Podcast
Questions and Answers
What is the general term of the expansion of (a + b)^n?
What is the general term of the expansion of (a + b)^n?
- Tr + 1 = nCr * a^(r) * b^(n-r)
- Tr + 1 = nCr * a^(n-r) * b^r (correct)
- Tr + 1 = nCr * a * b
- Tr + 1 = n! / (n-r)! * a^r * b^(n-r)
In the expansion (a + b)^n, if n is even, what is true about the middle term?
In the expansion (a + b)^n, if n is even, what is true about the middle term?
- There is one middle term (correct)
- There are two middle terms
- There are no middle terms
- The middle term has the highest degree
What is the name of the diagram used by ancient Indian mathematicians to represent coefficients in the expansions of (x + y)^n?
What is the name of the diagram used by ancient Indian mathematicians to represent coefficients in the expansions of (x + y)^n?
- Arithmetic Triangle
- Pascal's Triangle
- Binomial Diagram
- Meru-Prastara (correct)
Who was the first to introduce the term 'binomial coefficients'?
Who was the first to introduce the term 'binomial coefficients'?
When calculating the middle terms in the expansion (a + b)^n, how many middle terms are there if n is odd?
When calculating the middle terms in the expansion (a + b)^n, how many middle terms are there if n is odd?
Who constructed the arithmetic triangle, popularly known as Pascal’s triangle?
Who constructed the arithmetic triangle, popularly known as Pascal’s triangle?
In the expansion of (x + y)^n, where x ≠0, which term is considered the term independent of x or the constant term?
In the expansion of (x + y)^n, where x ≠0, which term is considered the term independent of x or the constant term?
What is the formula to calculate the (r + 1)th term in the expansion of (x + y)^n?
What is the formula to calculate the (r + 1)th term in the expansion of (x + y)^n?
In the expansion of (2 + a)^50, if the 17th and 18th terms are equal, what is the value of 'a'?
In the expansion of (2 + a)^50, if the 17th and 18th terms are equal, what is the value of 'a'?
What is the middle term in the expansion of (1 + x)^2n?
What is the middle term in the expansion of (1 + x)^2n?
Which term is considered as the middle term in the expansion of (2x - y)^7?
Which term is considered as the middle term in the expansion of (2x - y)^7?
What does the expression C_n^x represent in binomial expansions?
What does the expression C_n^x represent in binomial expansions?
In the expansion of (a + b)^n, what does the (r + 1)th term represent?
In the expansion of (a + b)^n, what does the (r + 1)th term represent?
If n is even in the expansion of (a + b)^n, how many terms are there in total?
If n is even in the expansion of (a + b)^n, how many terms are there in total?
For which value of n will the expression 9n + 1 - 8n - 9 be divisible by 64?
For which value of n will the expression 9n + 1 - 8n - 9 be divisible by 64?
What is the middle term in the expansion of (x + 2y)^8?
What is the middle term in the expansion of (x + 2y)^8?
Which term in the expansion of (x + y)^n has the form nCy * x^r * y^(n-r)?
Which term in the expansion of (x + y)^n has the form nCy * x^r * y^(n-r)?
What is the general term in the expansion of (a + b)^n?
What is the general term in the expansion of (a + b)^n?
