18 Questions
What is the general term of the expansion of (a + b)^n?
Tr + 1 = nCr * a^(n-r) * b^r
In the expansion (a + b)^n, if n is even, what is true about the middle term?
There is one middle term
What is the name of the diagram used by ancient Indian mathematicians to represent coefficients in the expansions of (x + y)^n?
Meru-Prastara
Who was the first to introduce the term 'binomial coefficients'?
Michael Stipel
When calculating the middle terms in the expansion (a + b)^n, how many middle terms are there if n is odd?
3
Who constructed the arithmetic triangle, popularly known as Pascal’s triangle?
Blaise Pascal
In the expansion of (x + y)^n, where x ≠ 0, which term is considered the term independent of x or the constant term?
The (n + 1)th term
What is the formula to calculate the (r + 1)th term in the expansion of (x + y)^n?
T(r + 1) = nCr * xr * y(n-r)
In the expansion of (2 + a)^50, if the 17th and 18th terms are equal, what is the value of 'a'?
16
What is the middle term in the expansion of (1 + x)^2n?
(2n - 1)xn
Which term is considered as the middle term in the expansion of (2x - y)^7?
(4th and 5th)th
What does the expression C_n^x represent in binomial expansions?
Combination of x chosen n times
In the expansion of (a + b)^n, what does the (r + 1)th term represent?
nCr * a^(n-r) * b^r
If n is even in the expansion of (a + b)^n, how many terms are there in total?
n+1
For which value of n will the expression 9n + 1 - 8n - 9 be divisible by 64?
All positive integers
What is the middle term in the expansion of (x + 2y)^8?
(5th term + 6th term) / 2
Which term in the expansion of (x + y)^n has the form nCy * x^r * y^(n-r)?
(r+1)th term
What is the general term in the expansion of (a + b)^n?
nCr * a^n-r * b^r
Test your skills in binomial expansion and divisibility with these challenging questions. Find and evaluate algebraic expressions, prove divisibility rules, and understand the pattern of general and middle terms in binomial expansions.
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