I presume it's parodying the post that I, a thirteen year old, could solve easily. Unfortunately, I believe some very kind people are helpful enough to have solved it themselves
This is a trap question. The people making the paper knew students would waste time in this question. It's a better strategy to leave extremely long questions like this because you simply don't have time.
Then my stupid ass will get obsessed over it and spend like 10 mins trying to solve it and even if I do manage to solve it I’ll still obsess over it and wonder if it’s right and keep going back to check all other alternatives 😩why am I like this 😭
No you fucking can't lol, you have to take log on both sides and write in integral summation form and then differentiate the expression, there is no " theory" for this one lol,source: this is a problem from jee advanced 2015 ( or 16 ) and I have done it within time control
Saala ye subreddit maths tuition kab ban gaya iski Maa ka. Abbe yaar, jaan bhoojkar humanities Lee thi. Ab fir se ussi gandigi(maths) mai haath dena padega.
Edit: Damn this comment blew up. And chill out mathematicians, I am joking.
Taylor MacLaurin method of solving series is often taught in calc two/three, so these series questions where you solve for divergence/convergence are actually common to calculus
Yeah the system is slightly different I think in the uk than the states we go from high school to 6th form or college then go to uni
Our gcse courses are pretty different to the SATs in the US and idk how hard the SATs are but the higher level maths course is pretty difficult
Nah our 6th form would be the equivalent of senior high in the US I think
The system is still fucked and mostly useless until u hit 6th form/ college
We have (in the 3 tier system) 5 years of first school 4 of middle and 3 of high then we can go to do college or 6th form before we go to uni (if we wanna do uni that is)
A piece of horror beyond comprehension that feeds on the distressed state consciousness of young people by forcing them through a torture that not even the mediaeval executioners could have imagined. A horror which originated from the unfathomable depths of cruelty of minds so bright and yet so dark at the same time.
Alright quick glance at this problem real quick.
We see that the series here is a comverging series as the bottom aspect of the problem grows bigger than the top aspect for all x > 1. However if X is less than 1 then the bottom part will actually shrink as the top part expands meaning that the f(x) for any number less than 1 is greater than the f(x) for any number greater than 1. This means we rule out D since at a quick glance it’s derivative will lead to a larger number than it’s non-derived form and that both numbers are bound to be greater than 1 I believe
We also see that this equation is bounded for all X’s greater than 0 but C is also saying for an X = 0 meaning that C is going to automatically be false as you cannot plug in 0 to this equation.
The last 2 ones we have are going to be manually calculated sadly. My gut is currently saying B but I’ve not taken any calculus classes so I cannot tell you if this is true or false
Alright, I think I got it, write everything as a product, with k a variable going from 1 to n, then take the log to transform all of that crap into a sum, and if you play around a little, you'll find that this is 1 classic Riemann sum which will converge to an integral (that won't depend on x) then you can just to try to calculate it and you'll have an actual function you can work with!
So I'm guessing the numerator can be rewritten as (n\^n \* x\^n / n!) \* (n/x+1) \* (n/x+2) \* ... \* (n/x+n)=(n\^n \* x\^n / n!)\*Gamma(n/x+n+1)/Gamma(n/x+1). Similarly, the denominator is n! \* x\^(2\*n) /(n!)\^2 \* (Gamma(n/x+n+1)\^2) / (Gamma(n/x+1)\^2), up to some 1/O(n) multiplicator (which is also less than 1). After cancelling most of this out, we get n\^n\*Gamma(n/x+n+1)/x\^n (up to a O(n) multiple). Taking the logarithm and using Stirling's approximation, we get n log(n) - n log (x)-n log(n) +n +O(1)= n(1-log(x)). Multiplying by x/n, we get x(1-log(x)). The exponent can be left like e\^x(1-log(x)), or rewritten as (e/x)\^x. The rest seems boring.
First of all, the equation inside the lim = [...]^x/n is "unsolvable" as the series (x+n) -> (x+n/2) -> ... ??? ... -> (x +n/n) could have literally anything in the ??? part, but essentially it boils down to [infinite/infinite]^(x/infinite).
Assuming that as n -> infinite, the value of x INSIDE the equation is irrevelant, the only thing of have to do is compare which infinite is "bigger or smaller" than the other by the exponent outside the brackets, the [...]^(x/n), where the bigger the x, the bigger is the result, even if we assume that [infinite/infinite] = 1.
