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𝐻𝑜𝑤 𝑡𝑜 𝑓𝑖𝑛𝑑 𝜆+𝜇, 𝑖𝑓𝑥+2𝑦−3𝑧=22𝑥+𝜆𝑦+5𝑧=514𝑥+3𝑦+𝜇𝑧=33 ℎ𝑎𝑠 𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑒 𝑚𝑎𝑛𝑦 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 | JEE main |
10:53
𝐻𝑜𝑤 𝑡𝑜 𝑓𝑖𝑛𝑑 𝜆+𝜇, 𝑖𝑓𝑥+2𝑦−3𝑧=22𝑥+𝜆𝑦+5𝑧=514𝑥+3𝑦+𝜇𝑧=33 ℎ𝑎𝑠 𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑒 𝑚𝑎𝑛𝑦 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 | JEE main |
How to 𝐹𝑖𝑛𝑑 𝒂 + 𝒃 ,𝒂^𝟑−𝟏𝟓𝒂^𝟐+ 𝟐𝟎𝒂 − 𝟓𝟎 = 𝟎 ,𝟖𝒃^𝟑−𝟔𝟎𝒃^𝟐−𝟐𝟗𝟎𝒃 + 𝟐𝟓𝟕𝟓 =𝟎 a, b 𝑟𝑒𝑎𝑙 | IRISH MathOlympiad
12:13
How to 𝐹𝑖𝑛𝑑 𝒂 + 𝒃 ,𝒂^𝟑−𝟏𝟓𝒂^𝟐+ 𝟐𝟎𝒂 − 𝟓𝟎 = 𝟎 ,𝟖𝒃^𝟑−𝟔𝟎𝒃^𝟐−𝟐𝟗𝟎𝒃 + 𝟐𝟓𝟕𝟓 =𝟎 a, b 𝑟𝑒𝑎𝑙 | IRISH MathOlympiad
𝑯𝒐𝒘 𝒕𝒐 𝑭𝒊𝒏𝒅 the value of ∑_(𝑘=1)^81▒𝑓(𝑘/82) 𝑖𝑓, 𝑓(𝑥)=2^𝑥/(2^𝑥+√2), 𝑥∈𝑅 | JEE Main | MCQ
6:41
𝑯𝒐𝒘 𝒕𝒐 𝑭𝒊𝒏𝒅 the value of ∑_(𝑘=1)^81▒𝑓(𝑘/82) 𝑖𝑓, 𝑓(𝑥)=2^𝑥/(2^𝑥+√2), 𝑥∈𝑅 | JEE Main | MCQ
Evaluate: ∫1_(𝑒^2)^(𝑒^4)▒〖1/𝑥 (𝑒^(〖(〖(𝑙𝑜𝑔〗_𝑒 〖𝑥)〗^2+1)〗^(−1) )/(𝑒^(〖(〖(6−𝑙𝑜𝑔〗_𝑒〖𝑥)〗^2+1)𝑑𝑥 |JEE |
7:25
Evaluate: ∫1_(𝑒^2)^(𝑒^4)▒〖1/𝑥 (𝑒^(〖(〖(𝑙𝑜𝑔〗_𝑒 〖𝑥)〗^2+1)〗^(−1) )/(𝑒^(〖(〖(6−𝑙𝑜𝑔〗_𝑒〖𝑥)〗^2+1)𝑑𝑥 |JEE |
𝐻𝑜𝑤 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟, 𝑤ℎ𝑒𝑛 7^103 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 17 | JEE Main 2023 | Number Theory | Olympiad
5:54
𝐻𝑜𝑤 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟, 𝑤ℎ𝑒𝑛 7^103 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 17 | JEE Main 2023 | Number Theory | Olympiad
