𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒 0:49 Nature of Chapter 2:13 Weightage of Chapter 2:37 *Topics* 2:48 *Critical Topics 📣* 5:18 *Notation: ⁿCᵣ* 7:45 *Properties of ⁿCᵣ* 8:03 1️⃣ 9:09 2️⃣ 10:38 3️⃣ 12:52 Values of ⁿC₀ & ⁿC₁ 15:25 4️⃣ 24:27 *Binomial Theorem for Positive Integral Index* 26:08 ① Total Number of Terms in Expansion 26:25 ② Sum of powers of x & y 26:36 ③ Equidistant Terms are equal 31:01 (x + y)ⁿ + (x - y)ⁿ 36:15 *General Term of Binomial expansion* 41:03 _Identifying coefficient of xʳ_ 43:31 _Term independent of x_ 48:33 _Counting Rational or Irrational Terms_ 54:32 Note 55:54 _Term from the End_ 58:04 Note (kᵗʰ term from end = ?ᵗʰ from beginning) 1:01:11 *Middle Term* 1:04:33 *Important Expansion: (1±x)ⁿ* 1:06:32 _Product of two expansions_ 1:22:00 _No. of terms in different powers of x_ 1:30:16 *Meaning of Expansion or Identity* 1:31:43 _Using Substitution to find Sum of Coefficients_ 1:38:31 *Application of Binomial Theorem* 1:40:28 Observe This!! 1:42:40 *Divisibility Problems* 1:51:47 NOTE: (x-1) is a factor of xⁿ-1 (x+1) is a factor of xⁿ+1; n∈odd 1:53:24 *Reminder Problems* 1:53:42 _Standard Question_ 1:57:40 _When remainder comes -ve_ 1:58:42 _Remainder of Expression in Addition_ 2:00:14 _When you can't find any powers of divedend that's at the gap of 1 with the multiples of divisor_ 2:04:13 _Finding last digits_ _(In case of Large Divisor)_ 2:08:37 _You can also make the number (whose remainder is required) closer to the multiple of divisor_ 2:12:49 _Method of Cyclicity_ 2:15:28 _Remainder of Dividend with Larger Base_ 2:19:32 *Greatest Binomial Coefficient* 2:20:53 *Greatest Term in the Expansion (a+bx)ⁿ* 2:23:34 *Steps* 2:26:16 Numerically Greatest Term 2:28:34 _Explanation & a Good Question_ 2:36:32 *R-f Factor Theorem* 2:39:34 Steps 2:46:18 _Why f+G=1 when added_ 2:52:47 *Binomial Theorem for any Index* 2:53:24 Expansion for (1+x)ⁿ only and |x| < 1 2:54:56 Some Special Cases 2:58:02 _If not in the form (1±x)ⁿ_ 2:59:59 *Multinomial Theorem* 3:02:52 Expansion 3:03:26 Number of Terms in the Expansion 3:05:15 _Finding Coefficient of xʳ_ 3:06:10 General Term 3:14:16 *Binomial Coefficient Problems* 3:15:18 Basic Series 3:16:29 *Categories:-* 3:18:31 Category ➊ 3:18:46 ⓐ n & r both changes 3:22:44 ⓑ Only n changes 3:25:08 ⓒ Only r changes 3:25:23 Note 3:26:38 _Half Series_ 3:31:14 _Good Question_ 3:36:39 Category ➋ (Result Based) 3:38:50 _Proof of the Result_ 3:40:29 Special Cases 3:49:30 _Ques (Sum of Product of two Coefficients)_ 3:52:39 _Complicated Expression_ 3:55:48 *_Product of Binomial Coefficient but with alternating signs_*
@@DreamIITM21 There's a subject called BJP, What's taught in it, How Godse killed Gandhi ? And how Godse was an atheist yet believed in cast supremacy? 😃
1:26:00 - 1:29:30 1:35:30 put x=-1 for alt + - and add coeffs sum with coeffs alt + - for sum of even coeffs even in multinomial 1:52:00 remainder qs 2:00:00 2:04:00 to 2:19:10 2:35:00 very very good question 2:38:00 R f factor theorem 3:26:00 Some qs 3:33:44 Repeat question again 3:36:00 results 3:43:30 question 3:45:00 see from here imp
@@annieone_1 are bhai general term me r=0 daal..it will become 10c0*2^5 * 3^0=32......ab r=10 daal it will become 10c10 *2^0 * 3^10/5=3^2=9 .......32+9=41
1:06:00 This is why we sometimes define nCr as the coefficient of x to the power of r in the expansion of (1+x) to the power n. Another method in 1:50:45 can be writing it as 9^(n+1) -8n-8-1= (8+1)^(n+1)-8(n+1)-1 which is divisble by 8² i.e. 64 2:07:30 We can also pull out 10² common from 200C1×10 since it is multiple of 100 so we can directly say that remainder is 1.