When it comes to the derivative part, we assume 1^(x/infinite), and 1 to the power of anything will be always 1, so the derivative is 0 for every x.
By these conclusions, we have that B and C are true and MAYBE the A, but as the inequality is written as >= instead of <= I would mark as wrong but tecnically is right too as all values of x is equal to 1, idk.
I'm not sure if anyone responded, but I'm quite sure the answer is (B) f(1/3) <= f(2/3) and (C) f'(2)<=0
It was a challenging question; would you mind answering a few more questions or providing the source of the book from whatever country you are from?
the answer is BC, the proof is quite long to type here
this is from the indian college entrance exam JEE' 2016 paper-2 (which is what u should search if u want the solution)
it was one of the toughest Question at that time
~~OP, I just want to tell you the answer is BD. C is incorrect, so it's not BC like you've been saying.~~
~~I plugged this into Mathematica (software for solving tough problems) and f(x) simplifies to e^x. Thus A is wrong since it's increasing on its domain, B is right by the opposite logic, C is wrong since d/dx e^x > 0 for all (real) x, and D is correct since the expression simplifies to 1 ≥ 1.~~
~~I'd love to know who / what materials say it's BC; unfortunately it's clear to me that C is false.~~
EDIT: This is what happens when you mix up your Σs and Πs, people. Turns out one Math undergrad can't defeat seven Indian Institutes of Technology; the answer is indeed BC.
I assume u are the math undergrad that you mentioned
If you dont mind me asking? What are the career opportunities for a person with a math degree?
Abstract mathematics is one field that is quite intriguing, yet I dont understand how is the skill used in real world.
Thanks in advance!
Unless you have to do that “show your work” BS just cheat. I don’t know the answer, and I’m making more money in my early 20s than my teachers will ever make.
Im in the 9th grade and what the fuckk happened. Where did it go wrong i knew that there would be less numbers as it progressed but what the fuckk. Like what the fuckk. Can someone tell me what the fuckk is this fuckk
This is pretty standard stuff for 16 year old indian students who want to pursue engineering. Been a while for me but i would say this is mediocre difficulty.
I feel terribly disappointed in myself provided I live in Singapore and actually cannot solve this, as an 18 yr old in an engineering school in polytechnic
I thinks it's B I'm chinese btw
BC is the answer :) and its a parody post
Nothings real everything is far away
I presume it's parodying the post that I, a thirteen year old, could solve easily. Unfortunately, I believe some very kind people are helpful enough to have solved it themselves
no ,he is parodying the post with same title .
You have an amazing talent of coming off really smug without even speaking.
I’m saving this comment so I can use it on the next asshole I come across
Oops yeah I realise that now
The fact that you're Chinese makes sense
Advanced PTSD
This one's pretty easy though. Just a hellofalot of writing
The problem is it's supposed to be done in a time limit
What else can you do? You need to write out at least some parts to see what to do.
This is a trap question. The people making the paper knew students would waste time in this question. It's a better strategy to leave extremely long questions like this because you simply don't have time.
Well of course if you see this in a test you'd skip it. I'm looking at it for what it is, not in a test scenario.
Oh ok
The problem is all questions look like this. Pretty hard to figure out which ones are worthy
Then my stupid ass will get obsessed over it and spend like 10 mins trying to solve it and even if I do manage to solve it I’ll still obsess over it and wonder if it’s right and keep going back to check all other alternatives 😩why am I like this 😭
I feel like i can solve this if i had a paper and a pen on me rn but even then its too much work
[удалено]
Th
truly educated
Is that an Amit Mahajan reference?
But the limit is always 1, right?
The limit will tend to 0 as n grows higher since the bottom of the function is greater
At the risk of sounding like an idiot...look at the power of the entire expression. X/(inf) = 0 Anything to the power of 0 is 1
I believe 0^0 is undefined
I was certain that 0^0 was still 1, no?
[удалено]
You can't solve this one just by using theory
Actually you can't do that.
