Question:
The coefficient of $ x^{-10}$ in $\left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is
The coefficient of $ x^{-10}$ in $\left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is
Updated On: Apr 27, 2024
- $-252$
- $-210$
- $-(5!)$
- $-120$
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The Correct Option is D
Solution and Explanation
Let the term containing $x^{-10}$ in the expansion of $ \left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is $T_{r+1} $
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Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.