𝐻𝑜𝑤 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟, 𝑤ℎ𝑒𝑛 7^103 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 23 | JEE Main 2025 | Number Theory | Olympiad
8:11
𝐻𝑜𝑤 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟, 𝑤ℎ𝑒𝑛 7^103 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 23 | JEE Main 2025 | Number Theory | Olympiad
𝑯𝒐𝒘 𝒕𝒐 𝒇𝒊𝒏𝒅 𝒎+𝒏 if 𝒕𝒉𝒆 𝒔𝒖𝒎 𝒐𝒇 𝒓𝒆𝒂𝒍 𝒓𝒐𝒐𝒕𝒔 𝒐𝒇 𝟐^(𝟑𝟑𝟑𝒙−𝟐)+𝟐^(𝟏𝟏𝟏𝒙+𝟐)=𝟐^(𝟐𝟐𝟐𝒙+𝟏)+𝟏 𝒊𝒔 𝒎/𝒏 | Olympiad
7:47
𝑯𝒐𝒘 𝒕𝒐 𝒇𝒊𝒏𝒅 𝒎+𝒏 if 𝒕𝒉𝒆 𝒔𝒖𝒎 𝒐𝒇 𝒓𝒆𝒂𝒍 𝒓𝒐𝒐𝒕𝒔 𝒐𝒇 𝟐^(𝟑𝟑𝟑𝒙−𝟐)+𝟐^(𝟏𝟏𝟏𝒙+𝟐)=𝟐^(𝟐𝟐𝟐𝒙+𝟏)+𝟏 𝒊𝒔 𝒎/𝒏 | Olympiad
Evaluate: (𝒆^(−𝝅/𝟒)+∫〖𝒆^(−𝒙) 〖𝒕𝒂𝒏〗^𝟓𝟎 𝒙𝒅𝒙〗)/(∫〖𝒆^(−𝒙) (〖𝒕𝒂𝒏〗^𝟒𝟗 𝒙+〖𝒕𝒂𝒏〗^𝟓𝟏 𝒙)𝒅𝒙〗) 0 to pi/4 |JEE |
7:35
Evaluate: (𝒆^(−𝝅/𝟒)+∫〖𝒆^(−𝒙) 〖𝒕𝒂𝒏〗^𝟓𝟎 𝒙𝒅𝒙〗)/(∫〖𝒆^(−𝒙) (〖𝒕𝒂𝒏〗^𝟒𝟗 𝒙+〖𝒕𝒂𝒏〗^𝟓𝟏 𝒙)𝒅𝒙〗) 0 to pi/4 |JEE |
𝑯𝒐𝒘 𝒕𝒐 𝑭𝒊𝒏𝒅 sum of [√𝟏]+[√𝟐]+[√𝟑]+…+[√𝟏𝟐𝟎] | [x] is greatest integer less then x | JEE Main | MCQ
8:18
𝑯𝒐𝒘 𝒕𝒐 𝑭𝒊𝒏𝒅 sum of [√𝟏]+[√𝟐]+[√𝟑]+…+[√𝟏𝟐𝟎] | [x] is greatest integer less then x | JEE Main | MCQ
𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 ∫_𝟎^(𝝅/𝟒)▒𝒙𝒅𝒙/(〖𝒔𝒊𝒏〗^𝟒 (𝟐𝒙)+〖𝒄𝒐𝒔〗^𝟒 (𝟐𝒙) ) | JEE Main | Definite Integral
9:53
𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 ∫_𝟎^(𝝅/𝟒)▒𝒙𝒅𝒙/(〖𝒔𝒊𝒏〗^𝟒 (𝟐𝒙)+〖𝒄𝒐𝒔〗^𝟒 (𝟐𝒙) ) | JEE Main | Definite Integral
How to 𝑃𝑟𝑜𝑣𝑒 : 𝒂/𝒄+𝒃/𝒂+𝒄/𝒃≥𝒂+𝒃+𝒄, abc is less than equal to 1 I IMO short listed
6:01
How to 𝑃𝑟𝑜𝑣𝑒 : 𝒂/𝒄+𝒃/𝒂+𝒄/𝒃≥𝒂+𝒃+𝒄, abc is less than equal to 1 I IMO short listed
How to find the Value of 𝒙 𝑰𝒇 〖𝒄𝒐𝒔〗^(−𝟏) (𝟐/𝟑𝒙)+〖𝒄𝒐𝒔〗^(−𝟏) (𝟑/𝟒𝒙)=𝝅/𝟐 ,(𝒙 greater 𝟑/𝟒) | JEE Main