TIMESTAMPS 0:00 Introduction and Nature of Chapter 2:39 Index and Critical Topics 5:18 Notation nCr 24:14 Binomial Theorem for positive integral index 36:15 General term of Binomial Expansion 1:04:33 Two particular Cases : (1 + x)^n and (1 - x)^n 1:30:16 Meaning of expansion or Identity 1:38:30 Application of Binomial Theorem (Remainder and divisibility) 2:19:21 Greatest Term in the expansion of (a + bx)^n 2:36:32 R-f Factor theorem 2:52:47 Binomial theorem for any index 2:59:59 Multinomial Theorem 3:14:16 Binomial Coefficient Problems
Sir the technique which you told in the last question of even and odd constants is not applicable for all questions. I tried other question with same concept but the sum of constant was 49 odd number and so the answer should be zero but the answer is (100) 51
sir at 3:38:05 you wrote sigma(r^3 nCr) = n*2^n-1 + n(n-1)2^n-2 + n(n-1)(n-2)*2^n-3 but the middle term comes out to be 3C2*n*(n-1)*2^n-2 (Proved using PnC logics) i might be wrong so could you please confirm the right expression for it
I asked them in plus class they said that theyre not planning to bring a phy faculty on Nexus channel cause unhe koi mil nhi rha tha can dedicate their time
Kisiko compitition ka matlab mohit tiyagi sir ka fast lane 2025 chahiye to dm me. Only 350..original price 29000 Each subject just 110 lectures 120 days left for jee mains
Sir aaj Mera jee ka exam tha school me aur trigonometry puchane wala tha is liye Maine aapki video pair bhi maths me question dekhke sirf 8 hi attempt kiye😢
𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒
0:49 Nature of Chapter
2:13 Weightage of Chapter
2:37 *Topics*
2:48 *Critical Topics 📣*
5:18 *Notation: ⁿCᵣ*
7:45 *Properties of ⁿCᵣ*
8:03 1️⃣
9:09 2️⃣
10:38 3️⃣
12:52 Values of ⁿC₀ & ⁿC₁
15:25 4️⃣
24:27 *Binomial Theorem for Positive Integral Index*
26:08 ① Total Number of Terms in Expansion
26:25 ② Sum of powers of x & y
26:36 ③ Equidistant Terms are equal
31:01 (x + y)ⁿ + (x - y)ⁿ
36:15 *General Term of Binomial expansion*
41:03 _Identifying coefficient of xʳ_
43:31 _Term independent of x_
48:33 _Counting Rational or Irrational Terms_
54:32 Note
55:54 _Term from the End_
58:04 Note (kᵗʰ term from end = ?ᵗʰ from beginning)
1:01:11 *Middle Term*
1:04:33 *Important Expansion: (1±x)ⁿ*
1:06:32 _Product of two expansions_
1:22:00 _No. of terms in different powers of x_
1:30:16 *Meaning of Expansion or Identity*
1:31:43 _Using Substitution to find Sum of Coefficients_
1:38:31 *Application of Binomial Theorem*
1:40:28 Observe This!!
