Answer to question 3.\[a^{2}-b^{2}=c(b-a)\]
This implies \[a+b+c=0 ...or... a=b\]
Case 1\[a+b+c=0\]
Solutions are \[(a,b,c)=(2,0,-2),(-2,0,2),(0,2,-2),(0,-2,2),(2,2,0),(2,-2,0),(-2,2,0),(-2,-2,0).\]
Case 2\[a=b \]
Therefore \[(a,b,c)=(2,2,0),(-2,-2,0).\].
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Shivam Jadhav
·
1 year, 9 months ago

@Brilliant Member
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Thanks but can you please search key for RMO telangana region. I am too busy ok. THANKS!!!
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Easha Manideep D
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1 year, 9 months ago

@Kush Singhal
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How many did you solve? Do you have any idea what is the cut-off and when the results will be declared?
–
Brilliant Member
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1 year, 9 months ago

In 6th one the difference between two consecutive squares must be greater than 125. Then you can find step of sqrt m becomes step of sqrt of m + 125 which the smaller square in which m, m+125 lies. I gave a hint.

@Easha Manideep D
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hi ... i had the same idea .. and proceeded in the same direction for Q6 ... i got 72 such integers ... is my answer right??

aand cud sum1 post a link where i can get full detailed solution for this paper ....
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Ganesh Ayyappan
·
1 year, 9 months ago

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Oh by the way results came out.
Go to isi Bangalore website and check out
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Kush Singhal
·
1 year, 9 months ago

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For 3rd break into cases like @Shivam Jadhav did. But he forgot some cases, the two cases gets 8 and 6 subcases more for a+b+c=0 and a=b respectively .
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Saarthak Marathe
·
1 year, 9 months ago

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How many questions do u need to get right to get qualify?
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Tarush Govil
·
1 year, 9 months ago

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Answer to 4th one is 40C3 - 20.34 - 40.36
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Easha Manideep D
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1 year, 9 months ago

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In Q 6, according to me, total no. of values of m are 8.
63^2 to 70^2. Verified.
In Q3, even i have written permutations of (2,-2,0), total 6. But it's wrong.
Someone pls do Q1 and 5. I wasted a lot of time on 1, have done something but couldn't conclude my answer. Pls do those 2 questions.
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Anoushka Gupta
·
1 year, 9 months ago

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Comment deleted
Dec 11, 2015

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@Brilliant Member
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My solution for 4th!(Tell mewhat is wrong in my solution)-(I'm writing in short)
There are 40 ways to select 1st object!
There are 36 ways to select 2nd!
And ,32 ways to select the 3rd!
In total there are 40×36×32=46080 ways!!
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Naitik Sanghavi
·
1 year, 9 months ago

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@Naitik Sanghavi
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There is a mistake. If the second object is two places away from the first object, you count the restricted object twice. Sorry. Good luck for getting selected.
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Brilliant Member
·
1 year, 9 months ago

@Naitik Sanghavi
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Also I don't think you can multiply 40 and 36 and so on because there will be several cases in which you choose the Same object. I just realized that repetitions are not allowed as they are placed around a circle. Hard luck.
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Brilliant Member
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1 year, 9 months ago

@Shashank Rammoorthy
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Count the number of integers greater than a square above \(63^2\) and which is strictly lesser than the next square by 125...
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Kush Singhal
·
1 year, 9 months ago

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Please tell your answers to 3,4,6 questions!!
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Naitik Sanghavi
·
1 year, 9 months ago

@Brilliant Member
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I solved 3,4,6
3rd is right!(One case left)
6th is half (or less than that)Wrong!
4th don't know
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Naitik Sanghavi
·
1 year, 9 months ago

## Comments

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TopNewestAnswer to question 3.\[a^{2}-b^{2}=c(b-a)\] This implies \[a+b+c=0 ...or... a=b\]

Case 1\[a+b+c=0\] Solutions are \[(a,b,c)=(2,0,-2),(-2,0,2),(0,2,-2),(0,-2,2),(2,2,0),(2,-2,0),(-2,2,0),(-2,-2,0).\]Case 2\[a=b \] Therefore \[(a,b,c)=(2,2,0),(-2,-2,0).\]. – Shivam Jadhav · 1 year, 9 months agoLog in to reply

– Brilliant Member · 1 year, 9 months ago

There is also two more solutions when a=b, (1,1,-3) and (-1,-1,3)Log in to reply

– Ranjana Kasangeri · 1 year, 9 months ago

Two more solutions! (4,4,3) and (-4,-4,-3)Log in to reply

@naitik sanghavi @Ranjana Kasangeri @Ganesh Ayyappan @Kush Singhal @easha manideep d Official answer key has been declared click here. – Brilliant Member · 1 year, 9 months ago

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– Naitik Sanghavi · 1 year, 9 months ago

Thanks !!!Log in to reply

– Easha Manideep D · 1 year, 9 months ago

Thanks but can you please search key for RMO telangana region. I am too busy ok. THANKS!!!Log in to reply

– Ganesh Ayyappan · 1 year, 9 months ago

thanksLog in to reply

– Kush Singhal · 1 year, 9 months ago

Thanx :DLog in to reply

– Brilliant Member · 1 year, 9 months ago

How many did you solve? Do you have any idea what is the cut-off and when the results will be declared?Log in to reply

– Kush Singhal · 1 year, 9 months ago

I think I got none :/Log in to reply

Check Answer key by Resonance !! – Naitik Sanghavi · 1 year, 9 months ago

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– Brilliant Member · 1 year, 9 months ago

Can you send the link please?Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

pccp.resonance.ac.inLog in to reply

In 6th one the difference between two consecutive squares must be greater than 125. Then you can find step of sqrt m becomes step of sqrt of m + 125 which the smaller square in which m, m+125 lies. I gave a hint.

