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Pre-RMO 2015 Gujarat Region

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.

                                                                  Part -B(Objective)

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!!

                                                                                                                End

Note by Naitik Sanghavi
2 years ago

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\(I^{st}\) 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 - 2 years ago

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Don't you think this Pre RMO is quite easy?

@naitik sanghavi I can't believe this is really Pre-RMO lol

Nihar Mahajan - 2 years ago

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@Nihar Mahajan This is really easy. I can't believe that the cutoff is 40.

Mehul Arora - 2 years ago

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@Mehul Arora 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!!

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi In question \(9\) there are two possible answers\(\rightarrow\)Wednesday OR Thursday. So what do u think \(B\) or \(D\)?

Akshat Sharda - 2 years ago

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@Akshat Sharda I was also confused with this ,that which option I should I go for???

Naitik Sanghavi - 2 years ago

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@Akshat Sharda Yes. There are two possibilities.

Mehul Arora - 2 years ago

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@Naitik Sanghavi I think this must be pre-pre-pre-pre RMO lol

Nihar Mahajan - 2 years ago

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@Nihar Mahajan Do you go school everyday?

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi Yes. Why ask?

Nihar Mahajan - 2 years ago

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@Nihar Mahajan 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!!

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi I study school stuff , just before the day of school exams. (Its an irony that I score well :P)

Nihar Mahajan - 2 years ago

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@Nihar Mahajan He doubted your capability to go to school :3

Mehul Arora - 2 years ago

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@Nihar Mahajan This is a good way of selecting the 9th standard students .So they can also participate in RMO!!!

Naitik Sanghavi - 2 years ago

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@Nihar Mahajan Lol yes. \({Pre}^ {\infty}\) RMO :P

Mehul Arora - 2 years ago

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

Naitik Sanghavi - 2 years ago

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

Aditya Kumar - 2 years ago

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Yes !! You are right !! \(\ddot \smile\)

Akshat Sharda - 2 years ago

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Can anyone please explain 12th one? Thanks

Aaryaman Gupta - 2 years ago

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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 - 2 years ago

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@Akshat Sharda Thanks a lot! I realized it was much easier than what i earlier thought.

Aaryaman Gupta - 2 years ago

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@Akshat Sharda Did you solve the 13th?

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi Nope!!

Akshat Sharda - 2 years ago

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@Akshat Sharda Ok!!Did anyone else solve this?@Mehul Arora @Nihar Mahajan

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi 13th one is 7C2 = (7!)/(5! * 2!) = (7*6)/(2) = 21

Aaryaman Gupta - 2 years ago

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@Aaryaman Gupta Gave the same solution!!Just wanted to check my answer!!!

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi @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 - 2 years ago

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@Mehul Arora Oh......Yes !!

Akshat Sharda - 2 years ago

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@Mehul Arora Thanks ,I also chose this answer only!!

Naitik Sanghavi - 2 years ago

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

Naitik Sanghavi - 2 years ago

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

Naitik Sanghavi - 2 years ago

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Yes ... you're right...actually I forgot the square root :-(

Akshat Sharda - 2 years ago

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

Mehul Arora - 2 years ago

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@Mehul Arora They both are same.

Nihar Mahajan - 2 years ago

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@Nihar Mahajan Oh yeah :3

Mehul Arora - 2 years ago

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

Akshay Yadav - 2 years ago

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I agree !!

Akshat Sharda - 2 years ago

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most answers are wrong

Dibyam Parida - 2 months ago

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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 - 2 years ago

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I have edited the note with subjective part!!

Naitik Sanghavi - 2 years ago

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

Naitik Sanghavi - 2 years ago

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Actually, I added and subtracted 129

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 - 2 years ago

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4th Question is the direct application of Eisenstein's Criterion.

Bhaskar Pandey - 3 months ago

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In this year's Mumbai pre-RMO I got 19/20

Saarthak Marathe - 1 year, 11 months ago

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Great ! Congrats...

Naitik Sanghavi - 1 year, 11 months ago

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@naitik sanghavi When are you going to get your results? (although I know that you will easily qualify)

Brilliant Member - 2 years ago

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

Naitik Sanghavi - 2 years ago

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Did you get the results?

Brilliant Member - 2 years ago

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@Brilliant Member 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!

Naitik Sanghavi - 1 year, 12 months ago

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@Naitik Sanghavi Wow sooooooo many people wrote PRE-RMO from Gujarat!!!!

Brilliant Member - 1 year, 12 months ago

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@Naitik Sanghavi Congratulations!!

Brilliant Member - 1 year, 12 months ago

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@Brilliant Member Thanks!!

Naitik Sanghavi - 1 year, 12 months ago

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@Brilliant Member 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!!!!!!!

Naitik Sanghavi - 2 years ago

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This is damn easy .pre-RMO of Mumbai region is better (even though this one is also easy).

Saarthak Marathe - 2 years 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 - 2 years ago

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

Naitik Sanghavi - 2 years 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 - 2 years 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 - 2 years ago

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Q4) Something's wrong with this. I think there can be a typo mistake.

Nihar Mahajan - 2 years ago

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Q3) Link

Nihar Mahajan - 2 years ago

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

Can you please post all questions?

Mehul Arora - 2 years ago

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Pre-RMO Gujarat ...

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 - 2 years ago

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Sure. Please do.

And do you have the answers?

Mehul Arora - 2 years ago

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@Mehul Arora No,I have given it today only so no answers!!

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi Okay. Please see to the answer I've given, and they might not be correct :)

Mehul Arora - 2 years ago

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Is it 384 or 385?

Adarsh Kumar - 2 years ago

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384 was written in the paper!!

Naitik Sanghavi - 2 years ago

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OHK!

Adarsh Kumar - 2 years ago

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@Adarsh Kumar Did you solve it?

Naitik Sanghavi - 2 years ago

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@Naitik Sanghavi No,lemme try.I had solved it for \(385\).

Adarsh Kumar - 2 years ago

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pls send me all answers i want to check

Tejash Surapaneni - 1 year ago

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