1:42:40 *Divisibility Problems*
1:51:47 NOTE: (x-1) is a factor of xⁿ-1
(x+1) is a factor of xⁿ+1; n∈odd
1:53:24 *Reminder Problems*
1:53:42 _Standard Question_
1:57:40 _When remainder comes -ve_
1:58:42 _Remainder of Expression in Addition_
2:00:14 _When you can't find any powers of divedend that's at the gap of 1 with the multiples of divisor_
2:04:13 _Finding last digits_
_(In case of Large Divisor)_
2:08:37 _You can also make the number (whose remainder is required) closer to the multiple of divisor_
2:12:49 _Method of Cyclicity_
2:15:28 _Remainder of Dividend with Larger Base_
2:19:32 *Greatest Binomial Coefficient*
2:20:53 *Greatest Term in the Expansion (a+bx)ⁿ*
2:23:34 *Steps*
2:26:16 Numerically Greatest Term
2:28:34 _Explanation & a Good Question_
2:36:32 *R-f Factor Theorem*
2:39:34 Steps
2:46:18 _Why f+G=1 when added_
2:52:47 *Binomial Theorem for any Index*
2:53:24 Expansion for (1+x)ⁿ only and |x| < 1
2:54:56 Some Special Cases
2:58:02 _If not in the form (1±x)ⁿ_
2:59:59 *Multinomial Theorem*
3:02:52 Expansion
3:03:26 Number of Terms in the Expansion
3:05:15 _Finding Coefficient of xʳ_
3:06:10 General Term
3:14:16 *Binomial Coefficient Problems*
3:15:18 Basic Series
3:16:29 *Categories:-*
3:18:31 Category ➊
3:18:46 ⓐ n & r both changes
3:22:44 ⓑ Only n changes
3:25:08 ⓒ Only r changes
3:25:23 Note
3:26:38 _Half Series_
3:31:14 _Good Question_
3:36:39 Category ➋ (Result Based)
3:38:50 _Proof of the Result_
3:40:29 Special Cases
3:49:30 _Ques (Sum of Product of two Coefficients)_
3:52:39 _Complicated Expression_
3:55:48 *_Product of Binomial Coefficient but with alternating signs_*
Thank you.
Thank you so much
@@kshitijarora2307 chal haat
Thanks
Which ai?
Sir truly u r the best maths teacher of INDIA
no
Lgta hai aap ko VK Bansal sir ka naam nhi pta .. by the way Arvind Kalia sir is also Love ❤️🫂
NO HE MUST BE A TEACHER OF BJP
@@DreamIITM21 There's a subject called BJP, What's taught in it, How Godse killed Gandhi ? And how Godse was an atheist yet believed in cast supremacy? 😃
Shut up bro he is not a good teacher.... A good teacher will never teach their students with short cut method....
