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Maths-

General

Easy

Question

$I f blank a comma b comma c$ and d are the sides of a quadrilateral, then the value of $fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator d to the power of 2 end exponent end fraction$ is always greater than

1
$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{4}$

The correct answer is: $fraction numerator 1 over denominator 3 end fraction$

$H i n t colon$
$table row cell left parenthesis a minus b right parenthesis to the power of 2 end exponent plus left parenthesis b minus c right parenthesis to the power of 2 end exponent plus left parenthesis c minus a right parenthesis to the power of 2 end exponent greater or equal than 0 end cell row cell rightwards double arrow 2 open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses greater or equal than 2 left parenthesis a b plus b c plus c a right parenthesis end cell row cell rightwards double arrow 3 open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses greater or equal than a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent plus 2 left parenthesis a b plus b c plus c a right parenthesis end cell row cell rightwards double arrow 3 open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses greater or equal than left parenthesis a plus b plus c right parenthesis to the power of 2 end exponent end cell row cell rightwards double arrow 3 open parentheses n to the power of 2 end exponent plus h to the power of 2 end exponent plus r to the power of 2 end exponent close parentheses greater than left parenthesis a plus h plus r right parenthesis to the power of 2 end exponent greater than d to the power of 2 end exponent end cell end table$
$left parenthesis blank a s comma blank a plus b plus c greater than d right parenthesis$
$rightwards double arrow fraction numerator open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses over denominator d to the power of 2 end exponent end fraction greater or equal than fraction numerator 1 over denominator 3 end fraction$

Related Questions to study

$l n invisible function application a capital delta A B C blank i f blank a to the power of 2 end exponent s i n invisible function application left parenthesis B minus C right parenthesis plus b to the power of 2 end exponent s i n invisible function application left parenthesis C minus A right parenthesis plus c to the power of 2 end exponent s i n invisible function application left parenthesis A minus B right parenthesis equals 0 blank comma blank t h e n text triangle is end text$

$l n invisible function application a capital delta A B C blank i f blank a to the power of 2 end exponent s i n invisible function application left parenthesis B minus C right parenthesis plus b to the power of 2 end exponent s i n invisible function application left parenthesis C minus A right parenthesis plus c to the power of 2 end exponent s i n invisible function application left parenthesis A minus B right parenthesis equals 0 blank comma blank t h e n text triangle is end text$

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$I f blank x comma y comma z$ are perpendicular drawn from the vertices of a triangle having a, band c, then $fraction numerator b x over denominator c end fraction plus fraction numerator c y over denominator a end fraction plus fraction numerator a z over denominator b end fraction$ is equal to

$I f blank x comma y comma z$ are perpendicular drawn from the vertices of a triangle having a, band c, then $fraction numerator b x over denominator c end fraction plus fraction numerator c y over denominator a end fraction plus fraction numerator a z over denominator b end fraction$ is equal to

parallel

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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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:
Which of the following will react fastest with sodium?

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