JEE: Binomial Theorem L4 | Applications | Unacademy JEE | JEE Maths | Sameer Chincholikar

[@UnacademyJEE]

To download notes, click here NOW: bit.ly/2QreZUj

[@Harshraj-io8gg]

Sir, videos download kyu nhi ho pa rhe h

[@sofisharma9195]

Ans of HW questions is 6, and 197

[@santraj9417]

Sir video download nhi ho raha ese pahle wala bhi nhi ho rha h

[@santraj9417]

Please kuch kar do

[@uy70019]

Use snaptube I use this to download youtube videos. It's illegal but I don't care about that .

[@divyansh_kala]

Homework Question Answers: 1 last digit of 32³² = 6 2 2 [ 8 + 60 + 30 + 1 ] = I + f + f' 198 = I + 1 I = 197 1) (32)³² = (2⁵)³² = 2¹⁶⁰ Therefore (32)³² can be rewritten as 2¹⁶⁰ The exponent of 2 has a regular pattern: 2¹ = 2 ----------- Pattern [ 1 ] 2² = 4 ----------- Pattern [ 2 ] 2³ = 8 ----------- Pattern [ 3 ] 2⁴ = 16 (last digit = 6) ------- Pattern [ 4 ] And then it repeats 160 ÷ 4 = 40 ⇒ It will fall into Pattern [ 4 ] ⇒ the last digit is 6 Answer: The last digit is 6

[@nnn8277]

Could you please explain How u got last digit as 6

[@divyansh_kala]

@@nnn8277 (32)³² = (2⁵)³² = 2¹⁶⁰ Therefore (32)³² can be rewritten as 2¹⁶⁰ The exponent of 2 has a regular pattern: 2¹ = 2 ----------- Pattern [ 1 ] 2² = 4 ----------- Pattern [ 2 ] 2³ = 8 ----------- Pattern [ 3 ] 2⁴ = 16 (last digit = 6) ------- Pattern [ 4 ] And then it repeats 160 ÷ 4 = 40 ⇒ It will fall into Pattern [ 4 ] ⇒ the last digit is 6 Answer: The last digit is 6

[@electric_deer2007]

@@divyansh_kala bhai JEE prep kaisa chal raha hai ?

[@divyansh_kala]

@@electric_deer2007 Mast bhag raha hai :)

[@akshatgupta2233]

@@divyansh_kalawhich year aspirant are you

[@Aryan-cu5ne]

Hw ques ans Option b (6) Soln - divide the number by 10 and the remainder would give us the ans 32^32. = (30+2 ) ^32 =*. 2^32 From here you can check that after every 4th power of 2 the last digit repeats itself

[@kiranbarnwal8503]

32^(32) = 2^(160) = 16^(40) Also we know that a number ending with six ki power something will always have last term (6) Ex - 16^2 , 16^3 , 16^4 , 16^5 all ends with (6)

[@ptr6334]

Sir 1:04:01 answer of homework question is C. 197

[@shazi11]

6:30

[@vkrs3315]

Thank you

[@pandyaakshat7473]

Jee live daily has got the best mathematics mentors for both 11 and 12 .

[@mohakchopra6499]

I absolutely agree

[@krishgupta5734]

Agree

[@AdityaKumar-jg2qr]

yupp... it is very hard to decide whether who is best between NV sir nd Sameer sir... both are 💕

[@pureevil1277]

@@AdityaKumar-jg2qr Sameer sir grasp of the subject is unparalleled

[@abhijeetabhay7394]

Sir, really your way of teaching is superb

[@roastlord6767]

lecture starts @ 7:00

[@Indaweer]

love u sir u actually made maths as my favourite subject

[@meenakshijasht7232]

sameer sir is brilliant case

[@VivekYadav-ds8oz]

HINT: Finding the last digit of a number is equivalent to finding its remainder when dividing by 10. Courtesy of Computer Sci where you have to do this kind of stuff constantly.

[@ayushkushwaha4389]

SIR THE ANSWER OF HW QUESTION NO. 2 IS 197 THANK YOU SIR FOR TEACHING IN THIS GREAT AND AMAZING WAY. I AM IN CLASS 9 AND EVEN I AM ABLE TO UNDERSTAND EVERYTHING WHAT YOU TEACH AND ALSO ABLE TO SOLVE QUESTIONS .. LOVE YOU SIR.