1:26:00 - 1:29:30
1:35:30 put x=-1 for alt + - and add coeffs sum with coeffs alt + - for sum of even coeffs even in multinomial
1:52:00 remainder qs
2:00:00
2:04:00 to 2:19:10
2:35:00 very very good question
2:38:00 R f factor theorem
3:26:00 Some qs
3:33:44 Repeat question again
3:36:00 results
3:43:30 question
3:45:00 see from here imp
bhai yaar aapne to pure lobrary hi bana di |
thanks
Bro do u have pdf of this session if u have pls give your telegram id so that I can reach you 🙏🙏
55:41
done and dusted
41
solution:-
values of k will be 0 and 10
at k=0,
T1 = 10C0 . 2^0 . 3^2 =9
at k=10,
T11=10C10 . 2^5 . 3^0 = 32
32 + 9 = 41
Bro do u have pdf of this session if u have pls give your telegram id so that I can reach you 🙏🙏
@@opferrogaming887 i dont have
55:50 Homework Answer- 41 Done and Dusted ✅
Thank you Arvind sir we are blessed to have you as a teacher 💝
mera 10 aarha. pls explain
Put value of r= 0,10 in general term then add it @@anweet
@@assketchup0_0 answer is still 10? explain please
@@annieone_1 are bhai general term me r=0 daal..it will become 10c0*2^5 * 3^0=32......ab r=10 daal it will become 10c10 *2^0 * 3^10/5=3^2=9 .......32+9=41
Mene to dekhte hi kar diya pen bhi nhi uthaya
40:00 Review
43:00 repeat
48:00 repeat
57:00 repeat
1:13:00 repeat
1:27:00 repeat
1:33:00 imp point
1:46:25 repeat
2:03:00 repeat
2:13:00 repeat
2:40:00 repeat
Revise rf theorm
3:28:00 repeat
3:45:00 repeat
Happy teacher's day bhaiii
I hope your health gets better ASAP
Thankyou for this amazing lecture
Will complete with repetition questions by tomorrow
What do u mean with repetition
Done
BROO 💀 found someone first time on yt in other video comments 😭
i mean adityansh ke comments me dekha tha tujhe lmao😭
@@justheyungunhavinquickfuseyoooo
@@justheyungunhavinquickfuse who is Adityansh
2:36:34 Rf factor problem
2:59:59 Multinomial Theorem
1:06:00
This is why we sometimes define nCr as the coefficient of x to the power of r in the expansion of (1+x) to the power n.
Another method in 1:50:45 can be writing it as 9^(n+1) -8n-8-1= (8+1)^(n+1)-8(n+1)-1 which is divisble by 8² i.e. 64
2:07:30
We can also pull out 10² common from 200C1×10 since it is multiple of 100 so we can directly say that remainder is 1.
Sir notes is not available on channel plz give
Did you get the pdf if you got please tell me where to find
Sir. Your the best teacher on TH-cam
48:27 coefficient of x power 25 is asked so answer should be option B) ⁵⁰C 25
-1 is also there buddy
Happy Teacher's Day ❤❤ Bhai ❤
Aaj bhai ka din hai 🎉
Happy teachers day
TIMESTAMPS
0:00 Introduction and Nature of Chapter
2:39 Index and Critical Topics
5:18 Notation nCr
24:14 Binomial Theorem for positive integral index
36:15 General term of Binomial Expansion
1:04:33 Two particular Cases : (1 + x)^n and (1 - x)^n
1:30:16 Meaning of expansion or Identity
1:38:30 Application of Binomial Theorem (Remainder and divisibility)
2:19:21 Greatest Term in the expansion of (a + bx)^n
2:36:32 R-f Factor theorem
2:52:47 Binomial theorem for any index
2:59:59 Multinomial Theorem
3:14:16 Binomial Coefficient Problems
In 3:53:48,
We can write nCr as n÷r(n-1C r-1) but sir wrote wrong
Best Underrated Teacher! 🎶🎶
he's not underrated dude
He is best
u are overrated schlawg
Sir the technique which you told in the last question of even and odd constants is not applicable for all questions. I tried other question with same concept but the sum of constant was 49 odd number and so the answer should be zero but the answer is
(100)
51
37:51 44:00 48:37 49:12 : Wo term batao jismein given khoobi ho.
• Write general term.
• Apply khoobi.
• Find k
1:36:29 1:37:06 1:38:16
1:47:56 1:48:14
Sir you clear all my concepts of binomial in these 4 hours of time
55:43 = r value will be 0 and 10.
r=0 then sum will 32
r=10 then sum will be 9
Total sum ( answer) =41.
Thanks me later😊.
2:07:16 error there... the remainder shall come as 1 only as 2000 is divisible by 100
watching this lecture sitting in hostel of IIT Delhi gives me goosebumps of my jee journey
bhai kitni rank thi
me abhi class 9 me prep kar raha hoo
Jut bol rha hai.
