# 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
4 years, 10 months ago

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Sort by:

- 2 years, 11 months ago

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

- 3 years ago

pls send me all answers i want to check

- 3 years, 9 months ago

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

- 4 years, 9 months ago

Great ! Congrats...

- 4 years, 9 months ago

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

- 4 years, 9 months ago

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

- 4 years, 9 months ago

Did you get the results?

- 4 years, 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!

- 4 years, 9 months ago

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

- 4 years, 9 months ago

Congratulations!!

- 4 years, 9 months ago

Thanks!!

- 4 years, 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!!!!!!!

- 4 years, 9 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

@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!!

- 4 years, 10 months ago

$I^{st}$ 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$\rightarrow B$

- 4 years, 10 months ago

Can anyone please explain 12th one? Thanks

- 4 years, 10 months ago

In $\triangle ABC$,

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

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

$\Rightarrow x+y=135°$

Therefore, $\angle DEF=45°$

- 4 years, 10 months ago

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

- 4 years, 10 months ago

Did you solve the 13th?

- 4 years, 10 months ago

Nope!!

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months 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,

- 4 years, 10 months ago

Oh......Yes !!

- 4 years, 10 months ago

Thanks ,I also chose this answer only!!

- 4 years, 10 months ago

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

They both are same.

- 4 years, 10 months ago

Oh yeah :3

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

I agree !!

- 4 years, 10 months ago

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

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

- 4 years, 10 months ago

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

- 4 years, 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!!

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

Yes. There are two possibilities.

- 4 years, 10 months ago

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

- 4 years, 10 months ago

Do you go school everyday?

- 4 years, 10 months ago

- 4 years, 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!!

- 4 years, 10 months ago

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

- 4 years, 10 months ago

He doubted your capability to go to school :3

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months 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 $24$.

- 4 years, 10 months 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 $a>b$.

- 4 years, 10 months ago

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

- 4 years, 10 months ago

- 4 years, 10 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.

- 4 years, 10 months ago

I have edited the note with subjective part!!

- 4 years, 10 months ago

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

- 4 years, 10 months ago

Actually, I added and subtracted 129

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

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

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

- 4 years, 10 months ago

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

Can you please post all questions?

- 4 years, 10 months 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...

- 4 years, 10 months ago

And do you have the answers?

- 4 years, 10 months ago

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

- 4 years, 10 months ago

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

- 4 years, 10 months ago

Is it 384 or 385?

- 4 years, 10 months ago

384 was written in the paper!!

- 4 years, 10 months ago

OHK!

- 4 years, 10 months ago

Did you solve it?

- 4 years, 10 months ago

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

- 4 years, 10 months ago
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