tǒng)考高考真題）若SKIPIF1<0，則SKIPIF1<0（

）A．40 B．41 C．SKIPIF1<0 D．SKIPIF1<03．（2023·全國·高三專題練習(xí)）SKIPIF1<0的展開式中SKIPIF1<0的系數(shù)是（

）A．60 B．80 C．84 D．1204．（2022秋·廣東汕頭·高三統(tǒng)考期末）SKIPIF1<0的展開式中SKIPIF1<0的系數(shù)為（

）A．60 B．24 C．SKIPIF1<0 D．SKIPIF1<05．（2023秋·重慶永川·高三重慶市永川北山中學(xué)校?？计谀┤鬝KIPIF1<0，則SKIPIF1<0（

）A．-448 B．-112 C．112 D．4486．（2023春·四川綿陽·高三四川省綿陽南山中學(xué)?？茧A段練習(xí)）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·重慶永川·重慶市永川北山中學(xué)校?？寄M預(yù)測）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0是數(shù)列SKIPIF1<0的前n項(xiàng)和，若SKIPIF1<0，數(shù)列SKIPIF1<0的首項(xiàng)SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2021 D．SKIPIF1<0二、多選題9．（2023·全國·高三專題練習(xí)）已知二項(xiàng)式SKIPIF1<0的展開式中各項(xiàng)系數(shù)之和是SKIPIF1<0，則下列說法正確的有（

）A．展開式共有7項(xiàng) B．二項(xiàng)式系數(shù)最大的項(xiàng)是第4項(xiàng)C．所有二項(xiàng)式系數(shù)和為128 D．展開式的有理項(xiàng)共有4項(xiàng)10．（2022·山東濟(jì)南·統(tǒng)考一模）SKIPIF1<0的展開式中，下列結(jié)論正確的是（

）A．展開式共6項(xiàng) B．常數(shù)項(xiàng)為64C．所有項(xiàng)的系數(shù)之和為729 D．所有項(xiàng)的二項(xiàng)式系數(shù)之和為6411．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0的展開式中第5項(xiàng)與第7項(xiàng)的二項(xiàng)數(shù)系數(shù)相等，且展開式的各項(xiàng)系數(shù)之和為1024，則下列說法正確的是（

）A．展開式中奇數(shù)項(xiàng)的二項(xiàng)式系數(shù)和為256B．展開式中第6項(xiàng)的系數(shù)最大C．展開式中存在常數(shù)項(xiàng)D．展開式中含SKIPIF1<0項(xiàng)的系數(shù)為4512．（2023·全國·高三專題練習(xí)）SKIPIF1<0，若SKIPIF1<0，則下列結(jié)論正確的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．二項(xiàng)式系數(shù)的和為SKIPIF1<0 D．SKIPIF1<0三、填空題13．（2022·全國·統(tǒng)考高考真題）SKIPIF1<0的展開式中SKIPIF1<0的系數(shù)為________________（用數(shù)字作答）．14．（2022·浙江·統(tǒng)考高考真題）已知多項(xiàng)式SKIPIF1<0，則SKIPIF1<0__________，SKIPIF1<0___________．15．（2022春·全國·高三專題練習(xí)）設(shè)SKIPIF1<0，則SKIPIF1<0…SKIPIF1<0______．16．（2022·全國·高三專題練習(xí)）若SKIPIF1<0，則SKIPIF1<0_______．【提能力】一、單選題17．（2023·全國·高三專題練習(xí)）若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．1 D．218．（2022秋·江蘇鹽城·高三阜寧縣東溝中學(xué)?？茧A段練習(xí)）已知SKIPIF1<0的展開式中各項(xiàng)的二項(xiàng)式系數(shù)之和為64，則其展開式中SKIPIF1<0的系數(shù)為（

）A．160 B．SKIPIF1<0 C．60 D．SKIPIF1<019．（2021·全國·高三專題練習(xí)）SKIPIF1<0的二項(xiàng)展開式中，奇數(shù)項(xiàng)的系數(shù)和為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．（2022·江蘇蘇州·蘇州中學(xué)?？寄M預(yù)測）SKIPIF1<0的展開式中SKIPIF1<0的系數(shù)是（

