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Class 11 Mathematics · Chapter 6 · Test 7

Harmonic Progression

38 MCQs This test covers the definition of an H.P., its nth term, the harmonic mean, inserting H.M.s and the relation between A.M., G.M. and H.M.

MCQs

38 questions · 30 min · 38 marks

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Sample questions

The first 5 of 38. Try each one, then tap to see the answer.

  1. Question 1

    A sequence is a harmonic sequence if the reciprocals of its terms are in

    • AG.P.
    • BA.P.
    • CH.P.
    • Dno progression
    Show answer

    Answer: B

    Reciprocals in A.P. define a harmonic sequence.

  2. Question 2

    The nth term of the H.P. 1/a_1, 1/(a_1 + d), 1/(a_1 + 2d), ... is

    • A1/(a_1 + (n - 1)d)
    • Ba_1 + (n - 1)d
    • C1/(a_1 + nd)
    • D(a_1 + (n - 1)d)/n
    Show answer

    Answer: A

    The reciprocals form an A.P. with nth term a_1 + (n - 1)d.

  3. Question 3

    Which of the following numbers cannot be a term of a harmonic sequence?

    • A1
    • B-1
    • C1/2
    • D0
    Show answer

    Answer: D

    The reciprocal of zero is not defined.

  4. Question 4

    The sequence 1, 1/3, 1/5, 1/7, ... is harmonic because its reciprocals

    • A1, 3, 5, 7, ... are in A.P.
    • B1, 3, 9, 27, ... are in G.P.
    • C1, 2, 3, 4, ... are in A.P.
    • D1, 3, 6, 10, ... are in A.P.
    Show answer

    Answer: A

    The reciprocals 1 and 3 and 5 and 7 have common difference 2.

  5. Question 5

    The 9th term of the H.P. 1/3, 1/5, 1/7, ... is

    • A1/19
    • B1/17
    • C1/21
    • D1/11
    Show answer

    Answer: A

    The reciprocals 3 and 5 and 7 form an A.P. with a_9 = 3 + 8(2) = 19.

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