@@mayur_krishna_devotee how many were you able to solve? I felt the paper to be on the tougher side this year. Like I was getting around 5/6 problems on an average, correct in my previous year attempts but this year, it felt like a disaster. I was just able to solve B1, B2, B5 completely and B3 partially. And I have no idea of how wrong I might have been in my Part A. Fingers crossed
@@rajkumarlakhmani3911 This year, yes it was much harder, I could do B1,B5(i), B6 (i),(ii) and wrote B5(ii) in a hurry. Part A was something to be very careful about, need to hope for the best
By menelau's theorem in triangle XYZ using transversal RPQ, ZQ/YQ*YR/XR*XP/PZ =1, So, k*XP/XR*(XY+XR) /(PW+WZ) =1, k*XP/XR*(XY+XR)/(XP+XY)k=1, XP(XY+XR)= XR(XY +XP), XY(XP-XR) =0, XP=XR, as XY can not be 0, Is my solution correct? I did it in this way
I always wonder in geometry, how someone can be as able to do such perfect constructions... Maybe lots of practice. And it's what is most important in geometry problems. I tried it very hard in cmi x'm, do some construction, Menelaus thm & all but nothing was satisfactory.
@@rajkumarlakhmani3911 differentiate x^3-x^2 you will get 0 and 2/3 as its roots . Now good pairs can only exists between f(2/3) to f(0) because only between this part function is many one. So largest such l is (0, other point where its value is f(0) i.e 1) and smallest such s is (2/3, other point where its value is f(2/3) i.e -1/3) so l=1 and s =-1/3.
@@sajaltuley1578 that's the easier part. I specifically asked for the second part of the question that required us to prove that there are infinite *rational* good pairs.
@@rajkumarlakhmani3911 the function is many one in infinite rational points that's only what I wrote. It's many one in an interval not at discrete points.
I want to admit online classes for my chaild who is in class eleven, and he is a math lovers, but can't enough study in agartala, plz help me to the right way to reach his goal.
@@rajkumarlakhmani3911 btw how much marks would i get in part B , i did B3 , B5 (i) i took f(x) = x^3-x^2 diff and showed that there exists no sol in -inf to 0 ) U ( 2/3 , inf) and left there and (ii) just wrote the hint and did some bullshit , B6 (i) showed that either x^2+x-1 can show atmost one sol when x^2+x-1 =p or atmost 1 when p/x^+x-1 ( didnt prove this part just stated it ) , same thing tried in (ii) , i wont clear the cutoff anyways but any rough guess of my marks
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HI, can't we directly use Menalaus Theorem? Beautiful construction, by the way. Thanks!
Yes we can, in fact that's how even I did in the exam
@@mayur_krishna_devotee have u proved then, how lengthy the proof was?
@@namantenguriyaYes, I could complete it, wasn't very lengthy, just one page along with diagram.
@@mayur_krishna_devotee how many were you able to solve? I felt the paper to be on the tougher side this year. Like I was getting around 5/6 problems on an average, correct in my previous year attempts but this year, it felt like a disaster. I was just able to solve B1, B2, B5 completely and B3 partially. And I have no idea of how wrong I might have been in my Part A. Fingers crossed
@@rajkumarlakhmani3911 This year, yes it was much harder, I could do B1,B5(i), B6 (i),(ii) and wrote B5(ii) in a hurry. Part A was something to be very careful about, need to hope for the best
By menelau's theorem in triangle XYZ using transversal RPQ, ZQ/YQ*YR/XR*XP/PZ =1,
So, k*XP/XR*(XY+XR) /(PW+WZ) =1,
k*XP/XR*(XY+XR)/(XP+XY)k=1,
XP(XY+XR)= XR(XY +XP),
XY(XP-XR) =0,
XP=XR, as XY can not be 0,
Is my solution correct? I did it in this way
XY can not be 0 by construction,
I always wonder in geometry, how someone can be as able to do such perfect constructions... Maybe lots of practice. And it's what is most important in geometry problems.
I tried it very hard in cmi x'm, do some construction, Menelaus thm & all but nothing was satisfactory.
Beautiful explanation sir ❤️❤️❤️❤️❤️❤️❤️❤️
Thank you for watching.
Beautiful solution!
Thank you.
I give cmi entrance exam I solved 29 questions in part a and 2 question in part b good pair and square cutting wala. What should I expect?
Excellent!!!
Glad you like it!
Around how many marks one should get in part B? I was also to solve only one question r^2+s^3 wala
Tell me about your approach for the second part of that question. That took a lot of brainstorming from my side
@@rajkumarlakhmani3911 differentiate x^3-x^2 you will get 0 and 2/3 as its roots . Now good pairs can only exists between f(2/3) to f(0) because only between this part function is many one. So largest such l is (0, other point where its value is f(0) i.e 1) and smallest such s is (2/3, other point where its value is f(2/3) i.e -1/3) so l=1 and s =-1/3.
@@sajaltuley1578 Nice, I followed the exact same approach in the exam.
@@sajaltuley1578 that's the easier part. I specifically asked for the second part of the question that required us to prove that there are infinite *rational* good pairs.
@@rajkumarlakhmani3911 the function is many one in infinite rational points that's only what I wrote. It's many one in an interval not at discrete points.
I want to admit online classes for my chaild who is in class eleven, and he is a math lovers, but can't enough study in agartala, plz help me to the right way to reach his goal.
You may apply at cheenta.com
nyyc
what could be the expected cutoff Part A and (Part A+Part B)
My estimation for part A lies around 17-18 as difficulty was similar to previous years and total around 52-55
@@rajkumarlakhmani3911 btw how much marks would i get in part B , i did B3 , B5 (i) i took f(x) = x^3-x^2 diff and showed that there exists no sol in -inf to 0 ) U ( 2/3 , inf) and left there and (ii) just wrote the hint and did some bullshit , B6 (i) showed that either x^2+x-1 can show atmost one sol when x^2+x-1 =p or atmost 1 when p/x^+x-1 ( didnt prove this part just stated it ) , same thing tried in (ii) , i wont clear the cutoff anyways but any rough guess of my marks
@@milindpatt4201
@@rajkumarlakhmani3911 previous year paper was easy as compared to this year paper so cut off might be around 40-44
@@rajsingh8372 I really don't have any idea. Mr. Balasundar says it'd be around 58. My guess is 52
THIS IS EASY BY MENELAUS THEORUM!!!