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

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


1. numbered
2. list

numbered
list

Note: you must add a full line of space before and after lists for them to show up correctly

paragraph 1

paragraph 2

paragraph 1

paragraph 2

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

example link

> This is a quote

This is a quote

    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"

# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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

Akshat Sharda - 5 years, 8 months ago

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

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

Nihar Mahajan - 5 years, 8 months ago

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

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

Aditya Kumar - 5 years, 8 months ago

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

naitik sanghavi - 5 years, 8 months ago

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

Mehul Arora - 5 years, 8 months ago

@Mehul Arora – 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!!

@Naitik Sanghavi – I think this must be pre-pre-pre-pre RMO lol

@Nihar Mahajan – Lol yes. ${Pre}^ {\infty}$ RMO :P

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

@Nihar Mahajan – Do you go school everyday?

@Naitik Sanghavi – Yes. Why ask?

@Nihar Mahajan – He doubted your capability to go to school :3

@Nihar Mahajan – 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!!

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

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

@Akshat Sharda – Yes. There are two possibilities.

@Akshat Sharda – I was also confused with this ,that which option I should I go for???

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

Akshay Yadav - 5 years, 8 months ago

I agree !!

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

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

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

@Mehul Arora – They both are same.

@Nihar Mahajan – Oh yeah :3

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

Can anyone please explain 12th one? Thanks

Aaryaman Gupta - 5 years, 8 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, $\angle DEF=45°$

@Akshat Sharda – Did you solve the 13th?

@Naitik Sanghavi – Nope!!

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

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

@Aaryaman Gupta – Gave the same solution!!Just wanted to check my answer!!!

@Naitik Sanghavi – @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,

@Mehul Arora – Thanks ,I also chose this answer only!!

@Mehul Arora – Oh......Yes !!

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

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.

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

Actually, I added and subtracted 129

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

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

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

I have edited the note with subjective part!!

@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!!

most answers are wrong

Dibyam Parida - 3 years, 10 months ago

Is it 384 or 385?

Adarsh Kumar - 5 years, 8 months ago

384 was written in the paper!!

OHK!

@Adarsh Kumar – Did you solve it?

@Naitik Sanghavi – No,lemme try.I had solved it for $385$ .

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

Can you please post all questions?

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...

Sure. Please do.

And do you have the answers?

@Mehul Arora – No,I have given it today only so no answers!!

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

Q3) Link

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

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 $a>b$ .

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

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

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

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

Saarthak Marathe - 5 years, 8 months ago

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

A Former Brilliant Member - 5 years, 8 months ago

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

Did you get the results?

A Former Brilliant Member - 5 years, 7 months ago

@A Former Brilliant Member – 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!!!!!!!

naitik sanghavi - 5 years, 7 months ago

@A Former Brilliant Member – 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!

@Naitik Sanghavi – Congratulations!!

@A Former Brilliant Member – Thanks!!

@Naitik Sanghavi – Wow sooooooo many people wrote PRE-RMO from Gujarat!!!!

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

Saarthak Marathe - 5 years, 7 months ago

Great ! Congrats...

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

Bhaskar Pandey - 3 years, 11 months ago

pls send me all answers i want to check

Tejash surapaneni - 4 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$