Quadratic Equations and Sequence & Series Advanced Problems | JEE Advanced 2024 | Arjuna Series

Best Advanced Problems on Quadratic Equations, Sequence & Series in One Shot | Arjuna Series | JEE Advanced 2024
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This specialized tutorial is meticulously crafted for JEE Advanced aspirants aiming to master some of the most challenging and high-scoring areas of the mathematics section.
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TIMESTAMPS
0:00 Introduction
1:45 Question-1 (SCQ)
5:28 Question-2 (SCQ)
8:20 Question-3 (SCQ)
13:10 Question-4 (SCQ)
21:25 Question-5 (SCQ)
26:05 Question-6 (SCQ)
31:43 Question-7 (SCQ)
34:35 Question-8 (SCQ)
39:55 Question-9 (SCQ)
41:07 Question-10 (MCQ)
45:16 Question-11 (MCQ)
51:30 Question-12 (MCQ)
58:39 Question-13 (MCQ)
1:04:10 Question-14 (MCQ)
1:09:30 Question-15 (MCQ)
1:17:29 Question-16 (MCQ)
1:21:05 Question-17 (MCQ)
1:25:43 Question-18 (MCQ)
1:29:37 Question-19 (Numerical)
1:33:19 Question-20 (Numerical)
1:35:48 Question-21 (Numerical)
1:40:48 Question-22 (Numerical)

[JEEnexus]

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[shivx]

❤Q-4❤
Σ x^n =(1-x)-¹

Differentiate with respect to x

Σ nx^(n-1)=(1-x)^-²

Multiply ✖️ both sides with x²

Σ nx^(n+1)=x²×(1-x)^-2

Differentiate with respect to x



Divide both sides with x as in
the question it is 2^n-1

Σ n(n+1)x^(n-1)=2/x [x(1-x)^-2+x²(1-x)^-3]
Now put x=1/2

We get the summation to be equal to 16 but we don't need the zeroth and first term so subtract them zeroth term is 0 and first term is 2

We get our answer as
📜14📜

Aim°JEE2025
❤Mera bhai ❤
Thia method might look long but it isn't it will only take around 20 to 30 second to get the Desired answer.

[sohambhattacharya]

ANALYSIS

Q1. Got the concept right but idk why answer didn't match....solved 2 3 times ig I'm missing something...have to recheck

Q2. Wrong attempt

Q3. Concept right but couldn't reach the answer

Q4. Made mistake at that k=0 point...rectification reqd
Repeat ❗️

Q5. Tried by Vn method...got in the wrong direction...else soln was easy

Q6. I didn't proceed due to inertia after seeing big big terms....apologies to myself

Q7. Learnt a new method for this....highlighted pt: sigma cannot handle terms like a^x

Q8. Millions of apologies to myself for making mistake in taking mod...else qn was easy

Q9. Got it right in first attempt

Q10. Got it right in first attempt

Q11. Majedar question....best feeling after understanding the soln
Repeat ❗️

Q12. Simple yet tricky...solved in the wrong direction
Repeat ❗️

Q13. Graphical approach was necessary
Repeat ❗️

Q14. Got it right in first attempt

Q15. Partially correct

Q16. Partially correct

Q17. Learnt a new way
Repeat ❗️

Q18. Wrong attempt

Q19. Got it right in first attempt

Q20. Got it right in first attempt

Q21. Got it right in first attempt

Q22. Couldn't solve....but method was damn easy

Result:
SCQ- 3/9
MCQ- 1/8
INTEGER- 3/4

Nazaaree overloaded❤...Love you bhai❤️❤️❤️

[ThanushReddyKatla]

Q.4 we can split k^2 + k/ 2^k-1
Sum(k/2^k-1) is solvable by simple infinite AGP
WE CAN WRITE k^2 as sum of first k odd numbers
Then we can apply method of difference bcoz we get again and AGP which is solvable....At last subtract 2 from ans., since s1=0 but according to k(k+1) we get 2.
This might be lengthy but helpful for different questions.

[AryanPatel-iyis]

Sir in Q3, You have find the MAX value of (a^2 + b^2 + c^2) / (ab + bc + ca). But sir why we not use Minimum value of the expression. As If K right side ki minimum value se chota hoga then Max value se bhi chota hoga.

[tusharprajapati]

Sir, 1:16:00 or MCQ 15, Ans will be option A and D.
As we know a + b = c + d
So for a2 + b2 < c2 + d2
Individually c and d must be greater than a and b.
Therefore, ab = 2 and cd = 7

[Riya-joshi]

Ekdm Nazaaredaaar Ssn Bhaii Mazaa aagyaa 🔥❤ Bahut saare nye concepts seekhe aaj promise repeat krlenge🔥
Ek doubt plss btadijiyega - Cosx Quadratic wle Qs me for all x given tha na usme x=0 lekr proceed krskte h kya?

Thank you so much LY3M ❤❤#Mera Bhai Mera Bhai ❤

[Itsme-zqnw]

sir, in 39:46 the question could be finished in 2 steps using differenciation using maxima minima

[empty_a.f]

Sir in q2, isn't a 3rd case possible where one of the polynomials is zero?

[ishanjunnare]

in qsn 1 it is given that f(x) is a polynomial but the f(x) you got is not a polynomial

[parth_.parmar]

In 01:09:27 we can solve option c and d via coefficient of equation

[happymoji]

sir ji q 13 me bola hia ki only one solution isk matlab dono diff functions ke y ke value should be equal at one value of x only par apne toh graph se do do points me cut karvaya correct me if i am wrong

[ThanushReddyKatla]

Sir @kaliaiit, I think there is a problem with Q.9, please correct me if I m wrong.
We can split 5/2^x as 1+1+3/2^x, then apply AM>=GM.
Like this we get min. Possible value of 5(6)^1/5 which is less than 8. Hence I request. to please check.

[sadbhavkhandelwal]

sir 31:39 mai limit as a sum of integral wala concept use nhi kr skte kya ?

[r.prudhvi]

Good evening sir
I am studying 12th now
Sir in my class I can understand what my lecture says but still Iam not able to do sums on my own
Can pls tell me sir how to overcome it.
I think you will see and reply for my problem.
Thank u sir.

[tss]

(scq)2. sir 2√2 * √2 = 4 = 2²
it is still a perfect square

[gargeevyas]

Sir, Q4 me aapne jo bola vo same galti ki and answer came as bohot obvious mistakes batate rehna becoz initially mujhe laga answer wrong hi hai...thanks for spotting the mistakes