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Fun with Mathematics
Индия
Добавлен 5 мар 2012
Channel for cracking Math problems for Olympiad.
Class XI XII JEE Engineering Entrance Relations Functions Unit 2
Mathematics - Relations & Functions (Unit 2)
For Class XI, XII, JEE, BITSAT, Engineering Entrance.
For students from Class 11 to Class 12.
𝐼𝑛 𝑡ℎ𝑖𝑠 𝑐ℎ𝑎𝑝𝑡𝑒𝑟 𝑤𝑒 𝑤𝑖𝑙𝑙 𝑙𝑒𝑎𝑟𝑛 ℎ𝑜𝑤 𝑡𝑜 𝑙𝑖𝑛𝑘 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑒𝑛𝑡𝑖𝑡𝑖𝑒𝑠 𝑜𝑟 𝑠𝑒𝑡𝑠 𝑜𝑓 𝑑𝑎𝑡𝑎.
𝐶𝑎𝑟𝑡𝑒𝑠𝑖𝑎𝑛 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑆𝑒𝑡𝑠
𝑅𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠
𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠
𝑁𝐶𝐸𝑅𝑇 𝐶ℎ𝑎𝑝𝑡𝑒𝑟 2 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 𝑠𝑜𝑙𝑣𝑖𝑛𝑔
𝑻𝒐𝒖𝒈𝒉 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒇𝒓𝒐𝒎 𝑱𝑬𝑬 𝒐𝒏 𝑹𝒆𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝒂𝒏𝒅 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏𝒔
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑓(𝑥) = √(𝑥^2−25𝑥+144)
𝐿𝑒𝑡 𝑓: 𝑁→𝑅𝑖𝑠 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑓(1)=1 𝑎𝑛𝑑 𝑓(1)+2𝑓(2)+…+𝑛𝑓(𝑛)=𝑛(𝑛+1)𝑓(𝑛) ∀𝑛≥2
𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓(2025)?
𝐿𝑒𝑡 𝐴 = {1,2,3,…,10} 𝑎𝑛𝑑 𝑓:𝐴→𝐴 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠 𝑓(𝑘)=𝑘+1 (𝑓𝑜𝑟 𝑜𝑑𝑑 𝑘) 𝑎𝑛𝑑 𝑓(𝑘)=𝑘 (𝑓𝑜𝑟 𝑒𝑣𝑒𝑛 𝑘)
𝑡ℎ𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝑔:𝐴→𝐴 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑔𝑂𝑓=𝑓 𝑖𝑠 [𝐽𝐸𝐸 𝑀𝐴𝐼𝑁𝑆]
[𝐽𝐸𝐸 𝑀𝑎𝑖𝑛𝑠] 𝑇ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑓(𝑥)= sin^(−1)((|𝑥|+...
For Class XI, XII, JEE, BITSAT, Engineering Entrance.
For students from Class 11 to Class 12.
𝐼𝑛 𝑡ℎ𝑖𝑠 𝑐ℎ𝑎𝑝𝑡𝑒𝑟 𝑤𝑒 𝑤𝑖𝑙𝑙 𝑙𝑒𝑎𝑟𝑛 ℎ𝑜𝑤 𝑡𝑜 𝑙𝑖𝑛𝑘 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑒𝑛𝑡𝑖𝑡𝑖𝑒𝑠 𝑜𝑟 𝑠𝑒𝑡𝑠 𝑜𝑓 𝑑𝑎𝑡𝑎.
𝐶𝑎𝑟𝑡𝑒𝑠𝑖𝑎𝑛 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑆𝑒𝑡𝑠
𝑅𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠
𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠
𝑁𝐶𝐸𝑅𝑇 𝐶ℎ𝑎𝑝𝑡𝑒𝑟 2 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 𝑠𝑜𝑙𝑣𝑖𝑛𝑔
𝑻𝒐𝒖𝒈𝒉 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒇𝒓𝒐𝒎 𝑱𝑬𝑬 𝒐𝒏 𝑹𝒆𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝒂𝒏𝒅 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏𝒔
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑓(𝑥) = √(𝑥^2−25𝑥+144)
𝐿𝑒𝑡 𝑓: 𝑁→𝑅𝑖𝑠 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑓(1)=1 𝑎𝑛𝑑 𝑓(1)+2𝑓(2)+…+𝑛𝑓(𝑛)=𝑛(𝑛+1)𝑓(𝑛) ∀𝑛≥2
𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓(2025)?
