Toughest Problem Of Matrix in JEE Advance Paper | IIT JEE 2010 Matrix Question
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- Опубліковано 15 бер 2023
- This is one of the toughest matrix questions asked in JEE Advanced.
In this video, we have covered an amazing paragraph/comprehension-type matrix question from the IIT JEE 2010 question paper.
This matrix question has three parts and will surely test your command of the properties of the matrix as well as mathematics.
This question is a good revision of JEE Advanced level matrix question & will surely help you learn good concepts of the matrix.
So if you feel that you have good practice of the matrix chapter of Mathematics, do attempt this question.
If you are stuck on the solution to the question, Aman sir is your savior.
Let's see the simplistic solution by Aman sir to this amazing question from JEE Advanced 2010 maths paper.
Check out the complete video for solutions to all the parts of this question.
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I solved this question in my first attempt by taking p=3……Now after been graduated from iit this video brought backs memories of my preparation days.
Which IIT bhaiya?
He is joking
@@Prism069 IIT Kanpur 2018 batch....I am an upsc aspirant and sometimes I do binge watch these videoes just for refreshment. I don't understand what's so unreal about it. everything is special till you have it , once you have it its charm fades out.
@@a.ksharma3614 adv. ki rank and branch bhi bta sakte ho bhaiya
People in the comment section cant just take the fact that someone can be better than them and so they find someway to demean others
was only able to solve the first part, but the second part was incredibly interesting. exam me bhot muskhil hota
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ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Love you sir ji.. according to my knowledge of coaching... today's teachers teach for just money but your teaching method gives us interest in math... teachers like you, are the best as students could tune well with your simple explanations
Yes sir, aur aise vids chahiya
Thank you 👍🏻
You are a legend .
Even when I am not preparing for jee.. I still love these type of videos sir.. pls continue them
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Toh kabhi kabhar padh bhi liya kar, fir ye videos samajh mein bhi aayenge.
you play krunker?
@@vaibhavsingh8933 my name is a bit suggestive of that
@@SierraHunter2106 yeahh loll , whats your in game name
one of my friend who got 99.98 percentile in 2023 mains asked this question to our teacher and sir said you wont be able to solve it easily without using examples .....he told when the question was asked in 2010 it took him nearly 1 hr to solve it using proper matrix methods.....was really a tough problem😃😃
Konse coaching se ho??
Allen?
@@PranitMahapatra_ FIITJEE RANCHI
99.98 percentile 😅😅
@@heisenberg0069 Aap bhi Ranchi se ho bhaiya?
This question is very easy if you know a little advanced maths. Hard for JEE students though. The numbers {1,...,p-1} form an abelian group under multiplication modulo p. What this means is that every element a has a UNIQUE element a' such that a*a' = 1 (mod p )
Now for part 1, since the trace is 2a and this is not divisible by p, a is non zero. So a^2 is non zero. Now we want a^2 = bc (mod p) . So you can pick any number a,b not equal to 0 and you get a unique c given by c = (a^2 * b^-1) (mod p) So answer is (p-1)^2.
For part 2, for determinant to be zero , we need a^2 = bc (mod p) . So either a=0 forcing one of b or c to be 0 and other value can be any of the p elements (2p -1 choices) , or a is non zero and again, we can pick any non zero value for one of the two and the other one will be uniquely determined ((p-1)^2 choices). So we have 2p -1+ (p-1)^2 = p^2. Total number of matrices is p^3 so answer is p^3 - p^2.
Not only these Question brother, Almost all the difficult problems in JEE advanced level can easily be solved by those who know advanced maths! For Example, if u know real & complex Analysis well, then most of the problems in Jee level calculus can easily be solved by Those adavanced people.
😢 jo Kota mi nahi hai unhe ye advance concepts kaha milega
@@MuskanKumari-dp4ki Kota me bhi itni advanced xheize nhi padai jati. Ye group theory ki properties hai ham ise MSc Maths me padte hain
I really want a good solution for this question, finally get it
Thanks a lot sir
Yes sir I want to have more and more videos like this and how to build matrices and determinants for advanced
In case of skew symmetric matrix
b,c belongs to +ve
c=-b not possible
There only one case possible b=c=0
Yes it is one of toughest problem for sure .. I had given paper that year
Thank you sir
Please continue the the jee advanced question series
Very helpful video to generate thoughts
SIR we really are in need of such questions
We can say a²-bc/p will be divisible by p only when bc is equal to constant term of a² like for a=p-1, a²=(p-1)²=p²+1-2p thus if bc = 1 it cancels out 1 in (p-1)² and we can divide the whole term by p now
So , further we can say if a=p-2 then (p-2)² = p²+4-8p in this case bc= 4 for this to be divisible by p which can be done in 3 cases (2×2,4×1,1×4)
So generally we can say at a =(p-n) where n is non zero , bc = n² which can be done in n²-1 cases
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Here you are missing a²=bc
To find the ways you have to find the no of GP in between (1 to p-1)
Nice way of solving the problem
this method is wrong because bc can be of the form {xp+ constant term of a²(x€ whole no.)}. Suppose p=7, a=6 (p-1)
here bc can be 1,8 (4,2),15(5,3).
