JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

If three real numbers

a,b,c

are in harmonic progression, then which of the following is true?

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Correct option: B

\frac{1}{{bc}},\frac{1}{{ca}},\frac{1}{{ab}}

are in HP

Option C (

ab,bc,ca

are in HP) is incorrect. Option D (

\frac{a}{b},\frac{b}{c},\frac{c}{a}

are in HP) is incorrect. Option A (

\frac{1}{a},b,\frac{1}{c}

are in AP) is incorrect. Option B (

\frac{1}{{bc}},\frac{1}{{ca}},\frac{1}{{ab}}

are in HP) is correct because if

a, b, c

are in HP, then

bc, ca, ab

are in AP, and thus

\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}

are in HP.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}