11 days ago he said "i will crack jee for you"@meGotabeat
@@AKASHJEEASPIRANT26 thik hai thank u
sir at 3:38:05
you wrote sigma(r^3 nCr) = n*2^n-1 + n(n-1)2^n-2 + n(n-1)(n-2)*2^n-3
but the middle term comes out to be 3C2*n*(n-1)*2^n-2 (Proved using PnC logics)
i might be wrong so could you please confirm the right expression for it
@@akshatagrawal333 search it on Google
Answer : n^2 . (n+3) . 2^(n-3)
Sigma toh mai huunn😂😂😂😂😂😂😂😂😂😂😂😂😂😂🎉🎉😂😂😂😂😅😅😅😊😂😂😂
Happy Teacher's Day sir❤
3:54:27 error 19c10 ×10
20:41 questions
26:17 nck
35:37 questions
3:09:25 question
3:29:31 questions
Sir,
3:45:30 answer I'm getting is 99, but answer given is 98. How is that possible?
57:30 good method
Sir you are the best ......😊😊😊
3:53:38 wrong 10cr ko 10/r * ( 10-1 c r-1 ) likhenge = 10/r * (9 c r-1 )
Sir ji ne 9c r likh diya by mistake
Haa bhai hota hai ek ek bhar ......
But good 👍😊
23:10
29:55
1:37:15
1:38:18
2:00:30
2:04:18
2:13:15
2:22:45
The coefficient of x² in the expansion of the product (2-x²)[(1+2x+3x²)⁶+(1-4x²)⁶] is
please solve it by sir's method
12
Best teacher ever seen in life 🎉
55:42 Answer is B 41
Not for students doing first time
I myself did first time and able to solve all pyqs comfortably .. dont gemeralise your low iq and impose it to everyone
😮 nah id win
Me too
Physics faculty??
Hehe😂
Pata nahi Bhai me bhi kabse wait kar rha hu
Nkc sir ka wait jo raha h, ki Kab woh unacademy rejoin karenge 😂😂
I asked them in plus class they said that theyre not planning to bring a phy faculty on Nexus channel cause unhe koi mil nhi rha tha can dedicate their time
Milgya finally @@atharva._.raichu
Happy Teachers Day Bhai ♥️♥️🥰
5:18 lecture starts
35 : 31 vale que me x>1 disabled tha aur option me 1 se bada toh 2 he tha, solve karne ki jarurat hee nhi thi 😅
Beauty of this session is smartly inclusion of questions (plenty in numbers) along with concept
Can I prefer these video for class 11 school exams. ..... Bs ye nhi samajh aa rha ki topic kon kon new sa padaya ja rha h andaar se 😅
Please increase the hour of live session....
There is nothing with increasing the timing he is explaining crisply so we can grab it easily so there is no need of repetitions that's why it's short
@Tripzy-ey7cw
Increase the hour mean add more number of questions
You can check the description for practice problem there you can find more variety of questions and solution by him
@@ALIMOHAMMAD-u3wAnd although it's not a paid one so there will be some........ I think you got it bro
Happy Birthday sir 🎉❤
Sir iske notes ki pdf open ni hori.......ab kya karee, pls help.....maine ye pura session dekha ha notes ni bnaee.....ab kaha se revision kru
Maza aa gaya bhai❤
Amazing lecture sir 😊
Kisiko compitition ka matlab mohit tiyagi sir ka fast lane 2025 chahiye to dm me. Only 350..original price 29000
Each subject just 110 lectures
120 days left for jee mains
@@We_Are_Collegians how to get the course?
Best teacher in yt love you sir 💓,
Lec 1: 38:00
the way BHAI teaches 😍
Such a beautifully crafted session. Such things are rare❤
Can I prefer these video for class 11 school exams. ..... Bs ye nhi samajh aa rha ki topic kon kon new sa padaya ja rha h andaar se 😅
@@END_STUDY_Z this is more than school level
@@atharv_008 but kya saare chapters cover honge ?