4:07
How to find the Value of 𝒙 𝑰𝒇 〖𝒄𝒐𝒔〗^(−𝟏) (𝟐/𝟑𝒙)+〖𝒄𝒐𝒔〗^(−𝟏) (𝟑/𝟒𝒙)=𝝅/𝟐 ,(𝒙 greater 𝟑/𝟒) | JEE Main
𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 ∫ |cosx|^3 𝒅𝒙 from 0 to 𝝅 Step-by-Step Solution JEE Main | Definite Integral
5:34
𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 ∫ |cosx|^3 𝒅𝒙 from 0 to 𝝅 Step-by-Step Solution JEE Main | Definite Integral
How to find : 𝒌 i𝒇 𝒕𝒉𝒆 𝒇𝒓𝒂𝒄𝒕𝒊𝒐𝒏𝒂𝒍 𝒑𝒂𝒓𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 (𝟐^𝟒𝟎𝟑 )/𝟏𝟓 𝒊𝒔 𝒌/𝟏𝟓 | JEE Main
4:00
How to find : 𝒌 i𝒇 𝒕𝒉𝒆 𝒇𝒓𝒂𝒄𝒕𝒊𝒐𝒏𝒂𝒍 𝒑𝒂𝒓𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 (𝟐^𝟒𝟎𝟑 )/𝟏𝟓 𝒊𝒔 𝒌/𝟏𝟓 | JEE Main
How to find : (√(𝜶−𝟏)+√(𝜷−𝟏))/|𝜶−𝜷| for 𝒙^𝟐−𝟕𝟎𝒙+𝝀=𝟎 , 𝜶 𝒊𝒔 𝒍𝒆𝒔𝒔 𝒕𝒉𝒂𝒏 𝟏𝟎 𝝀/𝟐 , 𝝀/𝟑 𝒏𝒐𝒕 𝒊𝒏𝒕𝒆𝒈𝒆𝒓𝒔
4:43
How to find : (√(𝜶−𝟏)+√(𝜷−𝟏))/|𝜶−𝜷| for 𝒙^𝟐−𝟕𝟎𝒙+𝝀=𝟎 , 𝜶 𝒊𝒔 𝒍𝒆𝒔𝒔 𝒕𝒉𝒂𝒏 𝟏𝟎 𝝀/𝟐 , 𝝀/𝟑 𝒏𝒐𝒕 𝒊𝒏𝒕𝒆𝒈𝒆𝒓𝒔
𝑯𝒐𝒘 𝒕𝒐 determine all the pair of integers (𝒙,𝒚) 𝒙^𝟐 𝒚+𝒙+𝒚 𝒊𝒔 𝒅𝒊𝒗𝒊𝒔𝒊𝒃𝒍𝒆 𝒃𝒚 𝒙𝒚^𝟐+𝒚+𝟕𝒙, 𝒚∈𝒁^+ | IMO |
12:40
𝑯𝒐𝒘 𝒕𝒐 determine all the pair of integers (𝒙,𝒚) 𝒙^𝟐 𝒚+𝒙+𝒚 𝒊𝒔 𝒅𝒊𝒗𝒊𝒔𝒊𝒃𝒍𝒆 𝒃𝒚 𝒙𝒚^𝟐+𝒚+𝟕𝒙, 𝒚∈𝒁^+ | IMO |
How to find the sum of ⌊𝟐^𝟎/𝟑⌋+⌊𝟐^𝟏/𝟑⌋+⌊𝟐^𝟐/𝟑⌋+….+⌊𝟐^𝟏𝟎𝟎𝟎/𝟑⌋ | Floor functions | Number Theory |
12:44
How to find the sum of ⌊𝟐^𝟎/𝟑⌋+⌊𝟐^𝟏/𝟑⌋+⌊𝟐^𝟐/𝟑⌋+….+⌊𝟐^𝟏𝟎𝟎𝟎/𝟑⌋ | Floor functions | Number Theory |
How to find the average of coefficient of consecutives in (𝒙+𝟏)^𝒏 if ratio given | JEE Main
5:16
How to find the average of coefficient of consecutives in (𝒙+𝟏)^𝒏 if ratio given | JEE Main
