The mean is zero that means kuch positive no. And kuch negative no rahe honge kyunki f(x) odd degree ka polynomial hai and it is symmetric abt origin (0,0) and odd Fn so that right mein jitne term ayenge uka negative left mein ajayega so f () mein har ek symmetric input pe at last output Zero ayega then g(0) =0 & f(0)=0
I thought of n=1, AP - 0 Bas ek term😁 Agar unka question ek term ki ap k liye valid nahi hua to vo meri galti nahi vaise bhi Just go for the easiest way
Sir if a1 a2 .... an are in ap and fx is odd then it is given that mean is also 0 so a1+a2...an/n=0 This also means a1+an/2=0 Hence a1=-an Similarily a2=-a(n-2) so alternate terms from beginning and last will be negative of each other Hence the given sum will be 0 f(g(0))= 0 Pranam gurudev
Mohit sir, you are goat ❤ Sir, i did this question about 15 mins ago, and i was scrolling yt and got your video 😂 So happy i approached this question with same method (im not so good at math,the idea just stricked me)
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sir but I think we don't even need to assume any AP because it is directly written mean is zero and the inner 2 terms written in that last expression are the mean itself it is only made to look complicated to scare weak souls
sir we can also take values like -2,-1,0,1,2, and so on this is also an AP with an positive common difference son in that case also if we add the terms there are of power 5 which gets cancel subsequently , and of 3 degree also negative sign comes out and the terms get subtracted ...so we can also do like this .....actually sir mere mind me kabhi exam me ata hi nhi ye ki 0,0,0,0, leke krlo ,, maybe ye -2,-1,0 wala phir bhi ajata soo thats my way to solve it ... thank you
One more logic by integration, Ifg(f(x))=x then f(g(x)) will also equal to x Jo find Krna h wo sirf summation Bala part h As terms are in A.P then we can concert the summation into integration using reimann sums Integ(f(x)dx) and limits will be from first term of ap to last one As First and last term are of opposite sign and equal magnitude then limits (a se -a ). If we find integral then it will become zero.
Sir , if we actually go by the real method it also comes out to be zero here is how I thought. In the the question we are getting f(g( *summation part*)) which basically gives me output as *summation part* so the question is to solve the summation only as we have removed all the composition of functions. Now the summation part can be treated as : here I am assuming "a" as alpha , "b" as beta and "c" as gamma. We have to find ( a( a1^5 + a2^5+a3^5+_____+an^5) + b(a1^3+a2^3+a3^3____+an^3)+c(a1+a2+a3+_______+an) )/n . As mean is given to be zero hence the coefficient of "c" comes out to be zero and the coefficient of "a" and "b" also comes out to be zero this is because any odd power summation can be written as the sum of its coefficient whose power is one times the decreasing values for example a^3+b^3=(a+b)(a^2+b^2-ab) or a^5+b^5 = (a+b)(something). Hence it will come out as zero.
sir aapne aapke sequence series ke video mein bata ya tha ki (a1+an)/2 = (a2+an-1)/2 = ... = (a1+a2+a3+...+an)/n toh idhar hume zero diya hai arithmetic mean of all toh usse hum bol sakte hai ki a1 = -an a2 = -an-1 and soo on and since idhar wknow ki jo function hume diya hai woh odd hai toh agar summation(f(ai)) lenge toh woh zero hi aayega, hence answer is zero.
#askcompetishun Sir please reply me , Maine mock test diya hai competishun digital app se but na to test solution mila aur na hi video solution nhi aaa rha . Kya kru ?
Respected Sir, I am a student preparing for JEE 2025. I Joined a coaching which was not so good in teaching/questions and tests. In beginning of Nov 2024, I discovered your channel and am studying for IITJEE Adv 2025. I have reached till 50% syllabus in phy, chem, maths . (In phy and math, i was not able to cover the Class 11 syllabus due to time constraints). I am giving CTS tests (UTS 1) and get about 100-125 marks out of 300. I plan to complete the syllabus of JEE Adv Level around 10 march 2025. (expect P&C, Probablity and some of class 11 mechanics like RBD, COM etc)(However, I will complete the basics of those chapters). Is it possible for me to crack IIT Adv 2025 sir? Kindly Respond
Everything is temporary but JERO is permanent, Love you sir
sir mocks mein itni silly mistakes kr chuka hu ke ese cheeze sochne pe lgta hai koi mathematical law break kr rha hunga shyd 😅
Lol true bhai
Ha bhai isi lie trick ek dam nahi lagate bas process pakad ke hi chalte h
🤣🤣
Same with me bhai but for chemistry.. accuracy to jhund hai bhyi 😭🙂🙏
wow . please continue this series
The mean is zero that means kuch positive no. And kuch negative no rahe honge kyunki f(x) odd degree ka polynomial hai and it is symmetric abt origin (0,0) and odd Fn so that right mein jitne term ayenge uka negative left mein ajayega so f () mein har ek symmetric input pe at last output Zero ayega then g(0) =0 & f(0)=0
Bhai zaruri nhi hai 1+2+29-32=0
@@TEN-r3r f to symmetric hai na
Nhi to galat hun to clarify karna
@@TEN-r3r Ye AP nahi hai
@@TEN-r3r not an ap
Yes
I think
About the AP like including -ve numbers,0 and +ve numbers and given function is odd
Answer should be zero
Yep
I thought of n=1, AP - 0
Bas ek term😁
Agar unka question ek term ki ap k liye valid nahi hua to vo meri galti nahi vaise bhi
Just go for the easiest way
Exactly!! had the same thought this side
What a smart move to save calculations
East or west MT Sir is the best
You are great sir
Sir if a1 a2 .... an are in ap and fx is odd then it is given that mean is also 0 so
a1+a2...an/n=0
This also means a1+an/2=0
Hence a1=-an
Similarily a2=-a(n-2) so alternate terms from beginning and last will be negative of each other
Hence the given sum will be 0
f(g(0))= 0
Pranam gurudev
My also same logic
sir maine -1,0,1 liya tha ya aise bhi observe kar sakte odd fn hai toh saare terms cancel hojayenge, hence summation zero.
