# 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 ago

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Sort by:

$$I^{st}$$ 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 ago

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

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

- 3 years ago

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

- 3 years 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!!

- 3 years ago

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

- 3 years ago

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

- 3 years ago

Yes. There are two possibilities.

- 3 years ago

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

- 3 years ago

Do you go school everyday?

- 3 years ago

- 3 years 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!!

- 3 years ago

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

- 3 years ago

He doubted your capability to go to school :3

- 3 years ago

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

- 3 years ago

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

- 3 years ago

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

- 3 years ago

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

- 3 years ago

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

- 3 years ago

Can anyone please explain 12th one? Thanks

- 3 years ago

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 ago

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

- 3 years ago

Did you solve the 13th?

- 3 years ago

Nope!!

- 3 years ago

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

- 3 years ago

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

- 3 years ago

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

- 3 years ago

@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 ago

Oh......Yes !!

- 3 years ago

Thanks ,I also chose this answer only!!

- 3 years ago

- 3 years ago

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

- 3 years ago

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

- 3 years ago

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

- 3 years ago

They both are same.

- 3 years ago

Oh yeah :3

- 3 years ago

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

- 3 years ago

I agree !!

- 3 years ago

- 1 year, 2 months ago

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 ago

I have edited the note with subjective part!!

- 3 years ago

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

- 3 years ago

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 ago

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

- 1 year, 2 months ago

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

- 2 years, 11 months ago

Great ! Congrats...

- 2 years, 11 months ago

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

- 3 years ago

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

- 3 years ago

Did you get the results?

- 2 years, 12 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!

- 2 years, 11 months ago

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

- 2 years, 11 months ago

Congratulations!!

- 2 years, 11 months ago

Thanks!!

- 2 years, 11 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!!!!!!!

- 2 years, 12 months ago

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

- 3 years ago

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

- 3 years ago

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

- 3 years ago

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 ago

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 ago

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

- 3 years ago

- 3 years ago

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

Can you please post all questions?

- 3 years ago

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 ago

And do you have the answers?

- 3 years ago

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

- 3 years ago

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

- 3 years ago

Is it 384 or 385?

- 3 years ago

384 was written in the paper!!

- 3 years ago

OHK!

- 3 years ago

Did you solve it?

- 3 years ago

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

- 3 years ago

pls send me all answers i want to check

- 2 years ago