No you fucking can't lol, you have to take log on both sides and write in integral summation form and then differentiate the expression, there is no " theory" for this one lol,source: this is a problem from jee advanced 2015 ( or 16 ) and I have done it within time control
People here can't hold conversations and don't know what a woman is, how do you expect them to know that shit?
non JEE aspirant moment
Feeling praud JEE army
[удалено]
chad JEE Aspirant
avg amrican
Americans are able to talk to women, just in a very degrading and misogynistic way
i mean we indians arent better honestly
some of us are far far worse
"Teri maa iti jaadi usko lagtay ptm matlab parent teacher mating" Lmao ded
Women are not real
Kids here in India preparing for jee(college entrance test) solve this shit like it's nothing
Exactly because of that reason
feeling paraud indian aarmy
Jung ke maidan mein kade na haarde
OooOOoooOOOo
Saade peeth piche waar ka irada sambh ke
Hum goli siddhi mathe ke beechale maarde
take time kadh veham yaar konna talde
🍇🍇🍇
B. Source: I'm Vietnamese, we have to deal with this shit if we are to graduate high school.
So I have to face this shit in the future
Same with the Indiana 🥲
Saala ye subreddit maths tuition kab ban gaya iski Maa ka. Abbe yaar, jaan bhoojkar humanities Lee thi. Ab fir se ussi gandigi(maths) mai haath dena padega. Edit: Damn this comment blew up. And chill out mathematicians, I am joking.
Errrrr... yes? Idk I'm bengali
Ke jane baba😂😂😂
😂😂 you're not wrong
fellow Bengali
me who is in humanities but still has math...
Ayo chill chill
XDDDDD
Bhai maths achha hai, ye subreddit maths ka nahin hai is ka ye matlab nahin hai ke main sirf gandagi mein hi achha huun
Let me guess class 12 ch Integrals jee ADV pyq by jee aspirants to troll foreigners. Am I right?
integral pyq. parody post of someone asking 10/x = 3
Yeah I saw that too
Definite integration*
use expansion formula then use lhl or effective degree term somthing like that i cant do it rn too busy
Okay thanks u/gaypopcorn
Hehe
Oh my god what is that
Maths
Ew
Your mom
Welcome to India
Calculus
No, it's precalc. Option D does involve calculus, but the question itself is precalculus level. By the way, ƒ(x) in this case is always equal to 1.
>By the way, ƒ(x) in this case is always equal to 1. Where'd you get that from?
No that's calculus source: I've taken pre calc calc1 2 and 3 I'm a math major
???
Taylor MacLaurin method of solving series is often taught in calc two/three, so these series questions where you solve for divergence/convergence are actually common to calculus
Russian
can confirm
Ahahaha
Advanced calculus: subtopic limits
Seems as though it's limits.
Yup limits … I categorise it under limit continuity and differentiability : Indian btw
Calculus xD
avg JEE ASSpirant
I would but I finished high school like 3 months ago this shit ain’t in my head no more
And you’re 16?
Yeah the system is slightly different I think in the uk than the states we go from high school to 6th form or college then go to uni Our gcse courses are pretty different to the SATs in the US and idk how hard the SATs are but the higher level maths course is pretty difficult
So are people in the UK smarter?
Nah our 6th form would be the equivalent of senior high in the US I think The system is still fucked and mostly useless until u hit 6th form/ college We have (in the 3 tier system) 5 years of first school 4 of middle and 3 of high then we can go to do college or 6th form before we go to uni (if we wanna do uni that is)
But you are just 16! I will be finishing my H.S. in my late 17
you finished highschool at 16? damn
You studied thi in highschool 😳
Functions? Yeah this was like year 10 stuff We had to do inverse functions too And I don’t think they appeared much on our GCSE papers either
Well what do you mean by year 10, as our country has different systems for schools. Tell me at what age does children go in year 10?
What the fuck is this
A piece of horror beyond comprehension that feeds on the distressed state consciousness of young people by forcing them through a torture that not even the mediaeval executioners could have imagined. A horror which originated from the unfathomable depths of cruelty of minds so bright and yet so dark at the same time.
In short, Maths
Which in even shorter form is just Math
Calculus. It's beautiful
It's a question based on the chapter LIMITS in Mathematics.
