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
```

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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\(\rightarrow B\)

Log in to reply

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

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

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

Can anyone please explain 12th one? Thanks

Log in to reply

In \(\triangle ABC\),

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

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

\(\Rightarrow x+y=135°\)

Therefore, \(\angle DEF=45°\)

Log in to reply

Log in to reply

Log in to reply

Log in to reply

@Mehul Arora @Nihar Mahajan

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

Log in to reply

Log in to reply

@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,

Log in to reply

Log in to reply

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply

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

Log in to reply

I agree !!

Log in to reply

most answers are wrong

Log in to reply

@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!!

Log in to reply

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.

Log in to reply

I have edited the note with subjective part!!

Log in to reply

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

Log in to reply

Actually, I added and subtracted 129

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

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

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

Log in to reply

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

Log in to reply

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

Log in to reply

Great ! Congrats...

Log in to reply

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

Log in to reply

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

Log in to reply

Did you get the results?

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

Q6) Let the required 2 digit number be \(x\). Then form a linear equation: \(27x=2(300+x)\) and solve for \(x\) to get \(24\).

Log in to reply

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 \(a>b\).

Log in to reply

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

Log in to reply

Q3) Link

Log in to reply

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

Can you please post all questions?

Log in to reply

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...

Log in to reply

Sure. Please do.

And do you have the answers?

Log in to reply

Log in to reply

Log in to reply

Is it 384 or 385?

Log in to reply

384 was written in the paper!!

Log in to reply

OHK!

Log in to reply

Log in to reply

Log in to reply

pls send me all answers i want to check

Log in to reply