# 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
3 years, 3 months ago

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## Comments

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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$$\rightarrow B$$

- 3 years, 3 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

- 3 years, 3 months ago

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Yes !! You are right !! $$\ddot \smile$$

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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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!!

- 3 years, 3 months ago

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I think this must be pre-pre-pre-pre RMO lol

- 3 years, 3 months ago

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Lol yes. $${Pre}^ {\infty}$$ RMO :P

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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Do you go school everyday?

- 3 years, 3 months ago

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Yes. Why ask?

- 3 years, 3 months ago

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He doubted your capability to go to school :3

- 3 years, 3 months ago

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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!!

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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In question $$9$$ there are two possible answers$$\rightarrow$$Wednesday OR Thursday. So what do u think $$B$$ or $$D$$?

- 3 years, 3 months ago

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Yes. There are two possibilities.

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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I agree !!

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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They both are same.

- 3 years, 3 months ago

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Oh yeah :3

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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Can anyone please explain 12th one? Thanks

- 3 years, 3 months 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, $$\angle DEF=45°$$

- 3 years, 3 months ago

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Did you solve the 13th?

- 3 years, 3 months ago

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Nope!!

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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Gave the same solution!!Just wanted to check my answer!!!

- 3 years, 3 months ago

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@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,

- 3 years, 3 months ago

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Thanks ,I also chose this answer only!!

- 3 years, 3 months ago

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Oh......Yes !!

- 3 years, 3 months ago

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

- 3 years, 3 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.

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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Actually, I added and subtracted 129

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

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

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

- 3 years, 3 months ago

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I have edited the note with subjective part!!

- 3 years, 3 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!!

- 3 years, 3 months ago

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most answers are wrong

- 1 year, 5 months ago

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Is it 384 or 385?

- 3 years, 3 months ago

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384 was written in the paper!!

- 3 years, 3 months ago

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OHK!

- 3 years, 3 months ago

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Did you solve it?

- 3 years, 3 months ago

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No,lemme try.I had solved it for $$385$$.

- 3 years, 3 months ago

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

Can you please post all questions?

- 3 years, 3 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...

- 3 years, 3 months ago

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Sure. Please do.

And do you have the answers?

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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Q3) Link

- 3 years, 3 months ago

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

- 3 years, 3 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 $$a>b$$.

- 3 years, 3 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 $$24$$.

- 3 years, 3 months ago

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Q7) The answer should be 4. $$(x,y,z)=(0,0,0) , (1,1,1) , (2,2,2) , (3,3,3)$$

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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

- 3 years, 3 months ago

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Did you get the results?

- 3 years, 3 months ago

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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!!!!!!!

- 3 years, 3 months ago

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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!

- 3 years, 2 months ago

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Congratulations!!

- 3 years, 2 months ago

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Thanks!!

- 3 years, 2 months ago

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Wow sooooooo many people wrote PRE-RMO from Gujarat!!!!

- 3 years, 2 months ago

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

- 3 years, 2 months ago

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Great ! Congrats...

- 3 years, 2 months ago

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

- 1 year, 6 months ago

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pls send me all answers i want to check

- 2 years, 3 months ago

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