𝐿𝑒𝑡 𝐴 = {1,2,3,…,10} 𝑎𝑛𝑑 𝑓:𝐴→𝐴 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠 𝑓(𝑘)=𝑘+1 (𝑓𝑜𝑟 𝑜𝑑𝑑 𝑘) 𝑎𝑛𝑑 𝑓(𝑘)=𝑘 (𝑓𝑜𝑟 𝑒𝑣𝑒𝑛 𝑘)
𝑡ℎ𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝑔:𝐴→𝐴 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑔𝑂𝑓=𝑓 𝑖𝑠 [𝐽𝐸𝐸 𝑀𝐴𝐼𝑁𝑆]
[𝐽𝐸𝐸 𝑀𝑎𝑖𝑛𝑠] 𝑇ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑓(𝑥)= sin^(−1)((|𝑥|+...
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Thanks I’m your number one fan
Thank you very much.
you made the best video😍😍
@@sovannarotnun7561 Thank you very much. These words helps a lot to make more such videos.
Speak in hindi
Thank you and sorry.. I can not speak that good Hindi to explain these complex problems. I may go wrong.
@@psk99999 oh!! But explanation in English is not up to the mark needs to be improved and keep it up
@@SagnikBiswas_69 Sure.. I will try to improve.. Thanks
Good explanation sir
Thank you for your kind words. We just started and we are trying to improve. We want more kids to take part in Mathematics Olympiad. We hope this will reach to kids who are really interested in excelling.
Thank you sir, you make tough questions look like a piece of cake.
You are most welcome. We are trying to help students and create interest in Olympiad. It's a great test.
You are most welcome. We are trying to help students and create interest in Olympiad. It's a great test.
Please note correction for the 7th Question. 4C2 = 3! = 6. But I mistakenly wrote as 3!/2. Correct answer below. Question: 𝑈𝑛𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 𝑑𝑖𝑐𝑒 𝑎𝑟𝑒 𝑡𝑜 𝑏𝑒 𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑠𝑖𝑥 𝑓𝑎𝑐𝑒𝑠 𝑎𝑟𝑒 𝑚𝑎𝑟𝑘𝑒𝑑 𝑤𝑖𝑡ℎ 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑓𝑟𝑜𝑚 1 𝑡𝑜 6 𝑤𝑖𝑡ℎ 1 𝑎𝑛𝑑 2 𝑎𝑝𝑝𝑒𝑎𝑟𝑖𝑛𝑔 𝑜𝑛 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑓𝑎𝑐𝑒𝑠. 𝐹𝑢𝑟𝑡ℎ𝑒𝑟, 𝑒𝑎𝑐ℎ 𝑓𝑎𝑐𝑒 𝑖𝑠 𝑐𝑜𝑙𝑜𝑟𝑒𝑑 𝑒𝑖𝑡ℎ𝑒𝑟 𝑟𝑒𝑑 𝑜𝑟 𝑦𝑒𝑙𝑙𝑜𝑤 𝑤𝑖𝑡ℎ 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑓𝑎𝑐𝑒𝑠 𝑎𝑙𝑤𝑎𝑦𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑐𝑜𝑙𝑜𝑟. 𝑇𝑤𝑜 𝑑𝑖𝑐𝑒 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑒𝑑 𝑡𝑜 ℎ𝑎𝑣𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑑𝑒𝑠𝑖𝑔𝑛 𝑖𝑓 𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒𝑚 𝑐𝑎𝑛 𝑏𝑒 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 𝑡𝑜 𝑜𝑏𝑡𝑎𝑖𝑛 𝑎 𝑑𝑖𝑐𝑒 𝑡ℎ𝑎𝑡 ℎ𝑎𝑠 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑎𝑛𝑑 𝑐𝑜𝑙𝑜𝑟𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑓𝑎𝑐𝑒𝑠 𝑎𝑠 𝑡ℎ𝑒 𝑜𝑡ℎ𝑒𝑟 𝑜𝑛𝑒. 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑑𝑖𝑐𝑒 𝑡ℎ𝑎𝑡 𝑐𝑎𝑛 𝑏𝑒 𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑. Correct Answer: 1, 2 𝑎𝑟𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑐𝑒. 3, 4, 5, 6 𝑐𝑎𝑛 𝑏𝑒 𝑎𝑟𝑟𝑎𝑛𝑔𝑒𝑑 𝑖𝑛 𝑎 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑓𝑎𝑠ℎ𝑖𝑜𝑛 𝑖𝑛 4𝐶2 𝑤𝑎𝑦𝑠 𝑜𝑟 3!=6 𝐴𝑛𝑦 𝑜𝑓 𝑡ℎ𝑒 2 𝑐𝑜𝑙𝑜𝑟𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑝𝑎𝑖𝑛𝑡𝑒𝑑 𝑜𝑛 𝑜𝑓 𝑑𝑖𝑐𝑒=2 𝑥 2 𝑥 2 (3 𝑜𝑝𝑝𝑜 𝑠𝑖𝑑𝑒𝑠 𝑎𝑛𝑑 2 𝑐𝑜𝑙𝑜𝑟𝑠 𝑒𝑎𝑐ℎ) 𝑫𝒊𝒔𝒕𝒊𝒏𝒄𝒕 𝒅𝒊𝒄𝒆 𝒘𝒉𝒊𝒄𝒉 𝒄𝒂𝒏 𝒃𝒆 𝒅𝒆𝒔𝒊𝒈𝒏𝒆𝒅 =𝟔𝒙𝟐𝒙𝟐𝒙𝟐=𝟒𝟖
To complete the problem, you need to find sum of squares of digits of N. Who will give me final answer?