[@aartiprajapati945]

Very good ...you definitely top in jee 2022 ... Keep dedication on your studies..👍👍👍👍👍👍

[@Rakesh_2801]

Jhuthe makkaar

[@gracysingh6108]

Sir answer to homework question is 6 and 197... Sir bs itna hi nhi aapne mere lofe m jo role play kra h use words m m express nhi kr skta hu.... Mene aapse 11 ki race m bhagne k bjay ruk kr saas lo fir rocket bnkr fire hona sikha h..♥️♥️♥️🔥🔥 # For me you r best teacher in the entore world....♥️♥️ Aap itna accha pdhate h... ki i seriously can't wait for episode 5 of this beautiful web series... Yes sir.... ek wqt pr ye lecture hote the...🔥🔥 but aapne ise web series ke episodes bna diya h sir..... Rhte bhle aap jha bhi ho... kosish puri krunga ki m aapse life m ek baar mil sku..... Bcoz for me defination of god is ... Everything beyond science..,, parents, and teachers.... Sor according to definition you r also my god sir...😍😍♥️♥️♥️♥️♥️

[@utpaldavlogs7556]

Yes gracy sameer sir means a lot to me... His teaching is so brilliant that if a 7th grade student who knew basics of algebra and geometry can easily become a fan of sir... in just 1 episode....

[@nridappers1274]

Wow So beautiful explanation of your Feelings If you purpose anyone like this You will get yes every time 😍😍😍😍😂😂😂 If you want to check then propose me 😂😂

[@utkarshmishra9871]

@@nridappers1274 the one for u r thinking for "she" is "he".

[@nridappers1274]

@@utkarshmishra9871 aapko kaise pata Ki mai he hu ya she??

[@utkarshmishra9871]

@@nridappers1274 it's magic,🧙🧙

[@pallavibarman6214]

Thank you sir❤️❤️❤️

[@ShivanshKaran]

What a trick! like👍 bina bole hi dil ❤️ se nikal jata hai

[@shreyasingh7339]

Lecture starts at 6:33

[@arjunans5139]

Thank you so much for saying this

[@adii18s]

Thanks

[@hinduhu594]

Tx searching for this

[@shivammahajan5424]

6 IS THE FIRST ANSWER AND 197 IS THE SECOND. ❤️❤️

[@shubhagnihotri4804]

UNACADEMY IS UNDERRATED!!!

[@Raghvendra7999]

Who said this? It is leading JEE channel

[@ArbazAnsari-ny4sj]

sir two improper fractions sum could be greater than 1 (55:30)

[@theknownunknown3904]

fractional part is always less than 1, fraction means a proper fraction

[@ArbazAnsari-ny4sj]

@@theknownunknown3904 thnks bhaia

[@sarvesh_soni]

ACTUALLY IN THAT QUESTION "I" denotes integer but actually it denotes GREATEST INTEGER FUNCTION means the greatest integral part it is denoted by [x] example -- [4.5] = 4 because it can be written as 4 + 0.5 [-3.72] = -4 because it can be written as -4 + 0.28 which satisfies I + f form so you will notice fractional part is always less than 1 which means a proper fraction

[@prasannapratapsingh3362]

Sir i was not able to attend the latest live class of binomial theorem but now the recorded video is private sir plz help😔

[@kulsummohammed4387]

Sirrrrr Lecture was🔥🔥🔥🔥🔥

[@ayusharyam4674]

Brilliant concept used 👌🏻😊

[@pureaccount1549]

At 1:02:44 Sir why you only take the value of (f+f')=1 as we know that 0

[@divyanshushekhar6252]

Sir answer to hw 1 is (b) 6 And 2nd is (c) 197

[@jatinjadon2137]

Sir 1st h.w ans is 6 and for the 2nd it's 197

[@sachin_sharma16]

answer of 1st homework question is 6 and 2nd is 197

[@utkarshkhandelwal593]

Bro can you tell how you have found answer of first question

[@piyushkala9707]

Sir at 25.46 we can also write (15+1)^n then we can't get our equation on solving this through bionomial

[@rohitjadhav7509]

Sir app her chap ka (one -two) shot. Video banaiye plz

[@mathslover3890]

Sir at 55:00 u said fraction + fraction made 1 🤔why can't any other integer

[@pureaccount1549]

See at 55:40

[@raushankumaryadav1522]

😂😂

[@charith6670]

Once check with examples ^_^

[@CreatorAll]

@ 30:20 Sir, What if we multiple and divide it with 5. We get the remainder 1/5.But remainder can't be fraction Plz doubt clarify kijiyena sir.

