Binomial Expansion

Greatest Coefficient Property: The binomial coefficients $(r n)$ increase until the middle and then decrease.
Middle Term Rule:
- If $n$ is even, the greatest coefficient is $(n /2 n)$ .
- If $n$ is odd, the greatest coefficients are $(( n - 1 ) /2 n)$ and $(( n + 1 ) /2 n)$ .
Application: For $n = 20$ (even), the greatest coefficient is $(10 20)$ (also written as $C (20, 10)$ ).

This easy difficulty mathematics question is from the chapter binomial theorem and its simple applications, covering the topic of binomial expansion. It appeared in the 2025 exam.

Looking for more practice? Explore all mathematics questions or browse binomial theorem and its simple applications questions on RankGuru.

Binomial Expansion

Select the correct option:

🔒 Solution Hidden from View

More binomial theorem and its simple applications Practice Questions

The number of terms in the expansion of (a + b)ⁿ is

If the coefficient of x⁷ and x⁸ in (2 + x/3)ⁿ are equal, then n equals

The ratio of the coefficient of x¹⁵ to the term independent of x in (x² + 2/x)¹⁵ is

The 4th term in the expansion of (x + 2)⁶ is

The coefficient of x⁵ in the expansion of (1 + x)¹⁰ is

The middle term in the expansion of (x + 1/x)¹⁰ is

The term independent of x in the expansion of (x² - 1/x)⁹ is

In the expansion of (1 + x)ⁿ with n > 10, if the coefficients of the 5th, 6th, and 7th terms are in ...

When the trinomial (1 + x + x^2)^{3} is expanded completely into a polynomial in x, the coefficient ...

Using the first-order binomial approximation for small quantities, the approximate value of (1.002)^...

Treating the binomial theorem for a negative index, the coefficient of x^3 in the series expansion o...

If the expansion of (1 + x)^n is split into terms with even index and terms with odd index, the sum ...

About This Question

Solution