𝑯𝒐𝒘 𝒕𝒐 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒆 ∫_𝟎^𝟏▒〖𝒙〖𝒄𝒐𝒕〗^(−𝟏) (𝟏−𝒙^𝟐+𝒙^𝟒 ) 〗 𝒅𝒙 Step-by-Step Solution | JEE Main Integral
8:30
𝑯𝒐𝒘 𝒕𝒐 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒆 ∫_𝟎^𝟏▒〖𝒙〖𝒄𝒐𝒕〗^(−𝟏) (𝟏−𝒙^𝟐+𝒙^𝟒 ) 〗 𝒅𝒙 Step-by-Step Solution | JEE Main Integral
How to 𝑃𝑟𝑜𝑣𝑒 : 𝟏/(𝟐𝒂+𝒃+𝒄)^𝟐 +𝟏/(𝟐𝒃+𝒄+𝒂)^𝟐 +𝟏/(𝟐𝒄+𝒂+𝒃)^𝟐 ≤𝟑/𝟏𝟔, 𝟏/𝒂+𝟏/𝒃+𝟏/𝒄=𝒂+𝒃+𝒄 I IMO short listed
18:58
How to 𝑃𝑟𝑜𝑣𝑒 : 𝟏/(𝟐𝒂+𝒃+𝒄)^𝟐 +𝟏/(𝟐𝒃+𝒄+𝒂)^𝟐 +𝟏/(𝟐𝒄+𝒂+𝒃)^𝟐 ≤𝟑/𝟏𝟔, 𝟏/𝒂+𝟏/𝒃+𝟏/𝒄=𝒂+𝒃+𝒄 I IMO short listed
How to solve : If α, β are the roots of, 𝒙^𝟐−𝒙−𝟏=0,𝑺_𝒏=𝟐𝟎𝟐𝟑𝜶^𝒏+𝟐𝟎𝟐𝟒𝜷^n | JEE Main | Sum of Series
5:53
How to solve : If α, β are the roots of, 𝒙^𝟐−𝒙−𝟏=0,𝑺_𝒏=𝟐𝟎𝟐𝟑𝜶^𝒏+𝟐𝟎𝟐𝟒𝜷^n | JEE Main | Sum of Series
𝑯𝒐𝒘 𝒕𝒐 𝒇𝒊𝒏𝒅 all complex Numbers such that (3z+1)(4z+1)(6z+1)(12z+1)=2
6:38
𝑯𝒐𝒘 𝒕𝒐 𝒇𝒊𝒏𝒅 all complex Numbers such that (3z+1)(4z+1)(6z+1)(12z+1)=2
𝑯𝒐𝒘 𝒕𝒐 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒆 : (𝟑(𝒆−𝟏))/𝒆 ∫_𝟏^𝟐▒〖𝒙^𝟐 𝒆^([𝒙^𝟑 ]+𝟏) 𝒅𝒙〗 | Step-by-Step Solution | JEE Main |
5:54
𝑯𝒐𝒘 𝒕𝒐 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒆 : (𝟑(𝒆−𝟏))/𝒆 ∫_𝟏^𝟐▒〖𝒙^𝟐 𝒆^([𝒙^𝟑 ]+𝟏) 𝒅𝒙〗 | Step-by-Step Solution | JEE Main |
𝑯𝒐𝒘 𝒕𝒐 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒆 ∫_(𝟏/𝟐)^𝟐▒〖(〖𝒕𝒂𝒏〗^(−𝟏) 𝒙)/𝒙 𝒅𝒙〗Step-by-Step Solution | JEE Main Definite Integral
4:56
𝑯𝒐𝒘 𝒕𝒐 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒆 ∫_(𝟏/𝟐)^𝟐▒〖(〖𝒕𝒂𝒏〗^(−𝟏) 𝒙)/𝒙 𝒅𝒙〗Step-by-Step Solution | JEE Main Definite Integral