）A．84 B．120 C．122 D．21021．（2023·全國·高三專題練習(xí)）已知二項(xiàng)式SKIPIF1<0的展開式的所有項(xiàng)的系數(shù)和為32，則SKIPIF1<0的展開式中常數(shù)項(xiàng)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<022．（2022·浙江·?？寄M預(yù)測）若二項(xiàng)式SKIPIF1<0SKIPIF1<0的展開式中只有第7項(xiàng)的二項(xiàng)式系數(shù)最大，若展開式的有理項(xiàng)中第SKIPIF1<0項(xiàng)的系數(shù)最大，則SKIPIF1<0（

）A．5 B．6 C．7 D．823．（2023·遼寧盤錦·盤錦市高級中學(xué)?？家荒＃┮阎瘮?shù)SKIPIF1<0在SKIPIF1<0處的切線與直線SKIPIF1<0平行，則二項(xiàng)式SKIPIF1<0展開式中SKIPIF1<0的系數(shù)為（

）A．70 B．－70 C．56 D．－5624．（2021·天津靜海·靜海一中?？既＃┮阎猄KIPIF1<0的二項(xiàng)展開式的奇數(shù)項(xiàng)二項(xiàng)式系數(shù)和為SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2022·全國·高三專題練習(xí)）楊輝是我國南宋末年的一位杰出的數(shù)學(xué)家．他在《詳解九章算法》一書中，畫了一個(gè)由二項(xiàng)式SKIPIF1<0展開式的系數(shù)構(gòu)成的三角形數(shù)陣，稱作“開方作法本源”，這就是著名的“楊輝三角”．在“楊輝三角”中，從第2行開始，除1以外，其他每一個(gè)數(shù)值都是它上面的兩個(gè)數(shù)值之和，每一行第SKIPIF1<0個(gè)數(shù)組成的數(shù)列稱為第SKIPIF1<0斜列．該三角形數(shù)陣前5行如圖所示，則該三角形數(shù)陣前2022行第SKIPIF1<0斜列與第SKIPIF1<0斜列各項(xiàng)之和最大時(shí)，SKIPIF1<0的值為（

）A．1009 B．1010 C．1011 D．1012二、多選題26．（2022·江蘇·模擬預(yù)測）若二項(xiàng)式SKIPIF1<0展開式中所有項(xiàng)的系數(shù)之和為SKIPIF1<0，所有項(xiàng)的系數(shù)絕對值之和為SKIPIF1<0，二項(xiàng)式系數(shù)之和為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．對任意SKIPIF1<0均有SKIPIF1<0 D．存在SKIPIF1<0使得SKIPIF1<027．（2022·全國·模擬預(yù)測）已知SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0的展開式中第1012項(xiàng)的系數(shù)最大C．SKIPIF1<0 D．SKIPIF1<028．（2022秋·遼寧·高三遼寧實(shí)驗(yàn)中學(xué)校考階段練習(xí)）已知SKIPIF1<0則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<029．（2022·湖北黃岡·黃岡中學(xué)?？既＃┰O(shè)SKIPIF1<0，下列結(jié)論正確的是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0除以SKIPIF1<0的余數(shù)是1三、填空題30．（2023·全國·模擬預(yù)測）已知SKIPIF1<0的展開式中所有項(xiàng)的系數(shù)和為8，則展開式中SKIPIF1<0的系數(shù)為______.31．（2023·遼寧沈陽·統(tǒng)考一模）若SKIPIF1<0，則SKIPIF1<0被5除的余數(shù)是______．32．（2023·江蘇南京·校考一模）在二項(xiàng)式SKIPIF1<0的展開式中，若所有項(xiàng)的系數(shù)之和等于64，那么在這個(gè)展開式中，SKIPIF1<0項(xiàng)的系數(shù)是__________．（用數(shù)字作答）33．（2023·甘肅蘭州·?？家荒＃┤鬝KIPIF1<0，則SKIPIF1<0的值為______．34．（2023·全國·深圳中學(xué)校聯(lián)考模擬預(yù)測）已知SKIPIF1<0，則SKIPIF1<0__________．35．（2022·上海楊浦·統(tǒng)考一模）已知SKIPIF1<0（n是正整數(shù)），SKIPIF1<0，則SKIPIF1<0________．四、解答題36．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0.（1）求SKIPIF1<0的值；（2）求SKIPIF1<0的值.37．（2020·江蘇蘇州·常熟中學(xué)校考模擬預(yù)測）設(shè)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）．（1）若展開式中第5項(xiàng)與第7項(xiàng)的系數(shù)之比為3∶8，求k的值；（2）設(shè)SKIPIF1<0（SKIPIF1<0），且各項(xiàng)系數(shù)SKIPIF1<0，SKIPIF1<0