[@akshatgupta2233]

Yes you can do that

[@sakshamsureka9309]

Sir, hw question jo aapne discuss kiya usme the greatest term will ultimately be the term with the greatest coefficient acc. to what i understood. So, why we considered them as 'r' and 'n' and later on equate them rather than taking only one variable

[@divyranjanroutray775]

30:20 why can't we express 3^99 as (18-13) ^99 and get our ans???? Why it's not a valid method??????

[@dhruvsavaliya1203]

Lecture start on 5:34 Lecture ends on 1:11:23

[@rajubotu2049]

Tq

[@dhyeysuvagiya7250]

no 6:42

[@bhavyapiplani746]

sir pls tell in first question of this session how can we decide whether we have to take (1+15)^n or (15+1)^n , sir although the answer will come same but by taking (15+1)^n , the complexity increases ..... so to prevent this what can we do

[@mohdsiddiqueumar4949]

Do practice,and you get to know that what is appropriate to use

[@sarathkumar1528]

(1+15)^n would be easy

[@abhinash5638]

There is not that much complexity on taking (15+1)ⁿ just the difference is that the powers of 1 will decrease and the powers of 15 will increase instead of being vice versal and in that case u just need to cancel the last two terms so overall you can take the order anyway it will not make that much diff

[@sugarkiddo]

Sir ye homework question kis lecture me discuss kiya hai?

[@godcolor9722]

Even I can't find it

[@amanisdreaming3914]

Noice Sor.... ❤❤

[@nitin.lohokare7895]

@Divyansh kala which year jee aspirant are you

[@botispro9212]

start- 6:30

[@chesswallah3]

We can use congruence modulo to find answer

[@devaramdabriya9308]

You are best teacher for iit, love you sir

[@karanbhanushali6756]

Sir I+F waale questions mein jo second assumed term lenge wo diye gaye term ka humesha conjugate hoga jaise 2+√3 mein assume kiya 2-√3

[@AplusEducation23]

L3 main ap kahan hint die the sir ki bionomial coefficient kaise nikala jata hain?

[@it_04_supriyaanchala41]

Mind blowing.......sir... I love your teaching style.... 😍😍😍😍😍

[@dahyaqalbee6958]

Beautifully explained topic.. ❤❤

[@rishugoyal3395]

Sir apka brain amazing h .I didn't believe that u have such a wonderful mind 🤯😍

[@vikashmahto6391]

Yes you are right

[@oPgAmEr-sz9ck]

1st Hw ans is 6 2nd HW ans is 197 🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌🙌

[@shivamparmar988]

X

[@riteshjain2221]

2^32 ques ans is 6 2^8 *2^8*2^8*2^8 256*256*256*256 6*6*6*6 216*6=====last digit 6

[@IITian_Madras283]

55:14 kaise 1 hoga, plzzz explain anyone

[@abhaysonu2844]

Last digit of 32 to the power 32 is 6 .

[@nawedalam8713]

55:19 fraction +fraction sirf one hi banta hai.. wo kaise..🤔

[@vivekthakur2659]

Guys for hw q refer to concept of cyclicity

[@AbhishekKumar-vt2oh]

Sameer sir maths ko easy kar dete hai

[@pinaktilavat7163]

54:35 CID VALI Feeling aarahi he

[@chiragbhalla4876]

Ans of 2nd H.w. is : 197

[@prathamdhiman764]

why we didn't divide -5 with 13 40:46

[@meherunnisabegum2767]

Sir lecture no 5 of binomial theorem is showing as it is private video

[@ayashakumarimandal8681]

Sir, kindly make a video on how to solve cengage or arihant or any other mathematics books

[@shazi11]

Ans of 2nd hw ques is 197

[@shrutijain2449]

Sir has not explained the ans. Of hw ques.. Can anyone plz explain (hints) as i am not able to do..

