Toughest Problem Of Matrix in JEE Advance Paper | IIT JEE 2010 Matrix Question

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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[@a.ksharma3614]

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.

[@Prism069]

Which IIT bhaiya?

[@itz_pgshadow]

He is joking

[@a.ksharma3614]

@@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.

[@Prism069]

@@a.ksharma3614 adv. ki rank and branch bhi bta sakte ho bhaiya

[@Amit1994-g9i]

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

[@snow5064]

was only able to solve the first part, but the second part was incredibly interesting. exam me bhot muskhil hota

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@omkarkamat1638]

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.

[@MuskanKumari-dp4ki]

😢 jo Kota mi nahi hai unhe ye advance concepts kaha milega

[@questionmark8326]

​@@MuskanKumari-dp4ki Kota me bhi itni advanced xheize nhi padai jati. Ye group theory ki properties hai ham ise MSc Maths me padte hain

[@heisenberg0069]

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😃😃

[@PranitMahapatra_]

Konse coaching se ho??

[@PranitMahapatra_]

Allen?

[@heisenberg0069]

@@PranitMahapatra_ FIITJEE RANCHI

[@031_sujay_mitra2]

99.98 percentile 😅😅

[@abhinavkumar9c017]

@@heisenberg0069 Aap bhi Ranchi se ho bhaiya?

[@SierraHunter2106]

Even when I am not preparing for jee.. I still love these type of videos sir.. pls continue them

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@scienceamateur5058]

Toh kabhi kabhar padh bhi liya kar, fir ye videos samajh mein bhi aayenge.

[@vaibhavsingh8933]

you play krunker?

[@SierraHunter2106]

@@vaibhavsingh8933 my name is a bit suggestive of that

[@vaibhavsingh8933]

@@SierraHunter2106 yeahh loll , whats your in game name

[@ojashgupta2020]

In case of skew symmetric matrix b,c belongs to +ve c=-b not possible There only one case possible b=c=0

[@tanishqraj3262]

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

[@Lucifer-pj8vc]

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

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@cryptosignal90]

Here you are missing a²=bc To find the ways you have to find the no of GP in between (1 to p-1)

[@adityadwivedi9159]

Nice way of solving the problem

[@jeeadv2024]

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).

[@Lucifer-pj8vc]

@@jeeadv2024 I got u yes you're right buddy

[@zachapple56]

Yes sir, aur aise vids chahiya Thank you 👍🏻 You are a legend .

[@avyakthaachar2.718]

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

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@prithwishsen4710]

Ur talking about congruebce modulo of number theory right?

[@avyakthaachar2.718]

Yes

[@dharmik2]

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

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@smirtysinha3540]

Yes sir I want to have more and more videos like this and how to build matrices and determinants for advanced

[@revkshp565]

Yes it is one of toughest problem for sure .. I had given paper that year

[@28aminoacids]

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.

[@vkhs562]

I really want a good solution for this question, finally get it Thanks a lot sir

[@IITIANJEE]

Sir we want more videos like this ☺️

[@mathq123]

Guru And Boss Of Mathematics...!! Lots of love from Pakistan..!! Sr Smart work ..!! Wonderful style of teaching..!!

[@curioushorse800]

Terrorism band karo

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@Prabhu108.]

Tumhare yaha bhi JEE hota hai kya

[@vasist2936]

@@Prabhu108. jihad entrance exam

[@abhimanrawat1837]

SIR, CENGAGE MATHS REVIEW KRIYE PLSS..OR FEW QUESTIONS BHI KARAIYE PLS

[@7msdbelieve]

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

[@rohandhiman-xo6km]

Definitely one of the hardest question

[@mysterio4230]

Sir different ke aise question karwao jisme alag alag concepts lag rhe ho

[@iitaeronauticsaerospace2003]

Sir ji maths mein chapterwise pyq of jee advanced last 20 years ke question ki series start kar dijiye🙏🙏

[@aadavanmurali9245]

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

[@Aditya-qg1rw]

Thank you sir Please continue the the jee advanced question series

[@jayadithyagunalan2020]

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..