@@END_STUDY_Z I think so
Bhai ye lecture enough hai kya jee ke liye
3:36:26 Repeat
55:36 done and dusted
Thank u arvind bhai app bohot achaa padhate ho
2:50:20
R + f
Is 0! = 1?
Yes
55:10 sir observation didn't understand... Why the will be no fraction if they ask for rational terms.. if they are positive and fractional?
Where are the notes of this lecture
i even did not get
Telegram
Or something sir deleted the pdf during class
Mile kya
Happy teachers day bhai❤❤❤❤
amazing lecture!
Thank you bahi❤ revesion plus solving will be done in next 48 hours promise 🔥
Happy Teacher's day sir❤❤❤
MOST UNDERRATED VIDEO
goat teacher of maths🐐
Bro do u have pdf of this session if u have pls give your telegram id so that I can reach you 🙏🙏
@@opferrogaming887 @anonymouslycrazy
@@opferrogaming887 msg @anonymouslycrazy
Binomial me jab one and only bole that means integer aur fraction barabar ho
14:45 R=3
Sir please upload straight line
54:51 why not fractional!!?
Happy teachers day Sir!!
Thankyou sir love you sir🔥❤️
Is this enough if i have no idea about this chapter?
tysm for this video!
3:03:38 PAR KIS METHOD KI BAAT HO RAHI HAI
Happy teacher day sir 💐
Sir please do coordinate geometry😊
Sir 1:25:03 pe jo dusra method tha usme zyada mushkil tha nikalna but aa gaya..clubbing 1 + ( x + 1/x) was easier
Sir aaj Mera jee ka exam tha school me aur trigonometry puchane wala tha is liye Maine aapki video pair bhi maths me question dekhke sirf 8 hi attempt kiye😢
Kahna kya chahte ho...
Jee ke mock test school mein nhi coaching mein hote hai school mein sirf bakchodi hoti hai
Kya school me jee ka exam vo bhi sep oct me kya bol rha hai bhai😅
@samyakbhansali1869 BHAI SCHOOL ME JEE FORMAT PAR EXAM LAGTE HAI MERE BHI
Amazing lecture❤
1:14:35 matched ❤ (without bhai's help😅)
Best mathematix teachr reward goes to arvind sirr🌸 U always build our concepts..completely suree everyone here will crack jee with amazing ranks...🎉
Happy teacher's day sir
1:36:00 revisit.
33:26 🤣
Sir I love you u r the best math teacher😊
1:15:16 someone please explain why qC2 will become q(q-1)/2
Because nCn can be written as n/r n-1Cr-1
@@Tacenda-s2c Thank you so much
1:14:31 sir Galti ho gayi x² mai thik kar rha hu abhi ke abhi
3:18:36 sir aapne n and r aur only n likha hai lekin pdf pe n and r aur only r hai
Sir plz give a one shot on probability class 12
Love you sir ❤❤❤❤
Much better than nv sir
Sir please upload videos of more chapters
Notes ?
55:51
1:14:27 sahi hogya
Happy teachers day bhai🎉🎉🎉
Enough for jee mains?
Kon h ye log,kha se aate hain 🤡
@@rohitgaur10 kya h9gya bhau
@@PraveenKumar-rv3zu bhai thumbnail par saaf saaf likha h for mains $ advanced,🤡
Bhai aise to kuch enough nahi hai mains aur adv. ke liye but agar is video ke baad question practice karega to bahut fayeda hoga 😊.
2:07:29 nhi smjhe sir
3:19:46 Sir hmare liye aap apne teachers day ke celebrations sacrifice krdi ❤🥺
many many thanks mere bhai!
Dusre question mein woh ncr method se r ki value nikali r maximum ne ke barabar hosakta iskeliye r= n-1 bola and 0 bola
1:49:30 sir galti ho gayi but thik kar di
won't repeat it again
Happy teachers day 😁🎉🎉🎉🎉🎉🎉🎉 0:21