Part-A(Subjective)

1)If *\(x=2+\sqrt{3}\)* then find the value of *\(\large \frac{(x-1)\sqrt{3}}{\sqrt{x^{2}+x+1}}\)*.

2)In a class 36 students took an exam,the average score of the students who passed in the exam was 60,while the average score of the students who failed the exam was 42.The average scores of all students was 53.Find the number of students who failed in the exam.

3)*1!3!5!7!=n!*. Find the value of *n*.

4)Factorize :*\(\large x^{3}+9x^2-57x-384\)*.

5)If *\(\large a^{2}+b^{2}=208\)*,*ab=96* and a>b>0.Then find the value of *\(\large a^{2}-b^{2}\)*.

6)There is a two digit number such that if you put 3 on the left side of the ten's digit you will get a three digit number. Two times the three digit number is 27 times the two digit number ,Then fin the two-digit number.

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Part -B(Objective)
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7)The number of solutions of \(\large x^{2}=yz,y^{2}=zx,z^{2}=xy\). For **x≤3** and x,y,z are positive integers.
A)0. B)1. C)2. D)3

8)\(\large -1^{2}+2^{2}-3^{2}+.....-2015^{2}+2016^{2}=2017×n\) .Then find *n*.
A)1007. B)1008. C)1009. D)1006

9)In a certain year,the month of December has four Thursdays and four Saturdays.Then what day would be on the1st day of January next year? A)Monday. B)Thursday. C)Friday. D)None of these.

10)In a rectangle if the length is increased by 20% and width is decreased by 20% then what will be the change in its area? A)No change. B)4% decrease. C)5% increase. D)None of these

11)The number of three digit multiples of 3? A)300. B)330. C)333. D)None of these

12)In ΔABC ,\(\angle B = 90°\),D,E,F are points that lie on AB,AC,CB respectively.AD=AE,CF=CE then \(\angle DEF= ?\). A)30° B)45° C)60° D)90°

13)In a cupboard there are seven compartments.Two identical balls are placed in the cupboard such that each compartment can have at most one ball.In how many ways can this be done?(A)17(B)18(C)20(D)21

14)I don't remember this question!!

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## Comments

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TopNewest\(I^{st}\) question\(\rightarrow \frac{\sqrt{30}}{5}\)

\(II^{nd}\) question\(\rightarrow 14\)

\(III^{rd}\) question\(\rightarrow 10\)

\(IV^{th}\) question\(\rightarrow\) Cannot be factorized.

\(V^{th}\) question\(\rightarrow 80\)

\(VI^{th}\) question\(\rightarrow 24\)

\(VII^{th}\) question\(\rightarrow D\)

\(VIII^{th}\) question\(\rightarrow B\)

\(IX^{th}\) question\(\rightarrow\) Two possibilities.

\(X^{th}\) question\(\rightarrow B\)

\(XI^{th}\) question\(\rightarrow A\)

\(XII^{th}\) question\(\rightarrow B\) – Akshat Sharda · 1 year, 10 months ago

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@naitik sanghavi I can't believe this is really Pre-RMO lol – Nihar Mahajan · 1 year, 10 months ago

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@Nihar Mahajan This is really easy. I can't believe that the cutoff is 40. – Mehul Arora · 1 year, 10 months ago

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– Naitik Sanghavi · 1 year, 10 months ago

Yeah!!Cutoff is 40 for our region and each subjective question carries 6 marks while each objective question carries 8 marks!! I know it was very easy so I didn't post all questions at first!!Log in to reply

– Akshat Sharda · 1 year, 10 months ago

In question \(9\) there are two possible answers\(\rightarrow\)Wednesday OR Thursday. So what do u think \(B\) or \(D\)?Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

I was also confused with this ,that which option I should I go for???Log in to reply

– Mehul Arora · 1 year, 10 months ago

Yes. There are two possibilities.Log in to reply

– Nihar Mahajan · 1 year, 10 months ago

I think this must be pre-pre-pre-pre RMO lolLog in to reply

– Naitik Sanghavi · 1 year, 10 months ago

Do you go school everyday?Log in to reply

– Nihar Mahajan · 1 year, 10 months ago

Yes. Why ask?Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

I asked coz I was surprised how could you all do so much study with school work!!I mean I have just learnt some of the topics of 11-12 standard!!Log in to reply