[@Lifechangingmotivational-tk5go]

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 🌎🌎 🙏🙏😭

[@surayaranjan]

Tum ak you tubar ho kya

[@Lifechangingmotivational-tk5go]

Nhi par channel hai esi se kuchh video Dale hai bro

[@techkoder7923]

another method take p as 3 or 5 and substitute values

[@DebangshuSaha-l6u]

You are a legend sir

[@shlokagrahari2898]

Done all three by self😎

[@jayadesara1612]

Sir 1st Question me a+b = 0 vala case bhi nhi Lena padega ?

[@krishnannarayanan5252]

Sir, is there an even prime. Then why adj. 'odd' for prime number? Sir, please clarify

[@mr_ajay___0939]

Hlo sir Aap offline classes kha पढ़ाते हो

[@avimathur6822]

Sir last vaale me (2p-1)×(p-1)² kyu nhi hua...... Sir pls ans

[@himanshurai2853]

Sir can u start a series of previous year question of jee advance it will be very helpful.....it is not on KZbin channel

[@justblank3296]

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 😢

[@mysterio4230]

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😢

[@harjitsingh8562]

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❤

[@tdxgamer2471]

Sir pls upload a video on history of math type videos

[@manavdixit4980]

Sir quadratic yaa progression ke upar bhi similar video Also sir calculus ka bhi aacha hoga plz especially functions ke upar🙏🙏 Love your video 😍😍

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@dineshvamja7526]

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...😢😢

[@subhashpatil2833]

Sir you are mathematical genius

[@pkjha5271]

U should bring tuff Ques of every chap in one video 100s of Questions

[@pacificpandey8748]

Love the way he starts

[@Ajay_Vector]

We want more such question

[@Radhe3shyam]

Yes sir jee advanced specific maths chapter ki kuch critical problems le k ana🙏💞 matrices,det,itf,complex,prob,3d vec, newly added statistics 🙏

[@Aditya10750]

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??

[@paramstudies9785]

a and b will be non integer in this case as p is a odd prime

[@abhishektripathi6600]

SIR we really are in need of such questions

[@_u_n_known_]

Sir kya aap problem 2 ko general tareeke (Bina kuch assume kare) se bata sakte hain kya.

[@electrowaltx]

10:52 sir how can matrix be skew symmetric? elements given are all positive

[@ayushrajaryan2834]

sir 1st part mein skew symmetric matrix to possible hi nahi hoga na kyunki abc ke values toh positive hi le sakte hai na.

[@anujasthana830]

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.

[@PranshuKumar77818]

Sir we want more videos of these types.

[@amalenduchakraborty5630]

Sir ji thoda fast bola kijiye 1.5x mein dekhni padti hainn🙂

[@satyamkumar7989]

sir very helpful sir jo ch adv mai moderate ques aate usske aap hard ques kara degeye ☺️☺️☺️

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@rinijn]

Sir binomial theorem ka bhi question solve karo na JEE Adv 2015 wala

[@sabitakumari6497]

16:47 Why cant a be p/2 since p is divisible by p and 2a=p

[@kartikverma3631]

Sir teaching us escaping from matrix ✨🥸😂

[@physicsstudent8484]

Sir, first part mein koi skew symmetric matrix nhi banega kyon ki matrix ke sare element + ve natural numbers hain

[@arvindea09]

Very helpful video to generate thoughts

[@NayanJainGaming]

Sir what will be answer of - Q. 2 log 1 0 or 1 ? Please answer with explanation. Thank you

[@kanhaiyajee2374]

It will be 0

[@kanhaiyajee2374]

2log1=log1^2 Now, from the property of the log, we have a=b^c. Thus, 1=10^c, c=0 because 10^0=1

[@shashwatsingh5048]

Zero

[@mishrasachin6596]

Yes sir aise hi questions aur layie

[@RONAKGHOSH]

Sir I love your maths

[@dezykumari4210]

Sir let p= 3 and solve manually solve 1,2 but not 3 and got damned it right thanks preparing for jee 2023# adv

[@Radon.........]

