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Maths-

General

Easy

Question

Statement 1:If $x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 25 z to the power of 2 end exponent equals x y z open parentheses fraction numerator 15 over denominator x end fraction plus fraction numerator 5 over denominator y end fraction plus fraction numerator 3 over denominator z end fraction close parentheses$ , then $x comma blank y comma blank z$ are in H.P.
Statement 2:If $a subscript 1 end subscript superscript 2 end superscript plus a subscript 2 end subscript superscript 2 end superscript plus horizontal ellipsis plus a subscript n end subscript superscript 2 end superscript equals 0$ , then $a subscript 1 end subscript equals a subscript 2 end subscript equals a subscript 3 end subscript equals horizontal ellipsis a subscript n end subscript equals 0$

Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
Statement 1 is True, Statement 2 is False
Statement 1 is False, Statement 2 is True

The correct answer is: Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

$x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 25 z to the power of 2 end exponent equals x y z open parentheses fraction numerator 15 over denominator x end fraction plus fraction numerator 5 over denominator y end fraction plus fraction numerator 3 over denominator z end fraction close parentheses$
$rightwards double arrow x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 25 z to the power of 2 end exponent minus 15 y z minus 5 x z minus 3 x y equals 0$
$rightwards double arrow 2 x to the power of 2 end exponent plus 18 y to the power of 2 end exponent plus 50 z to the power of 2 end exponent minus 30 y z minus 10 x z minus 6 x y equals 0$
$rightwards double arrow open parentheses x minus 3 y close parentheses to the power of 2 end exponent plus open parentheses 3 y minus 5 z close parentheses to the power of 2 end exponent plus open parentheses 5 z minus x close parentheses to the power of 2 end exponent equals 0$
$rightwards double arrow x minus 3 y equals 0 comma blank 3 y minus 5 z equals 0 comma blank 5 z minus x equals 0$
$rightwards double arrow x equals 3 y equals 5 z equals k$ (say)
$rightwards double arrow x equals k comma blank y equals k divided by 3 comma blank z equals k divided by 5$
Hence, $x comma blank y comma blank z$ are in H.P. Hence option ( (a) is correct

Related Questions to study

The harmonic mean of the roots of the equation $open parentheses 5 plus square root of 2 close parentheses x to the power of 2 end exponent minus open parentheses 4 plus square root of 5 close parentheses x plus 8 plus 2 square root of 5 equals 0$ is

The harmonic mean of the roots of the equation $open parentheses 5 plus square root of 2 close parentheses x to the power of 2 end exponent minus open parentheses 4 plus square root of 5 close parentheses x plus 8 plus 2 square root of 5 equals 0$ is

The sum to 50 terms of the series $fraction numerator 3 over denominator 1 to the power of 2 end exponent end fraction plus fraction numerator 5 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end fraction plus fraction numerator 7 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent end fraction plus horizontal ellipsis$ is

The sum to 50 terms of the series $fraction numerator 3 over denominator 1 to the power of 2 end exponent end fraction plus fraction numerator 5 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end fraction plus fraction numerator 7 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent end fraction plus horizontal ellipsis$ is

If $a comma blank x$ and $b$ are in A.P., $a comma blank y comma$ and $b$ are in G.P. and $a comma blank z comma blank b$ are in H.P. such that $x equals 9 z$ and $a greater than 0 comma blank b greater than 0$ , then

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parallel

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If $x comma blank y comma blank z$ are real and $4 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 16 z to the power of 2 end exponent minus 6 x y minus 12 y z minus 8 z x equals 0$ , then $x comma blank y comma blank z$ are in

If $x comma blank y comma blank z$ are real and $4 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 16 z to the power of 2 end exponent minus 6 x y minus 12 y z minus 8 z x equals 0$ , then $x comma blank y comma blank z$ are in

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parallel

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parallel

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parallel

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If $P subscript n end subscript$ denotes the $n to the power of t h end exponent$ foot of the perpendicular on $O A$ : then $O P subscript n end subscript$ is

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$P subscript 1 end subscript$ is the foot of the perpendicular from $P$ to $O A$ :
$M subscript 1 end subscript$ is that of $P subscript 1 end subscript$ from $O P$ ; $P subscript 2 end subscript$ is that of $M subscript 1 end subscript$ from $O A$ ; $M subscript 2 end subscript$ is that of $P subscript 2 end subscript$ from $O P$ ; $P subscript 3 end subscript$ is that of $M subscript 2 end subscript$ from $O A$ ; and so on.
If $P subscript n end subscript$ denotes the $n to the power of t h end exponent$ foot of the perpendicular on $O A$ : then $O P subscript n end subscript$ is
Maths-General

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The maximum sum of the series $20 plus 19 fraction numerator 1 over denominator 3 end fraction plus 18 fraction numerator 2 over denominator 3 end fraction plus horizontal ellipsis$ is

The maximum sum of the series $20 plus 19 fraction numerator 1 over denominator 3 end fraction plus 18 fraction numerator 2 over denominator 3 end fraction plus horizontal ellipsis$ is

parallel

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