Please refer to the full video for the detailed explanation. ruclips.net/video/RU6HysQsEwA/видео.html
It would be helpful if you mention the class for which the video is intended
Hi, IMO test is common for class 8 to class 10. The cut-off marks are decided by IMO depending on the paper's difficulty level. Ideally, these are for 8th to 10th grades.
Please refer to the full video for a detailed explanation. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for the detailed explanation. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for a detailed explanation. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for a detailed explanation. ruclips.net/video/M7iK6LpnERs/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/OIBefssjOwY/видео.htmlsi=GOauEXYMVm5e6wIB
Please refer to the full video for the detailed explanation. ruclips.net/video/OIBefssjOwY/видео.htmlsi=GOauEXYMVm5e6wIB
Math-62 Please refer to the full video for detailed explaination. ruclips.net/video/j4HfVFlNqPg/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/nPLqt2am_qE/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/nPLqt2am_qE/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/3F5zdCyvZvY/видео.html
Please refer to the full video for detailed explaination. ruclips.net/video/Q1QKC5nT9Vw/видео.htmlsi=_W8hRthCK7qcZGDo
Suprise to see first question in this video. I have solved and explained this problem exactly in my previous video sometime back. Check the following video. The problem is exactly same, even the numericals. ruclips.net/video/t69M_J-fuRc/видео.htmlsi=9BC3os6OzxjApLIr The question is: 𝐴 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑚 ℎ𝑎𝑠 𝑡ℎ𝑒 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑡ℎ𝑎𝑡 𝑚^2 𝑖𝑠 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑏𝑙𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚 4𝑛^2−5𝑛+16 𝑤ℎ𝑒𝑟𝑒 𝑛 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 (𝑜𝑓 𝑎𝑛𝑦 𝑠𝑖𝑔𝑛). 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 |𝑚−𝑛|.
For the Last Question (Binary sequence) The correct recurring equation is : F(n+1) = F(n) + F(n-2) + F(n-3). Please use this for calculation. The calculation is done based on this equation. Not the one mentioned in the video. All the values are correct. Just wrote the recurring equation wrong.
For problem "For a positive integer n let n denote the perfect square integer closest to n. For example, (74) = 81, (18) = 16 . If N is the smallest positive integer such that (91). (120) . (143). (180). (N) = 91.120.143 .180 .N Find the sum of the square of the digits of N." The final answer is 4^2 + 6^2 + 2^2 = 56
Thanks for completing
Wow
Thanks
Iam 45th subsciber
Thanks
Not that it really affects the solution, but under the given conditions point D lies outside of the circle.
Thanks Andy. Yes, I did not check that. But as you said, solution is same.
Awesome, simplified like anything, Awesome..!
Thank you!
Wow Awesome...!
Many many thanks
There are a few typos in the 3rd problem. Digit 7 came wrongly in a few places and -2 is missing in the final solution set. Listen to the explanation, that is correct.
Nice presentation
Thanks a lot
Congruence relation in number theory should be explained lucidly
Sure... I will make a video shortly explaining that.. Give me sometime
Please check the video on Congruence basics. ruclips.net/video/b3v-W-r6NnY/видео.html Also check all problems on play list
Wow. That's a nice , simple and good solution
Thank you. If you have any interesting problems to solve, please put in the comments. I will make video.
I want to make reminder theorem problem-solving videos. Please post in the comment section if you want to solve any reminder theorem problems till the 10th standard.
Planning to make reminder theorem problem-solving videos. Please post in the comment section, if you want to solve any reminder theorem problems till the 10th standard.