Binomial Expansion and Divisibility Quizzes
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Questions and Answers

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?

  • 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?

  • Arithmetic Triangle
  • Pascal's Triangle
  • Binomial Diagram
  • Meru-Prastara (correct)
  • Who was the first to introduce the term 'binomial coefficients'?

    <p>Michael Stipel</p> Signup and view all the answers

    When calculating the middle terms in the expansion (a + b)^n, how many middle terms are there if n is odd?

    <p>3</p> Signup and view all the answers

    Who constructed the arithmetic triangle, popularly known as Pascal’s triangle?

    <p>Blaise Pascal</p> Signup and view all the answers

    In the expansion of (x + y)^n, where x ≠ 0, which term is considered the term independent of x or the constant term?

    <p>The (n + 1)th term</p> Signup and view all the answers

    What is the formula to calculate the (r + 1)th term in the expansion of (x + y)^n?

    <p>T(r + 1) = nCr * xr * y(n-r)</p> Signup and view all the answers

    In the expansion of (2 + a)^50, if the 17th and 18th terms are equal, what is the value of 'a'?

    <p>16</p> Signup and view all the answers

    What is the middle term in the expansion of (1 + x)^2n?

    <p>(2n - 1)xn</p> Signup and view all the answers

    Which term is considered as the middle term in the expansion of (2x - y)^7?

    <p>(4th and 5th)th</p> Signup and view all the answers

    What does the expression C_n^x represent in binomial expansions?

    <p>Combination of x chosen n times</p> Signup and view all the answers

    In the expansion of (a + b)^n, what does the (r + 1)th term represent?

    <p>nCr * a^(n-r) * b^r</p> Signup and view all the answers

    If n is even in the expansion of (a + b)^n, how many terms are there in total?

    <p>n+1</p> Signup and view all the answers

    For which value of n will the expression 9n + 1 - 8n - 9 be divisible by 64?

    <p>All positive integers</p> Signup and view all the answers

    What is the middle term in the expansion of (x + 2y)^8?

    <p>(5th term + 6th term) / 2</p> Signup and view all the answers

    Which term in the expansion of (x + y)^n has the form nCy * x^r * y^(n-r)?

    <p>(r+1)th term</p> Signup and view all the answers

    What is the general term in the expansion of (a + b)^n?

    <p>nCr * a^n-r * b^r</p> Signup and view all the answers

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