Class 11 Exam > Class 11 Videos > Special case in Binomial theorem (Part - 5) - Binomial theorem, Mathematics, Class 11
Special case in Binomial theorem (Part - 5) - Binomial theorem, Mathematics, Class 11 Video Lecture
FAQs on Special case in Binomial theorem (Part - 5) - Binomial theorem, Mathematics, Class 11 Video Lecture
| 1. What is the binomial theorem? |  |
Ans. The binomial theorem is a formula that allows us to expand a binomial raised to a positive integer power. It states that for any real numbers a and b and a positive integer n, the expansion of (a + b)^n can be written as the sum of terms in the form C(n, r) a^(n-r) b^r, where C(n, r) represents the binomial coefficient.
| 2. What is a binomial coefficient? | |
Ans. A binomial coefficient, denoted as C(n, r), is a number that represents the number of ways to choose r items from a set of n items without regard to their order. It is calculated using the formula C(n, r) = n! / (r!(n-r)!), where n! represents the factorial of n.
| 3. How do you find the term with a specific power in the expansion of a binomial? | |
Ans. To find the term with a specific power in the expansion of a binomial, we use the binomial theorem formula. We look for the term with the desired power by setting the exponents of a and b in the formula equal to the desired power and its complement. Then, we calculate the corresponding binomial coefficient and multiply it with the appropriate powers of a and b.
| 4. What is the significance of the binomial theorem in mathematics? | |
Ans. The binomial theorem has significant applications in various branches of mathematics, including algebra, combinatorics, and calculus. It allows us to expand binomials quickly and efficiently, which is useful in simplifying expressions, solving equations, and solving problems involving counting and probability.
| 5. Can the binomial theorem be used for negative powers or non-integer powers? | |
Ans. No, the binomial theorem is valid only for positive integer powers. It is not applicable for negative powers or non-integer powers. However, there are generalizations of the binomial theorem, such as the multinomial theorem, that can be used for expanding binomials with negative or non-integer powers.
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