This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Harmonic Sequences”.

1. If a_{1}, a_{2}……… are in AP then a_{1}^{-1}, a_{2}^{-1}……… are in:

a) An airthmetic sequence

b) A geometic progression

c) Airthmetico-geometric progression

d) None of the mentioned

View Answer

Explanation: If a

_{1}, a

_{2}……… are in AP, then a

_{1}

^{-1}, a

_{2}

^{-1}……… are in Harmonic Progression.

2. The ninth term of ^{1}⁄_{3}, ^{1}⁄_{7}, ^{1}⁄_{11}, ^{1}⁄_{15}, ^{1}⁄_{19},……… is given by:

a) ^{1}⁄_{35}

b) ^{1}⁄_{36}

c) ^{1}⁄_{39}

d) None of the mentioned

View Answer

Explanation: Since here a

_{1}

^{-1}, a

_{2}

^{-1}……… are in AP thus a

_{9}= 3 + (9-1)4 = 35,

^{1}⁄

_{35}is h

_{9}term of the series.

3. If for some number a and d,if first term is ^{1}⁄_{a}, second term is 1/(a+d) ,thrid term is 1/(a+2d) and so on,then 5^{th} term of the sequence is :

a) a+4d

b) a-4d

c) 1/(a+4d)

d) None of the mentioned

View Answer

Explanation: The given sequence will form HP, thus 5

^{th}term will be (a+(5-1)d) – 1.

4. If a, b, c are in hp then a^{-1}, b^{-1}, c^{-1} are in:

a) GP

b) HP

c) AP

d) None of the mentioned

View Answer

Explanation: If a

_{1}, a

_{2}……… are in AP then a

_{1}

^{-1}, a

_{2}

^{-1}……… are in Harmonic Progression.

5. If a, b, c are in hp, then b is related with a and c as :

a) 2(^{1}⁄_{b}) = (^{1}⁄_{a} + ^{1}⁄_{c})

b) 2(^{1}⁄_{c}) = (^{1}⁄_{b} + ^{1}⁄_{c})

c) 2(^{1}⁄_{a}) = (^{1}⁄_{a} + ^{1}⁄_{b})

d) None of the mentioned

View Answer

Explanation:

^{1}⁄

_{a},

^{1}⁄

_{b},

^{1}⁄

_{c}willl be in airthmentic series and

^{1}⁄

_{b}will be the AM of a, c.

6. State whether the given statement is true or false

For number A, C if H is harmonic mean ,G is geometric mean then H>=G.

a) True

b) False

View Answer

Explanation: Geometric mean is always greater than or equal to harmonic mean.

7. State whether the given statement is true or false

For number B, C if H is harmonic mean, A is the airthmetic mean then H>=A.

a) True

b) False

View Answer

Explanation: Airthmetic mean is always greater than or equal to harmonic mean.

8. Which of the following gives the right inequality for AM, GM, HM?

a) AM>=HM>=GM

b) GM>=AM>=HM

c) AM>=GM>=HM

d) GM>=HM>=AM

View Answer

Explanation: Airthmetic mean is always greater than or equal to geometric mean,geometric mean is always greater than or equal to harmonic mean.

9. For two number a,b HM between them is given by:

a) (2b+2a )/3b

b) 2ab/(a+b)

c) (a+b)/2ab

d) 2b/(a+b)

View Answer

Explanation: Let c be the hm,

^{2}⁄

_{c}=

^{1}⁄

_{a}+

^{1}⁄

_{b}(AM property), c = 2b/(a+b).

10. If A, G, H are the AM, GM, HM between a and b respectively then:

a) A, G, H are in hp

b) A, G, H are in gp

c) A, G, H are in ap

d) None of the mentioned

View Answer

Explanation: A = (a+b)/2, G = (ab)

^{1/2}, H = 2b/(a+b), clearly AxH = G

^{2}thus A, G, H are in gp.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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