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Free Sequences and Series MCQs with Answers

163 Sequences and Series MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Sequences describe ordered terms formed by a pattern, while series represent the sum of those terms. Questions cover arithmetic and geometric sequences, their nth terms, common difference or ratio, finite sums, and applications, with the sequence itself kept distinct from the corresponding series.

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163 questions · page 6 of 9

101. The no. of terms is the expansion of (a + x)x-1 ls:

  • A. n + 1
  • B. n - 1
  • C. n
  • D. n - 2

Explanation: Correct Answer "n"Solution :No of terms = index + 1 = n - 1 + 1 = nHence Answer is "(C)"

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Correct answer: n

102. The expansion of (2xy - 2y / x)8 upto two terms is:

  • A. X3 / 256Y8 + X6 / y6
  • B. X3 / 256 y8
  • C. X8 / y8 - X5 / 8y6
  • D. X3 / 256y3 - X6 / 8y6

Explanation: Correct Answer X3 / 256y3 - X6 / 8y6Solution :Hence Answer is "(D)"

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Correct answer: X3 / 256y3 - X6 / 8y6

103. The term independent of x in the expansion of (√x/3+√3/2x2) is:

  • A. C1
  • B. 5/12
  • C. C. 1
  • D. None of these

Explanation: Correct Answer "None of these"Solution:Hence Answer is "(D)"

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Correct answer: None of these

104. The term independent of y in the expansion of (y1/6 - y1/3)4 is:

  • A. 84
  • B. 8,4
  • C. 0.84
  • D. None of these

Explanation: Correct Answer "None of these"Solution :Hence Answer is "(D)"

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Correct answer: None of these

105. The coefficient of in x2 and x3 in (2+x/3) are equal than n is equal to:

  • A. 56
  • B. 55
  • C. 45
  • D. 15

Explanation: Correct Answer "55"Solution :Hence Answer is "(B)"

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Correct answer: 55

106. In the expansion of (3x-1/x2)10,the 5th term from the end is:

  • A. 16486/x5
  • B. 13486/x5
  • C. 17010/x5
  • D. None of these

Explanation: Correct Answer "17010/x5"Solution :Hence Answer is "(C)"

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Correct answer: 17010/x5

107. The coefficient of in 1/y2 in (y+c/y2)10 is:

  • A. 18712
  • B. c12/210
  • C. 210/c12
  • D. 210c12

Explanation: Correct Answer "210/c12"Solution :Hence Answer is "(D)"

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Correct answer: 210/c12

108. If the rth term in the expansion of (x/3-2/x2)10 contains x4 then r is equal to:

  • A. 2
  • B. 4
  • C. 3
  • D. 5

Explanation: Correct Answer "2"Solution :Hence Answer is "(A)"

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Correct answer: 2

109. If the term independent of x in √x+k/x2)10 is 405, then

  • A. 3
  • B. ±3
  • C. -3
  • D. -2

Explanation: Correct Answer "±3"Solution:Hence Answer is "(B)"

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Correct answer: ±3

110. V n ∈ N.8x10-k is divisible by 6 if:

  • A. k=2
  • B. k=8
  • C. k=14
  • D. All are correct

Explanation: Correct Answer "All are correct"Solution :Hence Answer is "(D)"

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Correct answer: All are correct

111. The first three terms in the expansion of (1+ax)(n≠0) aге1,6x and 16x² then the value of a and n are respectively:

  • A. 2 and 9
  • B. 3 and 2
  • C. 2/3 and 9

Explanation: Correct Answer "⅔ and 9"Solution :Hence Answer is "(C)"

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Correct answer: 2/3 and 9

112. If the sum of the co-efficients in the expansion of (x+y)" is 1024 then the value of the greatest co-efficient in the expansion is:

  • A. 356
  • B. 252
  • C. 210
  • D. 120

Explanation: Correct Answer "252"Solution :Hence Answer is "(B)"

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Correct answer: 252

113. If the sum of coefficients of x and x², in the expansion of (1-2x), when n is positive is 16 then the coefficient of x is:

  • A. +32
  • B. -24
  • C. +24
  • D. -32

Explanation: Correct Answer "-32"Solution :Hence Answer is "(D)"

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Correct answer: -32

114. (1-2x)", coefficient of x is -8 then coefficient of x2 is:

  • A. 24
  • B. 29
  • C. 48
  • D. 96

Explanation: Correct Answer "24" Solution:Hence Answer is "(A)"

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Correct answer: 24

115. The binomial series are conveniently used for summation of:

  • A. Alternating series
  • B. Divergent
  • C. Fimite series
  • D. Infinite series

Explanation: Correct Answer "Infinite Series"Solution:By DefinitionHence Answer is "(D)"

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Correct answer: Infinite series

116. If h2 and higher powers of 'h' are neglected then √1+2h/1-h

  • A. 1-3/2h
  • B. 1+3/2h
  • C. 1-2/3h
  • D. 1+2/3h

Explanation: Correct Answer "1+3h/2"Solution :Hence Answer is "(B)"

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Correct answer: 1+3/2h

117. The coefficient xn in the expansion of (1-x)-1 is:

  • A. (-1)^2
  • B. 1
  • C. (-1)n (n+1)
  • D. (n+1)

Explanation: Correct Answer "(-1)n (n+1)" Solution :Hence Answer is "(C)"

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Correct answer: (-1)n (n+1)

118. Sum of series 1-1/2(1/4)+1.3/2.4(1/4)....is:

  • A. 1/√5
  • B. 4/√5
  • C. 2/√5
  • D. 3/√5

Explanation: Correct Answer "2/√5"Solution:Hence Answer is "(C)"

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Correct answer: 2/√5

119. 1-2x+3x²-4x +.........=

  • A. (1+x)-2
  • B. (1+x)-3
  • C. (1-x)
  • D. (1+x)-1

Explanation: Correct Answer "(1+x)-2"Solution:(1-x2)=1-2x-3x2-x2Hence Answer is "(A)"

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Correct answer: (1+x)-2

120. Expansion of √5+10x/3+8x by binomial series is valid if:

  • A. |x|<1
  • B. |x|<1/2
  • C. |x|<2
  • D. |x|<3/8

Explanation: Correct Answer "|x|<3/8"Solution:|10x/5| < 1, |8x/3| < 1Hence Answer is "(D)"

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Correct answer: |x|<3/8
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