– Nihar Mahajan · 1 year, 10 months ago

I study school stuff , just before the day of school exams. (Its an irony that I score well :P)Log in to reply

– Mehul Arora · 1 year, 10 months ago

He doubted your capability to go to school :3Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

This is a good way of selecting the 9th standard students .So they can also participate in RMO!!!Log in to reply

– Mehul Arora · 1 year, 10 months ago

Lol yes. \({Pre}^ {\infty}\) RMO :PLog in to reply

– Naitik Sanghavi · 1 year, 10 months ago

Yes,our region's pre-rmo was damn easy!! And the cutoff is just 40!!Log in to reply

– Aditya Kumar · 1 year, 10 months ago

Guess what last year's pre rmo cut off was 8/20. Couldn't resist my laughter.Log in to reply

– Akshat Sharda · 1 year, 10 months ago

Yes !! You are right !! \(\ddot \smile\)Log in to reply

– Aaryaman Gupta · 1 year, 10 months ago

Can anyone please explain 12th one? ThanksLog in to reply

In \(\triangle ABC\),

\( \Rightarrow \angle A+\angle B+\angle C=180°\)

\(\Rightarrow 180°-2x+90°+180°-2y=180°\)

\(\Rightarrow x+y=135°\)

Therefore, \(\angle DEF=45°\) – Akshat Sharda · 1 year, 10 months ago

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– Aaryaman Gupta · 1 year, 10 months ago

Thanks a lot! I realized it was much easier than what i earlier thought.Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

Did you solve the 13th?Log in to reply

– Akshat Sharda · 1 year, 10 months ago

Nope!!Log in to reply

@Mehul Arora @Nihar Mahajan – Naitik Sanghavi · 1 year, 10 months ago

Ok!!Did anyone else solve this?Log in to reply

– Aaryaman Gupta · 1 year, 10 months ago

13th one is 7C2 = (7!)/(5! * 2!) = (7*6)/(2) = 21Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

Gave the same solution!!Just wanted to check my answer!!!Log in to reply

@naitik sanghavi The question basically asks for choosing two of the seven compartments to keep a ball in. So according to me, the answer should be 21, – Mehul Arora · 1 year, 10 months ago

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– Akshat Sharda · 1 year, 10 months ago

Oh......Yes !!Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

Thanks ,I also chose this answer only!!Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

What about 13th question?I want to check my answers!!Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

How did you get 6 as your answer for (1)?I'm getting \(\large \frac{\sqrt{30}}{5}\).Log in to reply

– Akshat Sharda · 1 year, 10 months ago

Yes ... you're right...actually I forgot the square root :-(Log in to reply

– Mehul Arora · 1 year, 10 months ago

how did you get \(\dfrac {\sqrt {30}}{5}\)? I got \(\sqrt {\dfrac {6}{5}}\)Log in to reply

– Nihar Mahajan · 1 year, 10 months ago

They both are same.Log in to reply

– Mehul Arora · 1 year, 10 months ago

Oh yeah :3Log in to reply

– Akshay Yadav · 1 year, 10 months ago

I don't understand why there is such a huge difference in level of Pre-RMO and RMO!🙀Log in to reply

– Akshat Sharda · 1 year, 10 months ago

I agree !!Log in to reply

Q1 ) I'm not very sure, but is the answer could be \((x+9)(x^2-57)+129\)

Q2) I guess both Thursday and Wednesday are possibilities. – Mehul Arora · 1 year, 10 months ago

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– Naitik Sanghavi · 1 year, 10 months ago

I have edited the note with subjective part!!Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

How did you get the answer for first?coz it was asked in subjective part!!Log in to reply

So the given polynomial becomes \(x^3 + 9x -57x -517 +129\)

\(x^2(x+9)-57(x+9) +129\)

\((x^2+9)(x-57) +129\) – Mehul Arora · 1 year, 10 months ago

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4th Question is the direct application of Eisenstein's Criterion. – Bhaskar Pandey · 6 days, 10 hours ago

