https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/e/some-special-cases-of-a-b-n 2025-06-25T04:36:24.163902917Z (a+b)^n के कुछ विशेष प्रश्न (a+b)^n के कुछ विशेष प्रश्न Ashish Gupta exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/v/worked-example-special-cases 2025-03-24T05:52:22.847271672Z उदाहरण (विशेष परिस्थिति) (Worked example (special cases)) In this video, we'll apply what we know about expansions of (a+b)^n and (a-b)^n to solve problems. We'll first expand (x + 1/x)^6 and then (2x-3)^6 by carefully replacing as and bs with appropriate values. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw उदाहरण (विशेष परिस्थिति) (Worked example (special cases)) In this video, we'll apply what we know about expansions of (a+b)^n and (a-b)^n to solve problems. We'll first expand (x + 1/x)^6 and then (2x-3)^6 by carefully replacing as and bs with appropriate values. https://cdn.kastatic.org/ka-youtube-converted/WFa092kBrj0.mp4/WFa092kBrj0.mp4 441 द्विपद प्रमेय का अनुप्रयोग (Applications of Binomial Theorem) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/v/compute-powers-of-integers 2025-03-24T05:52:22.847271672Z पूर्णांको की घातों को ज्ञात करना (Compute powers of integers) We've learnt how to expand (a+b)^n and its special cases. In this video, we'll apply what we've learnt to find the values of powers of large numbers. We'll break them down into sums and then apply binomial expansion to get the results. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw पूर्णांको की घातों को ज्ञात करना (Compute powers of integers) We've learnt how to expand (a+b)^n and its special cases. In this video, we'll apply what we've learnt to find the values of powers of large numbers. We'll break them down into sums and then apply binomial expansion to get the results. https://cdn.kastatic.org/ka-youtube-converted/ixV4CrcBMXU.mp4/ixV4CrcBMXU.mp4 563 द्विपद प्रमेय का अनुप्रयोग (Applications of Binomial Theorem) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/e/powers-of-integers-using-binomial-theorem 2025-06-25T04:36:24.163902917Z पूर्णांकों की घात, द्विपद प्रमेय (Binomial Theorem) का प्रयोग करके पूर्णांकों की घात, द्विपद प्रमेय (Binomial Theorem) का प्रयोग करके Ashish Gupta exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/v/using-binomial-theorem-to-compare-numbers 2025-03-24T05:52:22.847271672Z दो संख्याओं की तुलना करने हेतु द्विपद प्रमेय का प्रयोग (Using Binomial theorem to compare numbers) We've learn't how to expand (a+b)^n and (1+x)^n. Let's use these expansions to compare powers of 1.1 and 1.01 with large numbers. We first expand 1.01^10,00,000 using (1+x)^n and compare the result with 10,000. We then expand 1.1^10,000 using (1+x)^n and compare the result with 5,00,000. In this video, we'll realise that we don't need lakhs of terms to figure things out, usually simplifying the first few terms does the job for us. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw दो संख्याओं की तुलना करने हेतु द्विपद प्रमेय का प्रयोग (Using Binomial theorem to compare numbers) We've learn't how to expand (a+b)^n and (1+x)^n. Let's use these expansions to compare powers of 1.1 and 1.01 with large numbers. We first expand 1.01^10,00,000 using (1+x)^n and compare the result with 10,000. We then expand 1.1^10,000 using (1+x)^n and compare the result with 5,00,000. In this video, we'll realise that we don't need lakhs of terms to figure things out, usually simplifying the first few terms does the job for us. https://cdn.kastatic.org/ka-youtube-converted/nu_LcFpkjxM.mp4/nu_LcFpkjxM.mp4 408 द्विपद प्रमेय का अनुप्रयोग (Applications of Binomial Theorem) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/e/comparing-numbers-using-binomial-theorem 2025-06-25T04:36:24.163902917Z द्विपद प्रमेय (Binomial Theorem) का प्रयोग करके संख्याओं की तुलना द्विपद प्रमेय (Binomial Theorem) का प्रयोग करके संख्याओं की तुलना Ashish Gupta exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/v/using-binomial-theorem-to-prove-statements 2025-03-24T05:52:22.847271672Z कथनों को सिद्ध करने के लिए द्विपद प्रमेय का प्रयोग (Using Binomial theorem to prove statements) In this video, we apply binomial theorem to prove statements on divisibility. In such problems, we're given an expression and a statement that is true for all values of n. Our task is to strategically expand a binomial such that the expansion gives terms that match the given statement. We first prove that a given expression is always divisible by 64. We then prove that a given expression always leaves remainder 1 when divided by 25. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw कथनों को सिद्ध करने के लिए द्विपद प्रमेय का प्रयोग (Using Binomial theorem to prove statements) In this video, we apply binomial theorem to prove statements on divisibility. In such problems, we're given an expression and a statement that is true for all values of n. Our task is to strategically expand a binomial such that the expansion gives terms that match the given statement. We first prove that a given expression is always divisible by 64. We then prove that a given expression always leaves remainder 1 when divided by 25. https://cdn.kastatic.org/ka-youtube-converted/MkUOvivj7RA.mp4/MkUOvivj7RA.mp4 471 द्विपद प्रमेय का अनुप्रयोग (Applications of Binomial Theorem) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/e/binomial-theorem-applications 2025-06-25T04:36:24.163902917Z द्विपद प्रमेय (Binomial Theorem) के अनुप्रयोग द्विपद प्रमेय (Binomial Theorem) के अनुप्रयोग Ashish Gupta exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/v/using-binomial-theorem-irrational-terms 2025-03-24T05:52:22.847271672Z द्विपद प्रमेय का प्रयोग (अपरिमेय पद) (Using Binomial theorem (irrational terms)) In this video, we'll apply binomial expansion on irrational terms. We'll consider pairs of expansions where almost half the terms cancel out because of symmetry. We'll use this technique to simplify the expressions. Finally, we'll replace the values of a, b, x, or y with appropriate irrational numbers to deduce the values of expressions given in the problem. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw द्विपद प्रमेय का प्रयोग (अपरिमेय पद) (Using Binomial theorem (irrational terms)) In this video, we'll apply binomial expansion on irrational terms. We'll consider pairs of expansions where almost half the terms cancel out because of symmetry. We'll use this technique to simplify the expressions. Finally, we'll replace the values of a, b, x, or y with appropriate irrational numbers to deduce the values of expressions given in the problem. https://cdn.kastatic.org/ka-youtube-converted/f2l-aiXRSX4.mp4/f2l-aiXRSX4.mp4 386 द्विपद प्रमेय का अनुप्रयोग (Applications of Binomial Theorem) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/e/applying-binomial-theorem-on-irrational-terms 2025-06-25T04:36:24.163902917Z अपरिमेय पदों पर द्विपद प्रमेय का अनुप्रयोग अपरिमेय पदों पर द्विपद प्रमेय का अनुप्रयोग Ashish Gupta exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/v/approximations-using-binomial-theorem 2025-06-25T04:36:24.163902917Z द्विपद प्रमेय से अनुमान लगाना In this video, we use binomial expansion to approximate powers of numbers close to 1. We use (1+x)^n for numbers greater than 1 and (1-x)^n for numbers less than 1. We realise through expansion that the first few terms matter much more than the remaining terms. So to approximate the value of these powers, we can ignore a lot of terms. We also realise that the approximations work better for smaller values of x. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw द्विपद प्रमेय से अनुमान लगाना In this video, we use binomial expansion to approximate powers of numbers close to 1. We use (1+x)^n for numbers greater than 1 and (1-x)^n for numbers less than 1. We realise through expansion that the first few terms matter much more than the remaining terms. So to approximate the value of these powers, we can ignore a lot of terms. We also realise that the approximations work better for smaller values of x. https://cdn.kastatic.org/ka-youtube-converted/qYYMlcXnPfM.mp4/qYYMlcXnPfM.mp4 573 द्विपद प्रमेय का अनुप्रयोग (Applications of Binomial Theorem) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:binomial-theorem-ncert-new/x808831787a7b08a2:applications-of-binomial-theorem/e/approximations-using-binomial-theorem 2025-06-25T04:36:24.163902917Z द्विपद प्रमेय (Binomial Theorem) का प्रयोग करके निकटतम मान ज्ञात करना द्विपद प्रमेय (Binomial Theorem) का प्रयोग करके निकटतम मान ज्ञात करना Ashish Gupta exercise