@@jeeadv2024 I got u yes you're right buddy
You are a legend sir
Sir we want more videos of these types.
Love the way he starts
Yes we want this type of videos
For part one to be true ....for skew symmetric and symmetric....b=±c as T+transpose(t) = either 0 or 2T so answer may be (p-1)² or 2p-1
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Definitely one of the hardest question
another method take p as 3 or 5 and substitute values
Solving this problem require some knowledge of residues and modular arithmetic. This is easy for students who are familiar with olympiad level math problems. But in a exam situation this is probably not that easy.
sir please solve more jee advanced pyq's it would be even better if you could do chapterwise so it canhelp us for our advanced prep also could you please sharefromwhere you got the research paper
We want more such question
Nice and daring explaination
Proper number theoretic proof for second sub question solution :-
Let m and n be two coprime natural numbers. Let set A={0, m, 2m, ..., (n-2)m, (n-1)m}. There are clearly 'n' elements in set A. Suppose two distinct elements of A leave the same remainder when divided by 'n'. Let these two distinct elements be (i*m) and (j*m), where 0≤i,j
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Ur talking about congruebce modulo of number theory right?
Yes
U made me luv with maths 😜😻
Sir you are mathematical genius
Done all three by self😎
Guru And Boss Of Mathematics...!!
Lots of love from Pakistan..!! Sr
Smart work ..!!
Wonderful style of teaching..!!
Terrorism band karo
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Tumhare yaha bhi JEE hota hai kya
@@Prabhu108. jihad entrance exam
why can't we hv a=3 and b=3 sir?other than a=0 and b=0 still both are symmetric and skew symmetric
a^2/p and b^2/p say p=any prime say 3,a^2/p=3^2/3=3
or are you trying to say a^2/p [p can be any prime],
so if a=b=0 we are sure shot it is divisible by p,
but if u take a=b=3 and p=5 we arent sure abt it being divisible or not..
Sir can u start a series of previous year question of jee advance it will be very helpful.....it is not on UA-cam channel
Plz please make video on your self...
I means ur study, student life, collage life, and how did u made ur maths very strong.😊
Also we all want to know how can we make our maths very sharp like you❤.
Sir, plzz don't ignore my request, plzzzz.
Please make a video on urself. I mean plzz make a video on Aman Malik.
We all want to know about your life...
Plzz also tell about your journey from school level to till now in your life❤
Sir we want more videos like this ☺️
Sir pls upload a video on history of math type videos
Yes sir aise hi questions aur layie
Love you sir ❤ bhaut ache videos banate ho sir maja aa gaya
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
U should bring tuff Ques of every chap in one video 100s of Questions
Mere ko toh ye sab dialogue pasand nhi mai skip kar deta hu sidhi baat☠️☠️☠️
🐃🐃🐃
Good 😂
Yes sir jee advanced specific maths chapter ki kuch critical problems le k ana🙏💞 matrices,det,itf,complex,prob,3d vec, newly added statistics 🙏
Sir i nearly watch all of ur videos but not those videos which contain pnc as I don't like it and can't do it... So how can i understand pnc for mains 😢
Sir ji maths mein chapterwise pyq of jee advanced last 20 years ke question ki series start kar dijiye🙏🙏
sir 1st part mein skew symmetric matrix to possible hi nahi hoga na kyunki abc ke values toh positive hi le sakte hai na.
Love you sir 🤩🤩
SIR, CENGAGE MATHS REVIEW KRIYE PLSS..OR FEW QUESTIONS BHI KARAIYE PLS
Sir quadratic yaa progression ke upar bhi similar video
Also sir calculus ka bhi aacha hoga plz especially functions ke upar🙏🙏
Love your video 😍😍
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Sir kya aap problem 2 ko general tareeke (Bina kuch assume kare) se bata sakte hain kya.