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In this year's Mumbai pre-RMO I got 19/20 – Saarthak Marathe · 1 year, 8 months ago

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– Naitik Sanghavi · 1 year, 8 months ago

Great ! Congrats...Log in to reply

@naitik sanghavi When are you going to get your results? (although I know that you will easily qualify) – Svatejas Shivakumar · 1 year, 9 months ago

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– Naitik Sanghavi · 1 year, 9 months ago

On question paper it was written that results will be available from 15th October on RMO Gujarat!Log in to reply

– Svatejas Shivakumar · 1 year, 9 months ago

Did you get the results?Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

The results are updated on https://sites.google.com/site/rmogujarat/. I got 84! (4)the question is given bonus to all .. I didn't attempt two questions,14th and 8th(very silly mistake) because I thought negative marking was there!Log in to reply

– Svatejas Shivakumar · 1 year, 9 months ago

Wow sooooooo many people wrote PRE-RMO from Gujarat!!!!Log in to reply

– Svatejas Shivakumar · 1 year, 9 months ago

Congratulations!!Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

Thanks!!Log in to reply

– Naitik Sanghavi · 1 year, 9 months ago

No, I don't why they are not publishing the results as they told to do so on 15th!!I'm waiting for the results from many days!!!!!!!Log in to reply

This is damn easy .pre-RMO of Mumbai region is better (even though this one is also easy). – Saarthak Marathe · 1 year, 9 months ago

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Q7) The answer should be 4. \((x,y,z)=(0,0,0) , (1,1,1) , (2,2,2) , (3,3,3)\) – Mehul Arora · 1 year, 10 months ago

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– Naitik Sanghavi · 1 year, 10 months ago

Sorry,forget to mention that x,y,z are positive integers!!Log in to reply

@Akshat Sharda @Akshay Yadav @Nihar Mahajan @Mehul Arora @Aditya Kumar @Anshuman Bais @Adarsh Kumar @Swapnil Das @Svatejas Shivakumar @Dev Sharma I have updated the note with the whole paper of Pre-RMO 2015 Gujarat Region!! – Naitik Sanghavi · 1 year, 10 months ago

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Q6) Let the required 2 digit number be \(x\). Then form a linear equation: \(27x=2(300+x)\) and solve for \(x\) to get \(24\). – Nihar Mahajan · 1 year, 10 months ago

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Q5) This is quite straightforward. Just use expansions of \((a+b)^2 , (a-b)^2\) and then compute the product \((a-b)(a+b)\) to get \(\pm80\). But discard \(-80\) since \(a>b\). – Nihar Mahajan · 1 year, 10 months ago

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Q4) Something's wrong with this. I think there can be a typo mistake. – Nihar Mahajan · 1 year, 10 months ago

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Q3) Link – Nihar Mahajan · 1 year, 10 months ago

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@naitik sanghavi Which region's Pre RMO is this?

Can you please post all questions? – Mehul Arora · 1 year, 10 months ago

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I do not have the question paper coz we had to attach it with the answer sheet!! Well!! I remember some of the questions which I can post here... – Naitik Sanghavi · 1 year, 10 months ago

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And do you have the answers? – Mehul Arora · 1 year, 10 months ago

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– Naitik Sanghavi · 1 year, 10 months ago

No,I have given it today only so no answers!!Log in to reply

– Mehul Arora · 1 year, 10 months ago

Okay. Please see to the answer I've given, and they might not be correct :)Log in to reply

Is it 384 or 385? – Adarsh Kumar · 1 year, 10 months ago

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– Naitik Sanghavi · 1 year, 10 months ago

384 was written in the paper!!Log in to reply

– Adarsh Kumar · 1 year, 10 months ago

OHK!Log in to reply

– Naitik Sanghavi · 1 year, 10 months ago

Did you solve it?Log in to reply

– Adarsh Kumar · 1 year, 10 months ago

No,lemme try.I had solved it for \(385\).Log in to reply

pls send me all answers i want to check – Tejash Surapaneni · 9 months, 1 week ago

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