[@manjuprakash318]

Look, we can write it as (30+2)³².ultimately the only things matter in 32c32 (30⁰)(2³²) is 2³². Further we can write it as 2⁸×2⁸×2⁸×2⁸ that will be 256*256*256*256 we can conclude that the last digit will be 6 for sure

[@shrutijain2449]

@@manjuprakash318 thnx😁

[@manjuprakash318]

@@shrutijain2449 oops...pardon,i wrote (30³²)by mistake

[@shrutijain2449]

@@manjuprakash318 np..i understood it.. Even i forgot i had asked this ques😂

[@explorer2.035]

how can u conclude if u multiply 256 *4 times will give u 6 as last digit? plz clarify

[@hemantporwal6766]

@jeelivedaily answer of hw question is 6

[@prasoonjha8319]

sir 2 hw question is 197

[@vardhandoodam6875]

Sir is 6 sir because last digit means remainder when divided by 10

[@superabgamer8855]

Answer of homework no.2 is 197.

[@yashparekh1614]

Mereko to ye samaj nhi aaya ki hamne (2-√3) ^ n ko fractional hi kyun le liya??????

[@abhishekrai682]

kyun ki root 3 ki value 1.732 hoti hai or 2-root3 is equal to o.27 isma integral part nahi hai isliya 2-root 3 ko fractional liya hai..

[@nivedithaniveditha4511]

Same doubt thank u for reply

[@rajatsingh5724]

u r great sir thank u for teaching us

[@rajat5649]

Homework answers are 6 and 197 respectively

[@Veebh-j9k]

Sir pata kaise chalta hai.. when to subtract and when to add jab hum integer and fractional part ka ques kar rhen hain..?

[@utkarshmishra9871]

It comes with experience ✍️✍️and practice ✍️✍️

[@KaushalSoni2205]

For remainder use Euler theorm

[@anokha593]

12/12/2021 start lecture... 14:33 time

[@mrpeace1]

Sir,,Why any no. Of power 0 is 1 ??why??

[@ut6582]

@vedant tiwari ikr, why does 2+2=4?? WHY??! Why does 2+2=4? When u get the answer tell me

[@arjunans5139]

Good question man

[@ut6582]

@Arjun ANS to whom r u talking to.

[@peacemaker2951]

@@ut6582 cuz we add 2 on 2 , now u tell me why any no. With power 0 is 1??

[@ut6582]

@Moiz Ul Munir ok take 1= x/x, right? U with me

[@RohitKumar-fo6rp]

Sir you are really great I think

[@yashsrivastava8255]

Answer of homework question 2 nd is 197

[@rishu.sharma31]

Like it for revision

[@shivamchaudhary8657]

HW (A)4

[@rajubotu2049]

Class starts at 6:39 Don't like it Save Urr time😊😊😊😊

[@SANTOSHKUMAR-kt1vc]

6is the and of first question

[@ashokburdak3978]

2nd Home work questions ka answer 197or option 2 hoga

[@sarathkumar1528]

1. hw 6

[@peacemaker2951]

Sir is intro 2x Mai Kyu chalta h?? 🤔🤔

[@somitmishra4705]

Advance question answer 1

[@yogesh_1607]

You're an absolute legend Sir:)

[@hirackmaji3958]

Sir r ka value n ke bara bar q kai

[@irshadirshad6795]

super class sir

[@sachinjadhav-hj2do]

1st Hw Ka answer -4

[@prasoonjha8319]

sir 1 st hw is 6

[@aryankundu4954]

1:4:20

[@vishnukumarpaswan9053]

superb lecture sir

[@nagendrakushwaha5495]

Sir how to solve (1+2x+xx)^n

[@havish6483]

HW ANS-B

[@pawanshah6280]

Second HW ,ans:197

[@maheshsingh3713]

6 ans 197. Thanks sir

[@NaveenJangala-xf7eb]

Thank u sir

[@sujeetyadav6558]

Thanks sir

[@anaydivayam8862]

Sir 58:03 samjh nahi aaya

[@NavinKumar-cn1qs]

First question ans B 6

[@IT_A__AnshumanSingh]

Sir video is not downloading please resolve it

[@himangshuhaloi20]

Sir video chal nehi raha error dikha raha he

[@rajnishsrivastava5931]

sir lecture 5 private q show kr rha h ?

[@chinmaypatade7224]

one good thing about sir is he is not much into live chats unlike Namo and Paras sir 😂

[@aryankundu4954]

7:21

[@princemaurya9853]

Sir integral part of root 2 + 1 power 6 is 197

[@SahilKumar-ug8fh]

Great... I have also cracked both the questions 👍