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AP Intermediate 1st Year Binomial Theorem — practice questions — page 2

Explore 50 free Binomial Theorem questions in AP Intermediate 1st Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Binomial Theorem questions and exercises with answers

Showing questions 31–50 of 50.

Spot the false statementRead the answer and worked solution →Knock out the true statementsRead the answer and worked solution →Expanding a binomial to a high power is made possible by the binomial:Read the answer and worked solution →The binomial theorem is studied here for which kind of indices?Read the answer and worked solution →The triangular array of binomial coefficients is named after Blaise:Read the answer and worked solution →What number appears at the beginning and end of each row of the triangle?Read the answer and worked solution →The coefficients occurring in the binomial theorem are known as binomial:Read the answer and worked solution →How many terms does the expansion of a binomial to index n contain?Read the answer and worked solution →In the expansion of a binomial squared, how many terms appear?Read the answer and worked solution →In each term of the expansion, what is equal to the index of the binomial?Read the answer and worked solution →Adding the two ones in the row for index one gives which entry below?Read the answer and worked solution →Building Pascal's triangle can be continued till any index of our:Read the answer and worked solution →Expanding to index twelve by the triangle needs all rows written till index:Read the answer and worked solution →Why is a general rule sought instead of Pascal's triangle?Read the answer and worked solution →The sought rule avoids writing which rows of Pascal's triangle?Read the answer and worked solution →Observing the coefficient pattern lets a row be written without the:Read the answer and worked solution →Adding one, two and two, one from the index two row gives which pair?Read the answer and worked solution →Higher powers of a binomial can also be expanded using Pascal's:Read the answer and worked solution →Pascal's triangle has a one at its top vertex and runs down two:Read the answer and worked solution →After finding the pattern, we can write the expansion to any positive integral:Read the answer and worked solution →

Worked practice questions

Spot the false statement

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Questions
  1. False statement
    The triangle stops at index seven
    Statements
    1. Every row starts and ends with one
    2. The triangle stops at index seven
    3. Adjacent entries add to give the row below
  2. False statement
    The index of b also falls through it
    Statements
    1. The theorem handles any positive whole index
    2. The index of a falls through the expansion
    3. The index of b also falls through it
  3. False statement
    Repeated multiplication is easy at high powers
    Statements
    1. Repeated multiplication is easy at high powers
    2. 98 is rewritten as 100 minus 2
    3. The indices in each term sum to n
  4. False statement
    Each row is shorter than the one above
    Statements
    1. Larger powers make the row building harder
    2. Each row is shorter than the one above
    3. Pascal gives his name to the triangle
Instructions
Two statements are true and one is false. Tap the false one.
_Source: syllabus Mathematics, Ch 7 'Binomial Theorem'_

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Knock out the true statements

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Questions
  1. Question
    Eliminate the true statements about the expansion.
    Choices
    1. Item
      Both indices rise together
      Correct
      Yes
    2. Explanation
      It falls by unity through the successive terms.
      Item
      The index of a decreases by one each term
    3. Explanation
      It starts at zero and ends at n in the last term.
      Item
      The index of b starts at zero
    4. Explanation
      In every term their sum equals the index of a plus b.
      Item
      The two indices always sum to n
Instructions
Remove the statements that are true. One false one should survive.
_Source: syllabus Mathematics, Ch 7 'Binomial Theorem'_

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Expanding a binomial to a high power is made possible by the binomial:

  1. Theorem
  2. Theory
  3. Thesis
  4. Theme
Show answer and solution

Correct answer: A. Theorem

1. Multiplying out by hand becomes impractical quickly. 2. A general result removes that labour. 3. This difficulty was overcome by a theorem known as binomial theorem. 4. So the answer is the theorem. _Source: syllabus Mathematics, Ch 7 'Binomial Theorem'_

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