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.

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Part -B(Objective)
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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!!

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## Comments

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TopNewest\(I^{st}\) 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\(\rightarrow B\)

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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

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

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

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

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

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Can anyone please explain 12th one? Thanks

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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, \(\angle DEF=45°\)

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@Mehul Arora @Nihar Mahajan

Ok!!Did anyone else solve this?Log in to reply

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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,

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

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

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

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

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

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I agree !!

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most answers are wrong

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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!!

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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.

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I have edited the note with subjective part!!

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

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Actually, I added and subtracted 129

So the given polynomial becomes \(x^3 + 9x -57x -517 +129\)

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

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

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

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

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Great ! Congrats...

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

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

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Did you get the results?

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

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

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

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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 \(24\).

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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 \(a>b\).

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

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Q3) Link

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

Can you please post all questions?

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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...

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Sure. Please do.

And do you have the answers?

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Is it 384 or 385?

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384 was written in the paper!!

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OHK!

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pls send me all answers i want to check

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