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Worksheet: General Term in the Binomial Theorem

Q1:

Find the third term in the expansion of ( 4 π‘₯ + 3 ) 3 .

  • A 1 0 8 π‘₯ 2
  • B 2 7 π‘₯
  • C 2 7 π‘₯ 2
  • D 1 0 8 π‘₯

Q2:

Find the value of π‘₯ that satisfies

Q3:

Consider the expansion of in ascending powers of . Given that the coefficient of is equal to the coefficient of , determine the value of .

Q4:

Find in the expansion of .

  • A
  • B
  • C
  • D
  • E

Q5:

Find in the expansion of .

  • A
  • B
  • C
  • D
  • E

Q6:

Find the third term in the expansion of ο€Ώ 2 π‘₯ + 5 √ π‘₯  5 .

  • A 2 0 0 π‘₯ 2
  • B 2 0 0 0 π‘₯ 3
  • C 2 0 0 π‘₯ 3
  • D 2 0 0 0 π‘₯ 2

Q7:

Find in the expansion of .

  • A
  • B
  • C
  • D
  • E

Q8:

Find in the expansion of .

  • A
  • B
  • C
  • D
  • E

Q9:

If the coefficient of the third term in the expansion of ο€Ό π‘₯ βˆ’ 1 4  𝑛 is 3 3 8 , determine the middle term in the expansion.

  • A 2 3 1 1 0 2 4 π‘₯ 7
  • B 9 9 5 1 2 π‘₯ 6
  • C 9 9 5 1 2 π‘₯ 7
  • D 2 3 1 1 0 2 4 π‘₯ 6

Q10:

If the ratio between the fourth term in the expansion of ο€Ό π‘₯ + 1 π‘₯  9 and the third term in the expansion of ο€Ό π‘₯ βˆ’ 1 π‘₯  2 8 equals 7 ∢ 1 2 , find the value of π‘₯ .

  • A 4 9 1 2 9 6
  • B 3 6 7
  • C 1 2 9 6 4 9
  • D 7 3 6

Q11:

Consider the binomial expansion of in ascending powers of . Given that when , find the value of .

Q12:

In the binomial expansion of , is a positive, whole number and is the th term, or the term which contains .

If , what is the value of ?

Q13:

Find the coefficient of in the expansion of .

Q14:

Find the coefficient of in the expansion of .

Q15:

Find the third term in the expansion of ο€½ π‘Ž + 𝑏 π‘Ž  1 9 1 1 1 4 1 9 βˆ’ 2 8 .

  • A 3 7 8 π‘Ž 𝑏 2 6 9 1 1 7
  • B π‘Ž 𝑏 8 3 1 1 7
  • C π‘Ž 𝑏 2 6 9 1 1 7
  • D 3 7 8 π‘Ž 𝑏 8 3 1 1 7

Q16:

Consider the binomial expansion of ( 2 π‘₯ βˆ’ 𝑦 ) 9 in ascending powers of π‘₯ . What is the seventh term?

  • A 5 3 7 6 π‘₯ 𝑦 6 3
  • B 6 7 2 π‘₯ 𝑦 3 6
  • C βˆ’ 6 7 2 π‘₯ 𝑦 3 6
  • D βˆ’ 5 3 7 6 π‘₯ 𝑦 6 3

Q17:

In a binomial expansion, where the general term is , determine the position of the term containing .

  • A
  • B
  • C
  • D

Q18:

Find in the expansion of .

  • A
  • B
  • C
  • D

Q19:

Let be the term in the expansion of in increasing powers of . Find all nonzero values of for which .

  • A4, 12
  • B2, 14
  • C2,
  • D2, 1

Q20:

Given that the sum of the first, middle, and last terms in the expansion of ( π‘₯ βˆ’ 1 ) 6 is 42 337, find all possible real values of π‘₯ .

  • A π‘₯ = βˆ’ 6 , π‘₯ = βˆ’ √ 1 9 6 3
  • B π‘₯ = 6 , π‘₯ = √ 1 9 6 3
  • C π‘₯ = βˆ’ 6 , π‘₯ = √ 1 9 6 3
  • D π‘₯ = 6 , π‘₯ = βˆ’ √ 1 9 6 3
  • E π‘₯ = 2 1 6 , π‘₯ = βˆ’ 1 9 6

Q21:

Find in the expansion of .

  • A
  • B
  • C
  • D

Q22:

Find in the expansion of .

  • A
  • B
  • C
  • D

Q23:

Find the second-to-last term in ( 2 + π‘₯ ) 3 4 .

  • A 3 4 π‘₯ 3 3
  • B 6 8 π‘₯
  • C 3 4 π‘₯
  • D 6 8 π‘₯ 3 3

Q24:

Let be the th term in the expansion of in descending powers of . Find all the nonzero values of for which .

  • A ,
  • B ,
  • C ,
  • D ,

Q25:

Find the general term in .

  • A
  • B
  • C
  • D
  • E