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Maths-

General

Easy

Question

If the harmonic mean between a and b is H, then $fraction numerator H plus a over denominator H minus a end fraction plus fraction numerator H plus b over denominator H minus b end fraction equals$

4
2
1
a+b

The correct answer is: 2

$text Putting end text H equals fraction numerator 2 a b over denominator a plus b end fraction$
$fraction numerator H plus a over denominator H minus a end fraction plus fraction numerator H plus b over denominator H minus b end fraction equals fraction numerator 2 open parentheses H to the power of 2 end exponent minus a b close parentheses over denominator left parenthesis H minus a right parenthesis left parenthesis H minus b right parenthesis end fraction equals fraction numerator 2 open square brackets fraction numerator 4 a b over denominator left parenthesis a plus b right parenthesis to the power of 2 end exponent end fraction minus a b close square brackets over denominator open square brackets fraction numerator 4 a b over denominator left parenthesis a plus b right parenthesis to the power of 2 end exponent end fraction minus a b close square brackets end fraction equals 2$
$text Trick: Let end text a equals 1 comma H equals fraction numerator 1 over denominator 2 end fraction text and end text b equals fraction numerator 1 over denominator 3 end fraction text . Then end text$
$fraction numerator H plus a over denominator H minus a end fraction plus fraction numerator H plus b over denominator H minus b end fraction equals fraction numerator 3 divided by 2 over denominator negative 1 divided by 2 end fraction plus fraction numerator 5 divided by 6 over denominator 1 divided by 6 end fraction equals 2$

Related Questions to study

If $fraction numerator a to the power of n plus 1 end exponent plus b to the power of n plus 1 end exponent over denominator a to the power of n end exponent plus b to the power of n end exponent end fraction$ is the harmonic mean between $a$ and $b$ , then the value of $n$ is

If $fraction numerator a to the power of n plus 1 end exponent plus b to the power of n plus 1 end exponent over denominator a to the power of n end exponent plus b to the power of n end exponent end fraction$ is the harmonic mean between $a$ and $b$ , then the value of $n$ is

If a ,b, c are three distinct positive real numbers which are in $text HP, then end text fraction numerator 3 a plus 2 b over denominator 2 a minus b end fraction plus fraction numerator 3 c plus 2 b over denominator 2 c minus b end fraction text is end text$

If a ,b, c are three distinct positive real numbers which are in $text HP, then end text fraction numerator 3 a plus 2 b over denominator 2 a minus b end fraction plus fraction numerator 3 c plus 2 b over denominator 2 c minus b end fraction text is end text$

If the $m to the power of text th end text end exponent$ term of an $H P$ is $n$ and $n to the power of text th end text end exponent$ is $m$ , then the $r to the power of text th end text end exponent$ term will be

If the $m to the power of text th end text end exponent$ term of an $H P$ is $n$ and $n to the power of text th end text end exponent$ is $m$ , then the $r to the power of text th end text end exponent$ term will be

parallel

If $left parenthesis a plus 2 b plus 2 c right parenthesis left parenthesis a minus 2 b plus 2 c right parenthesis equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent text , end text$ where a ,b, c are nonzero numbers. Then a ,b,c are in

If $left parenthesis a plus 2 b plus 2 c right parenthesis left parenthesis a minus 2 b plus 2 c right parenthesis equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent text , end text$ where a ,b, c are nonzero numbers. Then a ,b,c are in

The sum of infinite terms of a GP is x and on squaring the each term of it, the sum will be y. Then the common ratio of this series is

The sum of infinite terms of a GP is x and on squaring the each term of it, the sum will be y. Then the common ratio of this series is

Alcohols are ,acidic in nature because hydrogen is attached to oxygen which is an electronegative element. Alcohol is weaker acid than water because $O H to the power of minus end exponent$ ion is more stable than $R minus O to the power of minus end exponent$ ion $R minus 0 to the power of minus end exponent$ is less stable, due to +I effect of the alkyl group., Acidity of alcohols increases with increase:' in ' the stability of acid anion.

Some alcohols . like $C H subscript 3 end subscript minus O H comma C F subscript 3 end subscript minus C H subscript 2 end subscript minus O H$ , $blank open parentheses C F subscript 3 end subscript close parentheses subscript 3 end subscript C minus O H$
are more acidic than water:
The strongest conjugate base out of the following is :

Alcohols are ,acidic in nature because hydrogen is attached to oxygen which is an electronegative element. Alcohol is weaker acid than water because $O H to the power of minus end exponent$ ion is more stable than $R minus O to the power of minus end exponent$ ion $R minus 0 to the power of minus end exponent$ is less stable, due to +I effect of the alkyl group., Acidity of alcohols increases with increase:' in ' the stability of acid anion.

Some alcohols . like $C H subscript 3 end subscript minus O H comma C F subscript 3 end subscript minus C H subscript 2 end subscript minus O H$ , $blank open parentheses C F subscript 3 end subscript close parentheses subscript 3 end subscript C minus O H$
are more acidic than water:
The strongest conjugate base out of the following is :

Chemistry-General

parallel

Final product (D) in the sequence of reactions is:

Final product (D) in the sequence of reactions is:

Chemistry-General

How many isomers of C₅H₁₁OH will be primary alcohols?

How many isomers of C₅H₁₁OH will be primary alcohols?

Chemistry-General

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 0 , 2 pi right square bracket$ is

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 0 , 2 pi right square bracket$ is

parallel

$text If end text theta element of left square bracket 0 , 5 pi right square bracket text and end text r element of R text such that end text 2 s i n invisible function application theta equals r to the power of 4 end exponent minus 2 r to the power of 2 end exponent plus 3$ then the maximum number of values of the pair $left parenthesis r comma theta right parenthesis$ is

$text If end text theta element of left square bracket 0 , 5 pi right square bracket text and end text r element of R text such that end text 2 s i n invisible function application theta equals r to the power of 4 end exponent minus 2 r to the power of 2 end exponent plus 3$ then the maximum number of values of the pair $left parenthesis r comma theta right parenthesis$ is

Which of the following will be the major product when

is treated with dil. H₂SO₄ in the presence of HgSO₄ ?

Which of the following will be the major product when

is treated with dil. H₂SO₄ in the presence of HgSO₄ ?

Chemistry-General

When undergoes dehydration reaction in presence of concentrated H₂SO₄ then what will be the major product?

When undergoes dehydration reaction in presence of concentrated H₂SO₄ then what will be the major product?

Chemistry-General

parallel

(A) Di-tert. butyl ether cannot be prepared by Williamson's ether synthesis.
(R) Tert. butyl bromide on n:eatment with sodium tert. butoxide preferentially undergoes elimination to form isobutylene and tert. butyl alcohol.

(A) Di-tert. butyl ether cannot be prepared by Williamson's ether synthesis.
(R) Tert. butyl bromide on n:eatment with sodium tert. butoxide preferentially undergoes elimination to form isobutylene and tert. butyl alcohol.

Chemistry-General

In the following reaction,

‘A' is:

In the following reaction,

‘A' is:

Chemistry-General

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 0 , 2 pi right square bracket$ is

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 0 , 2 pi right square bracket$ is

parallel

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