ENJOY!!!! – Easha Manideep D · 1 year, 9 months ago

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aand cud sum1 post a link where i can get full detailed solution for this paper .... – Ganesh Ayyappan · 1 year, 9 months ago

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Oh by the way results came out. Go to isi Bangalore website and check out – Kush Singhal · 1 year, 9 months ago

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For 3rd break into cases like @Shivam Jadhav did. But he forgot some cases, the two cases gets 8 and 6 subcases more for a+b+c=0 and a=b respectively . – Saarthak Marathe · 1 year, 9 months ago

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How many questions do u need to get right to get qualify? – Tarush Govil · 1 year, 9 months ago

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Answer to 4th one is 40C3 - 20.34 - 40.36 – Easha Manideep D · 1 year, 9 months ago

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In Q 6, according to me, total no. of values of m are 8. 63^2 to 70^2. Verified. In Q3, even i have written permutations of (2,-2,0), total 6. But it's wrong. Someone pls do Q1 and 5. I wasted a lot of time on 1, have done something but couldn't conclude my answer. Pls do those 2 questions. – Anoushka Gupta · 1 year, 9 months ago

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– Naitik Sanghavi · 1 year, 9 months ago

My solution for 4th!(Tell mewhat is wrong in my solution)-(I'm writing in short) There are 40 ways to select 1st object! There are 36 ways to select 2nd! And ,32 ways to select the 3rd! In total there are 40×36×32=46080 ways!!Log in to reply

– Brilliant Member · 1 year, 9 months ago

There is a mistake. If the second object is two places away from the first object, you count the restricted object twice. Sorry. Good luck for getting selected.Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

So this case can be taken separately!and then we can solve ??Log in to reply

– Brilliant Member · 1 year, 9 months ago

Also I don't think you can multiply 40 and 36 and so on because there will be several cases in which you choose the Same object. I just realized that repetitions are not allowed as they are placed around a circle. Hard luck.Log in to reply

– Anoushka Gupta · 1 year, 9 months ago

Yes, even I realized just after writing this comment, hard luck.Log in to reply

When will the results be out? – Shashank Rammoorthy · 1 year, 9 months ago

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The 6th question's answer is 73 I think... – Kush Singhal · 1 year, 9 months ago

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– Ranjana Kasangeri · 1 year, 9 months ago

Well, may be its 72! Please add the list of numbers if you can!Log in to reply

– Kush Singhal · 1 year, 9 months ago

I got it wrong :( It's 72...Log in to reply

– Shashank Rammoorthy · 1 year, 9 months ago

How?Log in to reply

– Kush Singhal · 1 year, 9 months ago

Count the number of integers greater than a square above \(63^2\) and which is strictly lesser than the next square by 125...Log in to reply

Please tell your answers to 3,4,6 questions!! – Naitik Sanghavi · 1 year, 9 months ago

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– Adarsh Kumar · 1 year, 9 months ago

But 40 c 3 =9880Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

In 4th ,my answer is 46080Log in to reply

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– Adarsh Kumar · 1 year, 9 months ago

But your number is too large.Just look at your number once.Log in to reply

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– Adarsh Kumar · 1 year, 9 months ago

I solved 3 perfectly but have a doubt in the combi one,if that is correct then 4.Log in to reply

– Brilliant Member · 1 year, 9 months ago

Did you also have the same paper?Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

You solved 3 perfectly ,you will surely appear for INMO!0Log in to reply

@Nihar Mahajan @Saarthak Marathe @Shrihari B @Harsh Shrivastava @Dev Sharma @Swapnil Das – Brilliant Member · 1 year, 9 months ago

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– Harsh Shrivastava · 1 year, 9 months ago

How many did you solved?Log in to reply

– Brilliant Member · 1 year, 9 months ago

Completely left question no.1 and did question no.5 with less than 5 minutes left :(Log in to reply

– Brilliant Member · 1 year, 9 months ago

solved 3 not sure about question no.4Log in to reply

– Harsh Shrivastava · 1 year, 9 months ago

Which 3?Log in to reply

– Brilliant Member · 1 year, 9 months ago

What do you think would be the cutoff for this paper?Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

I think minimum would be 34-40,and maximum 45-51!Log in to reply

– Shashank Rammoorthy · 1 year, 9 months ago

So is 34 like 2 questions fully right?Log in to reply

– Brilliant Member · 1 year, 9 months ago

yesLog in to reply

– Brilliant Member · 1 year, 9 months ago

How many did you solve?Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

In 3,i left one case where a=b!Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

I solved 3,4,6 3rd is right!(One case left) 6th is half (or less than that)Wrong! 4th don't knowLog in to reply

– Brilliant Member · 1 year, 9 months ago

You too had the same paper!Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

Each region had very similar paper!!Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

Yes but I'm from GujaratLog in to reply

– Brilliant Member · 1 year, 9 months ago

How about you?Log in to reply

– Brilliant Member · 1 year, 9 months ago

2,3,6Log in to reply