Alright quick glance at this problem real quick. We see that the series here is a comverging series as the bottom aspect of the problem grows bigger than the top aspect for all x > 1. However if X is less than 1 then the bottom part will actually shrink as the top part expands meaning that the f(x) for any number less than 1 is greater than the f(x) for any number greater than 1. This means we rule out D since at a quick glance it’s derivative will lead to a larger number than it’s non-derived form and that both numbers are bound to be greater than 1 I believe We also see that this equation is bounded for all X’s greater than 0 but C is also saying for an X = 0 meaning that C is going to automatically be false as you cannot plug in 0 to this equation. The last 2 ones we have are going to be manually calculated sadly. My gut is currently saying B but I’ve not taken any calculus classes so I cannot tell you if this is true or false
This was a very nice attempt. option c is 0 for derivitive of f not f itself. you are supposed to make it into an integral and get answer B and C
Cool I don’t know how to do that. Ask me in 3 years once I take calc im still in Algebra 2 lmao And yeah looking at it now it doesn’t say f(0)
Are these jee advance questions? Damn maybe i should switch to bio while im ahead
well yes, but this was the toughest problem of one of the toughest years
2016? I heard that was a hellish paper
It is
[detailed solution with proper explanation](https://youtu.be/qFM0mhpbmnQ)
Allenite spotted"_"
Mujhe kya ,me to NEET wala hu
69th drop year hoga na tumhara /s
This seems like the type of thing that would come up on the Cambridge STEP 3 or the MAT. In fact,it's probs even harder than that...
Lol as a Brit those exams (plus the Imperial College AMAT) are very easy compared to the JEE adv.
Op u r in 11th or in 12th?
12th
Oh well mai 11th mai ho or mujhse ye ques ho nahi Raha
JEE me bhi 1% logo se ho paya tha lol. this was one of the hardest Q in 2016
Proud Indian moment, also both B n C are true
c
Was that correct
Yes it's B and C
Mains ka question hai ya Advance ka??
Advanced 2016, it was the toughest question that year, less than 1% people were able to solve it
From the question i knew this had to be something from an Indian school test
Indian men of culture know which exam this question has been taken from
JEE ADVANCED, entrance exam for top enginnering collages throughout india
Jee advanced 2016, it was the toughest question that year, less than 1% students were able to solve it
sorry, i thought you were asking lol
Alright, I think I got it, write everything as a product, with k a variable going from 1 to n, then take the log to transform all of that crap into a sum, and if you play around a little, you'll find that this is 1 classic Riemann sum which will converge to an integral (that won't depend on x) then you can just to try to calculate it and you'll have an actual function you can work with!
Yesss, Although, the integral does depend on x, but you are correct for rest of the part
Bc bicharo ko advanced ka question kyun de diya. Gaand phatt gayi non-jee waalon ki yahaan pe.
wohi toh plan he B)
Bhai logo ke reactions dekh ke maja aa rahi hai lol
Haan, mujhe bhi
When I was preparing for IIT-JEE it was an easy question _"_
Saale 2016 ka sbse hard q tha ye
Iykyk
Naa bro simple question tha, log le ke differtiate karna tha , simple shit bro
So I'm guessing the numerator can be rewritten as (n\^n \* x\^n / n!) \* (n/x+1) \* (n/x+2) \* ... \* (n/x+n)=(n\^n \* x\^n / n!)\*Gamma(n/x+n+1)/Gamma(n/x+1). Similarly, the denominator is n! \* x\^(2\*n) /(n!)\^2 \* (Gamma(n/x+n+1)\^2) / (Gamma(n/x+1)\^2), up to some 1/O(n) multiplicator (which is also less than 1). After cancelling most of this out, we get n\^n\*Gamma(n/x+n+1)/x\^n (up to a O(n) multiple). Taking the logarithm and using Stirling's approximation, we get n log(n) - n log (x)-n log(n) +n +O(1)= n(1-log(x)). Multiplying by x/n, we get x(1-log(x)). The exponent can be left like e\^x(1-log(x)), or rewritten as (e/x)\^x. The rest seems boring.
Is that what maths looks like? Bro what happened to simple 2+2
Ah finally, assemble my Indian bros Also, is the answer B? #JEEmoment
BC
angrej lodo ki maiya chud gyi XD
Tu kar sakta hain ye question?
