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Maths-

General

Easy

Question

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

AP
GP
HP
None of these

The correct answer is: GP

$left parenthesis a plus 2 b plus 2 c right parenthesis left parenthesis a minus 2 b plus 2 c right parenthesis equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent$
$table row cell rightwards double arrow left parenthesis a plus 2 c right parenthesis to the power of 2 end exponent minus left parenthesis 2 b right parenthesis to the power of 2 end exponent equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent end cell row cell rightwards double arrow a to the power of 2 end exponent plus 4 a c plus 4 c to the power of 2 end exponent minus 4 b to the power of 2 end exponent equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent end cell row cell rightwards double arrow 4 a c minus 4 b to the power of 2 end exponent equals 0 rightwards double arrow b to the power of 2 end exponent equals a c end cell end table$
Hence, a, b, c are in GP.

Related Questions to study

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

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

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

Chemistry-General

parallel

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

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

parallel

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

(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

parallel

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

Which of the following is dihydric alcohol?

Which of the following is dihydric alcohol?

Chemistry-General

parallel

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

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

parallel

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