What was your rank in adv

[@ayanbhattacharjeeXB]

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.

[@jaharuddinahmed7883]

HCF is defined to be positive

[@mathmagic8577]

Yes we want this type of videos

[@kunaljaju646]

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

[@veertejaji36]

Who want sir saare pyq kara de line se ❤❤

[@cascabellah]

U made me luv with maths 😜😻

[@mathmagic8577]

Love you sir ❤ bhaut ache videos banate ho sir maja aa gaya

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@jinesh_dugar]

Notes : - Taking Transpose doesn't change value of Determinant

[@satyamshah1729]

Mere ko toh ye sab dialogue pasand nhi mai skip kar deta hu sidhi baat☠️☠️☠️

[@theunity9299]

🐃🐃🐃

[@Singh_ankit758]

Good 😂

[@seemarani6387]

My teacher taught me that beta left the question because a new queston like this is not done in paper

[@mayankgoyal7842]

Yes sir make more videos iit pyQ questions pls sir

[@nayana2006]

Yes sir bring more videos

[@sakshamsingh7325]

what a fun problem!!

[@garvitjain2790]

Yes more jee advanced problems

[@antarippal3344]

Love you sir 🤩🤩

[@drishtibharadwaj9486]

Bilkul banao sirji 🙂🙂

[@fundergaming9457]

Matrix Chapter class 11 me hai ya 12 me hai?😅

[@Amit1994-g9i]

This is actually a problem of number theory and has very less to do with combinatorics and matrix

[@Anonymous-Indian..2003]

I didn't understand why this video come on my KZbin home page during my 4th semester exam preparation...... But still, nostalgia....even I also took more than two hours for solving this..... लेकिन मेहनत रंग लाई.....😅

[@rockyjohnson6248]

2nd question mein a ^2=1 ka case nahi consider kiya

[@jayprakashthakur1629]

Why in total ways, you are sometimes adding all ways and in second question you have multiplied all ways???

[@varun1702]

Mujhe to isse tough and calculative 2019 Adv ka matrix que laga

[@hggaming9870]

Sir 11th jee ka course kardo. Please

[@OffTheBlaze.]

in the last part why should b.c should be 0?

[@y_a_s_h_1_7_0_7]

Bhai mai 10th me hu aur maths lene ja raha hu lekin ye matrix dekh ke phat gayi😂

[@hidayathali8003]

Nice and daring explaination

[@rohan5641]

ap sir bengal board pyq dekhna sir

[@legendarymathematician]

Sir 11nth kei topics Mei iss type kei question

[@dineshvamja7526]

Sir please advanced questions leke aooo....

[@tanver7439]

Why the values of the principle diagonal was 0 at the case of skew symmetric?

[@gk_study_208]

kzbin.info/www/bejne/a3q6XmiZmbF2kNU

[@kavi5990]

Search for definition of skew symmetric matrix(it's a direct inference from the definition)

[@Vision_CR]

i love your video i sittle watching the video in my life

[@chetanangira2974]

More questions sir

[@vrajesh.k]

sir collage ka maths bhi lao sir ❤️❤️❤️❤️❤️ i love maths

[@cascabellah]

How to crack jee in 2nd attempt bta do airji pls

[@sagarkumarjha75]

Please advance ka pyq series laye sir

[@Dream_king_aman]

16:25 a = p/2 bhi ho sakta hai

[@pushkarc28]

it was not a matrix problem but a number theory problem. the part wtih matrices is minimal

[@low_elo_chess]

31:34 More videos please