Mohit sir, you are goat ❤
Sir, i did this question about 15 mins ago, and i was scrolling yt and got your video 😂
So happy i approached this question with same method (im not so good at math,the idea just stricked me)
Very nice
Here if we see a1 + an = 0 and a2+a(n-1) =0 and so on
So a1³ = - an³ so they cancel
Similarly for power 5
And we get zero then qlso
please make more videos like this before Jan JEE Main 2025
#askCompetishun Sir please tell will there be any online crash course targeting only Jee Advance 2025?
We have a CATS batch specifically designed for JEE Advanced 2025. You can purchase it from this link: fcldn.courses.store/598409?. For more information, feel free to contact us hassle-free at +91 74109 00906.
Thank You Sir
Sirji, gif related all questions solve kara dijiye
2:50 sir 0 toa lai liya!...lekin kyaa common difference zero he raha toa AP consider hoga????
Yeah sequence is considered Ap even if common diff is 0
if mean of ap is zero that means half of them are positive and half of them are negative so sigma f(ai) is always zero
sir but I think we don't even need to assume any AP because it is directly written mean is zero and the inner 2 terms written in that last expression are the mean itself it is only made to look complicated to scare weak souls
sir we can also take values like -2,-1,0,1,2, and so on this is also an AP with an positive common difference son in that case also if we add the terms there are of power 5 which gets cancel subsequently , and of 3 degree also negative sign comes out and the terms get subtracted ...so we can also do like this .....actually sir mere mind me kabhi exam me ata hi nhi ye ki 0,0,0,0, leke krlo ,, maybe ye -2,-1,0 wala phir bhi ajata soo thats my way to solve it ... thank you
One more logic by integration,
Ifg(f(x))=x then f(g(x)) will also equal to x
Jo find Krna h wo sirf summation Bala part h
As terms are in A.P then we can concert the summation into integration using reimann sums
Integ(f(x)dx) and limits will be from first term of ap to last one
As First and last term are of opposite sign and equal magnitude then limits (a se -a ). If we find integral then it will become zero.
Sir can't we find the full videos of all questions in a single test in UTS
kindly contact +91 74108 33330 they will guide you
@MohitTyagi thank you sir
Sir , if we actually go by the real method it also comes out to be zero here is how I thought. In the the question we are getting f(g( *summation part*)) which basically gives me output as *summation part* so the question is to solve the summation only as we have removed all the composition of functions. Now the summation part can be treated as : here I am assuming "a" as alpha , "b" as beta and "c" as gamma. We have to find
( a( a1^5 + a2^5+a3^5+_____+an^5) + b(a1^3+a2^3+a3^3____+an^3)+c(a1+a2+a3+_______+an) )/n . As mean is given to be zero hence the coefficient of "c" comes out to be zero and the coefficient of "a" and "b" also comes out to be zero this is because any odd power summation can be written as the sum of its coefficient whose power is one times the decreasing values for example a^3+b^3=(a+b)(a^2+b^2-ab) or a^5+b^5 = (a+b)(something). Hence it will come out as zero.
sir aapne aapke sequence series ke video mein bata ya tha ki
(a1+an)/2 = (a2+an-1)/2 = ... = (a1+a2+a3+...+an)/n
toh idhar hume zero diya hai arithmetic mean of all toh usse hum bol sakte hai ki
a1 = -an
a2 = -an-1 and soo on
and since idhar wknow ki jo function hume diya hai woh odd hai toh agar summation(f(ai)) lenge toh woh zero hi aayega, hence answer is zero.
Yo
😲 wow
Sir mujhe online batch nhi mil paaya meri badnaseebi 😢
But yt channel se padh ke mein jarrur JEE adv crack karunga 😊😊
Koi tipes nhi h means hi likha hua h f(g()) ke andar aur vo zero diya hua h and f and g inverse diya hua h
Jabardast
Maine alpha beta gamma teeno ko 0 maan liya.. ik question maj positive diya h.. bass le liya aur aa gya ans😝
wowww
#askcompetishun
Sir please reply me ,
Maine mock test diya hai competishun digital app se but na to test solution mila aur na hi video solution nhi aaa rha . Kya kru ?
Kindly contact our support team +91 74109 00908
they will guide you
0 hai answer
Respected Sir,
I am a student preparing for JEE 2025. I Joined a coaching which was not so good in teaching/questions and tests. In beginning of Nov 2024, I discovered your channel and am studying for IITJEE Adv 2025. I have reached till 50% syllabus in phy, chem, maths . (In phy and math, i was not able to cover the Class 11 syllabus due to time constraints). I am giving CTS tests (UTS 1) and get about 100-125 marks out of 300. I plan to complete the syllabus of JEE Adv Level around 10 march 2025. (expect P&C, Probablity and some of class 11 mechanics like RBD, COM etc)(However, I will complete the basics of those chapters).
Is it possible for me to crack IIT Adv 2025 sir? Kindly Respond
In maths, i get around 50 to 60/100. Chem - 40 to 50/100. Physics - 20-50/100
Brother if you have your own plan why are you asking sir about confirming it. See brother just study,you will do it