CBSE GMO 2015 Paper discussion

Group Mathematical Olympiad is conducted by CBSE . It is only for CBSE students . Every CBSE school can send 5 students for it. Around 30 students are selected from the country and are eligible to write INMO.

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

Sort by:

Top Newest

Answer to question 3. $\frac{6l-1}{4l-3}=\frac{7k-5}{5k-3}$ After cross multiplication we get $8k+l+lk=6$ Adding 8 to both sides $8k+8+l+lk=14$ $8(k+1)+l(1+k)=14$ $(8+l)(1+k)=14$ Since $l,k$ are integers therefore the solutions of $(l,k)=(-1,1),(-6,6),(6,0),(-7,13),(-15,-3),(-22,-2),(-10,-8),(-9,-15)$ Therefore the required fractions are $1,\frac{43}{31},\frac{5}{3},\frac{37}{27},\frac{13}{9},\frac{19}{13},\frac{61}{43},\frac{55}{39}$

Shivam Jadhav - 4 years, 11 months ago

Can anybody please post a proper solution for question $4$ with explanation?

Saurabh Mallik - 4 years, 10 months ago

Number of ways of selecting points from points is 28C3=3276

Now, we will eliminate some conditions..

Number of ways of selecting all 3 as adjacent points is 28.

Number of ways of selecting 2 adjacent points and one not adjacent with them is 28×24=672

Number of ways of selecting two points opposite diametrically along with the third point not adjacent to the former points is 14×22=308.

Hence, the desired result will be 3276-28-672-308=2268

Manisha Garg - 4 years, 10 months ago

1 will be rejected as it isn't a fraction.

Gaurav Manwani - 3 years, 1 month ago

Answer to question number 2. $P_{1}(m)-P_{2}(n)=a_{1}-a_{2}=\frac{2(b_{2}-b_{1})}{m-n}$ This implies that $a_{1}-a_{2}=even$ . $P_{1}(m)-P_{2}(n)=a_{1}+a_{2}=-2(m+n)$ This implies that $a_{1}+a_{2}=even$ . Hence proved.

Shivam Jadhav - 4 years, 11 months ago

when will the results of gmo will be declared

Nikhil Shah - 4 years, 11 months ago

Can anyone tell the answer of 5th question

Devansh Shah - 4 years, 11 months ago

it is 4/3

aryan goyat - 4 years, 11 months ago

I m getting 1/3

Devansh Shah - 4 years, 11 months ago

@Devansh Shah – see i can't post my solution because it is too long but you can verify it by construction.

aryan goyat - 4 years, 11 months ago

I was able to do 4.5 questions do i stand a chance to get selected...

Divyansh Choudhary - 4 years, 11 months ago

Is the answer to question 4 2268?

Divyansh Choudhary - 4 years, 11 months ago

Yes it is

Adarsh Kumar - 4 years, 11 months ago

Can you tell me what is the expected cutoff for gmo?

Divyansh Choudhary - 4 years, 11 months ago

Answer to question 6. Let $a=m+\frac{b}{c}$ where $m$ is any integer and $0<b<c$ . Then $a(a-3{a})=( m+\frac{b}{c})( m-2\frac{b}{c})$ $m^{2}-\frac{bm}{c}+\frac{2b^{2}}{c^{2}}$ . $m^{2}-\frac{2b^{2}-bcm}{c^{2}}$ Now, $m$ is an integer . Let's consider $\frac{2b^{2}-bcm}{c^{2}}=k$ where $k$ is an integer . After solving we get $\frac{b}{c}=\frac{m+_{-}\sqrt{m^{2}+8k}}{4}$ .....(I) But $\frac{b}{c}<1$ ....(II) Now putting value of $\frac{b}{c}$ from (I) to (II). We get $m+k<2$ Therefore there are infinitely many integers $m,k$ such that $m+k<2$ . Hence proved.

Shivam Jadhav - 4 years, 11 months ago

Bro ur equation which is quadratic in m is wrong also we will get 4 values of a

Devansh Shah - 4 years, 11 months ago

A general solution $a=(2n+1)+0.5$ where $n$ is a integer.

Shivam Jadhav - 4 years, 11 months ago

@Shivam Jadhav This ques is a little different from the RMO one , we have to find all values of 'a' between 3 & 4. @Devansh Shah is right , there will be 4 values.

Aditya Chauhan - 4 years, 11 months ago

m cant be 'any' integer as 3<a<4. So a will be 3.something or a = 3 + b/c

Yatharth Chowdhury - 4 years, 11 months ago

you can try the 6 question posted by me they all are of gmo.

aryan goyat - 4 years, 11 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}`	$\boxed{123}$