Bro how old are you? This shit's elementary 💀
Orzz
Wdym
이 이게뭐고
엄마 나 울고 싶어
I literally have no idea what I’m looking at
First of all, the equation inside the lim = [...]^x/n is "unsolvable" as the series (x+n) -> (x+n/2) -> ... ??? ... -> (x +n/n) could have literally anything in the ??? part, but essentially it boils down to [infinite/infinite]^(x/infinite). Assuming that as n -> infinite, the value of x INSIDE the equation is irrevelant, the only thing of have to do is compare which infinite is "bigger or smaller" than the other by the exponent outside the brackets, the [...]^(x/n), where the bigger the x, the bigger is the result, even if we assume that [infinite/infinite] = 1. When it comes to the derivative part, we assume 1^(x/infinite), and 1 to the power of anything will be always 1, so the derivative is 0 for every x. By these conclusions, we have that B and C are true and MAYBE the A, but as the inequality is written as >= instead of <= I would mark as wrong but tecnically is right too as all values of x is equal to 1, idk.
Lol never studied calculus did you . So you say 1^infinite would be 1 ? Lol you destroyed poor Euler's whole career
I forgot the lim, but it is implicit at the start of the equation.
Still bro 1^x limit x goes to infinity isn't 1 bruh 💀
I'll be honest i don't remember all these special cases as I progressed in the course, was just going by logic of what I learned sorry
Please no JEE😭😭😭😭😭
B
my life got 648x worse when f(x)
I'm not sure if anyone responded, but I'm quite sure the answer is (B) f(1/3) <= f(2/3) and (C) f'(2)<=0 It was a challenging question; would you mind answering a few more questions or providing the source of the book from whatever country you are from?
JEE Advanced is the name of the Exam . You can search for past papers
the answer is BC, the proof is quite long to type here this is from the indian college entrance exam JEE' 2016 paper-2 (which is what u should search if u want the solution) it was one of the toughest Question at that time
Avg JEE aspirant moment. Feels better being a NEET Aspirant
~~OP, I just want to tell you the answer is BD. C is incorrect, so it's not BC like you've been saying.~~ ~~I plugged this into Mathematica (software for solving tough problems) and f(x) simplifies to e^x. Thus A is wrong since it's increasing on its domain, B is right by the opposite logic, C is wrong since d/dx e^x > 0 for all (real) x, and D is correct since the expression simplifies to 1 ≥ 1.~~ ~~I'd love to know who / what materials say it's BC; unfortunately it's clear to me that C is false.~~ EDIT: This is what happens when you mix up your Σs and Πs, people. Turns out one Math undergrad can't defeat seven Indian Institutes of Technology; the answer is indeed BC.
I assume u are the math undergrad that you mentioned If you dont mind me asking? What are the career opportunities for a person with a math degree? Abstract mathematics is one field that is quite intriguing, yet I dont understand how is the skill used in real world. Thanks in advance!
Answer is B I am Indian btw
omg i took JEE Advanced this sunday. why do you have to remind me of that thing by posting a question on a random teenagers subreddit omfg
Unless you have to do that “show your work” BS just cheat. I don’t know the answer, and I’m making more money in my early 20s than my teachers will ever make.
bro i just started algrebra this year what in the fuck is this
This is the jee adv 2016 paper
i think im gonna get an F on this quiz
What the fuck
What the fuck
Im in the 9th grade and what the fuckk happened. Where did it go wrong i knew that there would be less numbers as it progressed but what the fuckk. Like what the fuckk. Can someone tell me what the fuckk is this fuckk
Limits
Im a nerd Im great at maths But here is the time i surrender
How are you still a Teenager
We solve shit like this daily to prepare for engineering entrance exams
JEE gang rise
Well in india we have to solve these kind of questions when we are 16-17
This is pretty standard stuff for 16 year old indian students who want to pursue engineering. Been a while for me but i would say this is mediocre difficulty.
I feel terribly disappointed in myself provided I live in Singapore and actually cannot solve this, as an 18 yr old in an engineering school in polytechnic
Jee advanced just built different man.
Gandalf, what is this new devilry?
ur making me feel dumb 💀💀
It's one of most difficult questions asked in JEE exam in the year 2016. 2016 got the worst paper I'd say.
C is false. I think
I'm 17 and I'm confused 🙂
I’m glad i’m still in Algebra 2 💀
I am talking calc this year, ask me about this at the end of semester 2
Bro took solving problems seriously.