𝑯𝒐𝒘 𝒕𝒐 determine pair of integers (𝒎,𝒏) : √(𝒏+√𝟐𝟎𝟏𝟔) + √(𝒎− √𝟐𝟎𝟏𝟔) ∈𝑸 | Junior Math Olympiad |
10:13
𝑯𝒐𝒘 𝒕𝒐 determine pair of integers (𝒎,𝒏) : √(𝒏+√𝟐𝟎𝟏𝟔) + √(𝒎− √𝟐𝟎𝟏𝟔) ∈𝑸 | Junior Math Olympiad |
How to 𝑃𝑟𝑜𝑣𝑒 : ((𝑎^3+𝑏^3+𝑐^3 )^2 (𝑎^4+𝑏^4+𝑐^4 ))/(𝑎^5+𝑏^5+𝑐^5 )^2 =18/25 IRISH Math Olympiad
11:45
How to 𝑃𝑟𝑜𝑣𝑒 : ((𝑎^3+𝑏^3+𝑐^3 )^2 (𝑎^4+𝑏^4+𝑐^4 ))/(𝑎^5+𝑏^5+𝑐^5 )^2 =18/25 IRISH Math Olympiad
How to 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑺=𝒂/𝒃+𝒃/𝒄+𝒄/𝒅 +𝒅/𝒂, (𝑎+𝑐)(𝑏+𝑑)=𝑎𝑐+𝑏𝑑 | IMO Shortlisted
5:53
How to 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑺=𝒂/𝒃+𝒃/𝒄+𝒄/𝒅 +𝒅/𝒂, (𝑎+𝑐)(𝑏+𝑑)=𝑎𝑐+𝑏𝑑 | IMO Shortlisted
How to 𝐹𝑖𝑛𝑑 𝒑 + 𝒒 + 𝒓 if 𝑞= 𝑝(4 − 𝑝), 𝑟= 𝑞(4 − 𝑞), 𝑝= 𝑟(4 − 𝑟), 𝑝, 𝑞, 𝑟 𝑟𝑒𝑎𝑙 | IRISH Math Olympiad
4:39
How to 𝐹𝑖𝑛𝑑 𝒑 + 𝒒 + 𝒓 if 𝑞= 𝑝(4 − 𝑝), 𝑟= 𝑞(4 − 𝑞), 𝑝= 𝑟(4 − 𝑟), 𝑝, 𝑞, 𝑟 𝑟𝑒𝑎𝑙 | IRISH Math Olympiad
How to 𝑷𝒓𝒐𝒗𝒆: 𝟖(𝒂^𝟒+𝒃^𝟒)≥(𝒂+𝒃)^𝟒 , 𝑎, 𝑏, positive 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠, | Olympiad Inequality |
5:13
How to 𝑷𝒓𝒐𝒗𝒆: 𝟖(𝒂^𝟒+𝒃^𝟒)≥(𝒂+𝒃)^𝟒 , 𝑎, 𝑏, positive 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠, | Olympiad Inequality |
How to 𝑷𝒓𝒐𝒗𝒆: 𝒂^𝟐 𝒃^𝟐 𝒄^𝟐≤𝟏/𝟓𝟒, 𝑎, 𝑏, 𝑐 𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠, 𝒂+𝒃+𝒄=𝟎, 𝒂^𝟐+𝒃^𝟐+𝒄^𝟐=𝟏| Inequality
6:59
How to 𝑷𝒓𝒐𝒗𝒆: 𝒂^𝟐 𝒃^𝟐 𝒄^𝟐≤𝟏/𝟓𝟒, 𝑎, 𝑏, 𝑐 𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠, 𝒂+𝒃+𝒄=𝟎, 𝒂^𝟐+𝒃^𝟐+𝒄^𝟐=𝟏| Inequality