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Introduction to Binomial Theorem, Quantitative Aptitude Video Lecture - UPSC
FAQs on Introduction to Binomial Theorem, Quantitative Aptitude Video Lecture - UPSC
| 1. What is the Binomial Theorem? |  |
Ans. The Binomial Theorem is a mathematical formula that provides a way to expand the powers of a binomial expression (an expression with two terms). It states that for any positive integer n, the expansion of (a + b)^n can be written as the sum of the coefficients multiplied by the respective powers of a and b.
| 2. How is the Binomial Theorem useful in quantitative aptitude for the UPSC exam? | |
Ans. The Binomial Theorem is useful in quantitative aptitude for the UPSC exam as it helps in solving problems related to permutations, combinations, and probability. It allows for the simplification of complex expressions involving binomial coefficients, making calculations easier and more efficient.
| 3. Can you explain the concept of binomial coefficients in the context of the Binomial Theorem? | |
Ans. In the context of the Binomial Theorem, binomial coefficients refer to the coefficients of the terms in the expanded form of a binomial expression. They are calculated using the formula nCr, where n is the power of the binomial and r is the power of the term being considered. Binomial coefficients play a crucial role in determining the pattern and values of the terms in the expansion.
| 4. How can the Binomial Theorem be applied to solve problems involving probability? | |
Ans. The Binomial Theorem can be applied to solve problems involving probability by providing a systematic way to calculate the probabilities of different outcomes. By expanding a binomial expression raised to a power, the coefficients represent the probabilities of obtaining a specific number of successful outcomes in a series of independent trials. These coefficients can then be used to determine the probability of different events.
| 5. Can you provide an example of how the Binomial Theorem can be used in quantitative aptitude problems for the UPSC exam? | |
Ans. Sure! Let's say you have to find the 4th term in the expansion of (x + 2)^6. Using the Binomial Theorem, we can determine the term by applying the formula nCr * a^(n-r) * b^r. In this case, n = 6, r = 4, a = x, and b = 2. Plugging in these values, we can calculate the 4th term as 15 * x^2 * 2^4, which simplifies to 240x^2.
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