Pre-RMO 2015 Gujarat Region

Part-A(Subjective)

1)If x=2+3x=2+\sqrt{3} then find the value of (x1)3x2+x+1\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 :x3+9x257x384\large x^{3}+9x^2-57x-384.

5)If a2+b2=208\large a^{2}+b^{2}=208,ab=96 and a>b>0.Then find the value of a2b2\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 x2=yz,y2=zx,z2=xy\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)12+2232+.....20152+20162=2017×n\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 ,B=90°\angle B = 90°,D,E,F are points that lie on AB,AC,CB respectively.AD=AE,CF=CE then DEF=?\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
3 years, 11 months ago

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IstI^{st} question305\rightarrow \frac{\sqrt{30}}{5}


IIndII^{nd} question14\rightarrow 14


IIIrdIII^{rd} question10\rightarrow 10


IVthIV^{th} question\rightarrow Cannot be factorized.


VthV^{th} question80\rightarrow 80


VIthVI^{th} question24\rightarrow 24


VIIthVII^{th} questionD\rightarrow D


VIIIthVIII^{th} questionB\rightarrow B


IXthIX^{th} question\rightarrow Two possibilities.


XthX^{th} questionB\rightarrow B


XIthXI^{th} questionA\rightarrow A


XIIthXII^{th} questionB\rightarrow B

Akshat Sharda - 3 years, 11 months 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 - 3 years, 11 months ago

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Yes !! You are right !! ¨\ddot \smile

Akshat Sharda - 3 years, 11 months ago

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

Aditya Kumar - 3 years, 11 months ago

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

naitik sanghavi - 3 years, 11 months ago

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

Mehul Arora - 3 years, 11 months 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 - 3 years, 11 months ago

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

Nihar Mahajan - 3 years, 11 months ago

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

Mehul Arora - 3 years, 11 months 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 - 3 years, 11 months ago

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@Nihar Mahajan Do you go school everyday?

naitik sanghavi - 3 years, 11 months ago

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@Naitik Sanghavi Yes. Why ask?

Nihar Mahajan - 3 years, 11 months ago

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

Mehul Arora - 3 years, 11 months 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 - 3 years, 11 months 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 - 3 years, 11 months ago

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@Naitik Sanghavi In question 99 there are two possible answers\rightarrowWednesday OR Thursday. So what do u think BB or DD?

Akshat Sharda - 3 years, 11 months ago

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@Akshat Sharda Yes. There are two possibilities.

Mehul Arora - 3 years, 11 months ago

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

naitik sanghavi - 3 years, 11 months 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 - 3 years, 11 months ago

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I agree !!

Akshat Sharda - 3 years, 10 months ago

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How did you get 6 as your answer for (1)?I'm getting 305\large \frac{\sqrt{30}}{5}.

naitik sanghavi - 3 years, 11 months ago

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

Akshat Sharda - 3 years, 11 months ago

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how did you get 305\dfrac {\sqrt {30}}{5}? I got 65\sqrt {\dfrac {6}{5}}

Mehul Arora - 3 years, 11 months ago

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@Mehul Arora They both are same.

Nihar Mahajan - 3 years, 11 months ago

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@Nihar Mahajan Oh yeah :3

Mehul Arora - 3 years, 11 months ago

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

naitik sanghavi - 3 years, 11 months ago

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Can anyone please explain 12th one? Thanks

Aaryaman Gupta - 3 years, 10 months ago

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In ABC\triangle ABC,

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

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

x+y=135°\Rightarrow x+y=135°

Therefore, DEF=45°\angle DEF=45°

Akshat Sharda - 3 years, 10 months ago

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@Akshat Sharda Did you solve the 13th?

naitik sanghavi - 3 years, 10 months ago

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@Naitik Sanghavi Nope!!

Akshat Sharda - 3 years, 10 months ago

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

naitik sanghavi - 3 years, 10 months ago

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

Aaryaman Gupta - 3 years, 10 months ago

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

naitik sanghavi - 3 years, 10 months 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 - 3 years, 10 months ago

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

naitik sanghavi - 3 years, 10 months ago

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

Akshat Sharda - 3 years, 10 months ago

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

Aaryaman Gupta - 3 years, 10 months ago

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Q1 ) I'm not very sure, but is the answer could be (x+9)(x257)+129(x+9)(x^2-57)+129

Q2) I guess both Thursday and Wednesday are possibilities.

Mehul Arora - 3 years, 11 months ago

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

naitik sanghavi - 3 years, 11 months ago

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Actually, I added and subtracted 129

So the given polynomial becomes x3+9x57x517+129x^3 + 9x -57x -517 +129

x2(x+9)57(x+9)+129x^2(x+9)-57(x+9) +129

(x2+9)(x57)+129(x^2+9)(x-57) +129

Mehul Arora - 3 years, 11 months ago

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I have edited the note with subjective part!!

naitik sanghavi - 3 years, 11 months ago

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@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 - 3 years, 11 months ago

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most answers are wrong

Dibyam Parida - 2 years ago

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Is it 384 or 385?

Adarsh Kumar - 3 years, 11 months ago

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384 was written in the paper!!

naitik sanghavi - 3 years, 11 months ago

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OHK!

Adarsh Kumar - 3 years, 11 months ago

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@Adarsh Kumar Did you solve it?

naitik sanghavi - 3 years, 11 months ago

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@Naitik Sanghavi No,lemme try.I had solved it for 385385.

Adarsh Kumar - 3 years, 11 months ago

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

Can you please post all questions?

Mehul Arora - 3 years, 11 months 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 - 3 years, 11 months ago

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Sure. Please do.

And do you have the answers?

Mehul Arora - 3 years, 11 months ago

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

naitik sanghavi - 3 years, 11 months ago

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

Mehul Arora - 3 years, 11 months ago

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Q3) Link

Nihar Mahajan - 3 years, 11 months ago

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

Nihar Mahajan - 3 years, 11 months ago

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Q5) This is quite straightforward. Just use expansions of (a+b)2,(ab)2(a+b)^2 , (a-b)^2 and then compute the product (ab)(a+b)(a-b)(a+b) to get ±80\pm80. But discard 80-80 since a>ba>b.

Nihar Mahajan - 3 years, 11 months ago

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Q6) Let the required 2 digit number be xx. Then form a linear equation: 27x=2(300+x)27x=2(300+x) and solve for xx to get 2424.

Nihar Mahajan - 3 years, 11 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)(x,y,z)=(0,0,0) , (1,1,1) , (2,2,2) , (3,3,3)

Mehul Arora - 3 years, 11 months ago

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

naitik sanghavi - 3 years, 11 months 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 - 3 years, 10 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 - 3 years, 10 months ago

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

naitik sanghavi - 3 years, 10 months ago

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Did you get the results?

Brilliant Member - 3 years, 10 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 - 3 years, 10 months 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 - 3 years, 10 months ago

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@Naitik Sanghavi Congratulations!!

Brilliant Member - 3 years, 10 months ago

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@Brilliant Member Thanks!!

naitik sanghavi - 3 years, 10 months ago

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

Brilliant Member - 3 years, 10 months ago

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

Saarthak Marathe - 3 years, 9 months ago

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Great ! Congrats...

naitik sanghavi - 3 years, 9 months ago

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

Bhaskar Pandey - 2 years, 1 month ago

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pls send me all answers i want to check

Tejash surapaneni - 2 years, 10 months ago

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