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Maths-

General

Easy

Question

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

$\frac{x^{2} - y^{2}}{x^{2} + y^{2}}$
$\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$
$\frac{x^{2} - y}{x^{2} + y}$
$\frac{x^{2} + y}{x^{2} - y}$

The correct answer is: $fraction numerator x to the power of 2 end exponent minus y over denominator x to the power of 2 end exponent plus y end fraction$

We have
$fraction numerator a over denominator 1 minus r end fraction equals x$
$text and end text table row cell fraction numerator a to the power of 2 end exponent over denominator 1 minus r to the power of 2 end exponent end fraction equals fraction numerator a over denominator 1 minus r end fraction times fraction numerator a over denominator 1 plus r end fraction equals y end cell row cell rightwards double arrow y equals x times fraction numerator a over denominator 1 plus r end fraction equals x times fraction numerator x left parenthesis 1 minus r right parenthesis over denominator 1 plus r end fraction rightwards double arrow fraction numerator y over denominator x to the power of 2 end exponent end fraction equals fraction numerator 1 minus r over denominator 1 plus r end fraction end cell row cell rightwards double arrow fraction numerator x to the power of 2 end exponent over denominator y end fraction equals fraction numerator 1 plus r over denominator 1 minus r end fraction rightwards double arrow fraction numerator x to the power of 2 end exponent over denominator y end fraction left parenthesis 1 minus r right parenthesis equals 1 plus r end cell row cell rightwards double arrow r open square brackets 1 plus fraction numerator x to the power of 2 end exponent over denominator y end fraction close square brackets equals negative 1 fraction numerator x to the power of 2 end exponent over denominator y end fraction rightwards double arrow r equals fraction numerator x to the power of 2 end exponent minus y over denominator x to the power of 2 end exponent plus y end fraction end cell end table$

Related Questions to study

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

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

parallel

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

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

parallel

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

(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

parallel

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

Which of the following is dihydric alcohol?

Which of the following is dihydric alcohol?

Chemistry-General

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

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

parallel

The number of pairs $left parenthesis x comma y right parenthesis$ satisfying $4 x to the power of 2 end exponent minus 4 x plus 2 equals s i n to the power of 2 end exponent invisible function application y text and end text blank x to the power of 2 end exponent plus y to the power of 2 end exponent less or equal than 3$ are

The number of pairs $left parenthesis x comma y right parenthesis$ satisfying $4 x to the power of 2 end exponent minus 4 x plus 2 equals s i n to the power of 2 end exponent invisible function application y text and end text blank x to the power of 2 end exponent plus y to the power of 2 end exponent less or equal than 3$ are

The number of values of x in the interval the number of values of x in the interval $blank left square bracket 0 , 5 pi right square bracket$ satisfying the equation $text end text 3 s i n to the power of 2 end exponent invisible function application x minus 7 s i n invisible function application x plus 2 equals 0 text end text$ is

The number of values of x in the interval the number of values of x in the interval $blank left square bracket 0 , 5 pi right square bracket$ satisfying the equation $text end text 3 s i n to the power of 2 end exponent invisible function application x minus 7 s i n invisible function application x plus 2 equals 0 text end text$ is

The number of solutions of the equation $vertical line s i n invisible function application x vertical line equals vertical line x minus 1 vertical line$ in the interval $text end text left square bracket 0 comma pi right square bracket text is end text$

The number of solutions of the equation $vertical line s i n invisible function application x vertical line equals vertical line x minus 1 vertical line$ in the interval $text end text left square bracket 0 comma pi right square bracket text is end text$

parallel

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