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Maths-

General

Easy

Question

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

greater than or equal to 10
less than or equal to 10
only equal to 10
None of these

The correct answer is: None of these

We have $fraction numerator 1 over denominator a end fraction comma fraction numerator 1 over denominator b end fraction comma fraction numerator 1 over denominator c end fraction text are in AP. Let end text fraction numerator 1 over denominator a end fraction equals p minus q comma fraction numerator 1 over denominator b end fraction equals p text and end text fraction numerator 1 over denominator c end fraction equals p plus q text , end text$
$text where end text p comma q greater than 0 text and end text p greater than q text . Now, substitute these values in end text$
$fraction numerator 3 a plus 2 b over denominator 2 a minus b end fraction plus fraction numerator 3 c plus 2 b over denominator 2 c minus b end fraction$
$text Then it reduces to end text 10 plus fraction numerator 14 q to the power of 2 end exponent over denominator p to the power of 2 end exponent minus q to the power of 2 end exponent end fraction text which is obviously greater end text$
$text than end text 10 stack 0 with bar on top left parenthesis text as end text p greater than q greater than 0 text ) end text$
$text Trick: Put end text a equals 1 comma b equals fraction numerator 1 over denominator 2 end fraction comma c equals fraction numerator 1 over denominator 3 end fraction$
$text The expression has value end text fraction numerator 3 plus 1 over denominator 2 minus fraction numerator 1 over denominator 2 end fraction end fraction plus fraction numerator 1 plus 1 over denominator fraction numerator 2 over denominator 3 end fraction minus fraction numerator 1 over denominator 2 end fraction end fraction equals fraction numerator 8 over denominator 3 end fraction plus 12 greater than 10$

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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

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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.

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are more acidic than water:
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Chemistry-General

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Which of the following will be the major product when

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Which of the following is dihydric alcohol?

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The most general values of $theta$ which satisfy $s i n invisible function application theta equals negative fraction numerator 1 over denominator 2 end fraction comma t a n invisible function application theta equals fraction numerator 1 over denominator square root of 3 end fraction$ are

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