The only way I know by which it can be solved without taking examples is by using the congruence of numbers and the properties of uniqueness of inverse in congruences.
Bilkul banao sirji 🙂🙂
I just analysed all of them by putting p=1,3,5 would have done it in exam like that as well the last one was so damn easy by this method
what a fun problem!!
Hlo sir
Aap offline classes kha पढ़ाते हो
Sir different ke aise question karwao jisme alag alag concepts lag rhe ho
Guru ji ke charno ne sadar pranam 🙏🙏 guru ji aap bhut hi achhe teacher ho logo ke to hote honge sab hero par mere liye aap mere real hero ho sir my super hero real hero sab aap hai sir you are the best teacher in the world 🌎🌎 🙏🙏😭
Tum ak you tubar ho kya
Nhi par channel hai esi se kuchh video Dale hai bro
Sir, is there an even prime. Then why adj. 'odd' for prime number? Sir, please clarify
Sir 1st Question me a+b = 0 vala case bhi nhi Lena padega ?
Sir apne second part remainder ko kyu consider Kiya agar hum a^2 ko 5 se divide krenge toh quotient aayega laikin apne side mai 2/5 =4 likha hai please koi bta do😢
i love your video i sittle watching the video in my life
Sir last vaale me (2p-1)×(p-1)² kyu nhi hua...... Sir pls ans
10:52 sir how can matrix be skew symmetric? elements given are all positive
My teacher taught me that beta left the question because a new queston like this is not done in paper
Yes more jee advanced problems
Yes sir bring more videos
Who want sir saare pyq kara de line se ❤❤
Yes sir make more videos iit pyQ questions pls sir
Sir maine jitna concept sikha hn 11 12 me ushka used kr ke maine ek quess created kiya hn ...kafi acha question hn sir😅 mai aap se kafi kuch sikhta hu...sir kya. App Suh ques ko dekhege mai chahta hu ke wah quess ko sb log ek baar try jarur kre😅kafi concept clear hoga sbkaaa
16:47
Why cant a be p/2 since p is divisible by p and 2a=p
More questions sir
Sir I love your maths
Sir teaching us escaping from matrix ✨🥸😂
Sir we want more videos like this☺
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
It's a property of skew symmetric matrix.
Bhai mai 10th me hu aur maths lene ja raha hu lekin ye matrix dekh ke phat gayi😂
Notes : - Taking Transpose doesn't change value of Determinant
Sir binomial theorem ka bhi question solve karo na JEE Adv 2015 wala
MORE LIKE THIS
sir very helpful
sir jo ch adv mai moderate ques aate usske aap hard ques kara degeye
☺️☺️☺️
ua-cam.com/video/5IW-5cdLCZs/v-deo.html
Sir ji thoda fast bola kijiye 1.5x mein dekhni padti hainn🙂
Sir, first part mein koi skew symmetric matrix nhi banega kyon ki matrix ke sare element + ve natural numbers hain
Sir in first part we say that (a+b)Max and. (a-b)Max ...
Why we took Max and why did not take min or any thing ...
For some value of (a-b) it is divisible by p...😢😢
in the last part why should b.c should be 0?
Sir let p= 3 and solve manually solve 1,2 but not 3 and got damned it right thanks preparing for jee 2023# adv
What was your rank in adv
Matrix Chapter class 11 me hai ya 12 me hai?😅
Why in total ways, you are sometimes adding all ways and in second question you have multiplied all ways???
Please advance ka pyq series laye sir
How to crack jee in 2nd attempt bta do airji pls
More jee adv videos
Sir 11nth kei topics Mei iss type kei question
31:34 More videos please
Sir 11th jee ka course kardo. Please
Sir I have a doubt which I believe only you can clear.
Sir Can HCF be negative means sir,e.g.
HCF(-3,-2)= ?
I am not clear even with Google.
Please tell sir.
HCF is defined to be positive
Sirrr aur chahiyeee research krkeeee
we want more adv videros
🙏❤️
Ye a-b ka max. kyun le rhe hain???
ap sir bengal board pyq dekhna sir
sir collage ka maths bhi lao sir ❤️❤️❤️❤️❤️ i love maths
In Part 1,One case
i.e. a=b=p/2 is counted in both a = b and a + b = p so we have to subtract it from 2p-1 cases,so answer should be 2p-2 i.e. 2(p-1).Am I right??
a and b will be non integer in this case as p is a odd prime
How people solve this much difficult questions in exam !!!
Sir please advanced questions leke aooo....