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Maths-

General

Easy

Question

Statement – 1: Two circles of radii $square root of 3 & 1$ cut orthogonally then area of common region is $fraction numerator 5 pi minus 6 square root of 3 over denominator 6 end fraction$ square unit.
Statement -2: Area $text end text left parenthesis A union B right parenthesis equals text AreaA end text plus text Area end text left parenthesis B right parenthesis minus text Area end text left parenthesis A intersection B right parenthesis$ , where A & B represents two regions

Statement –1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1
Statement –1 is True, Statement – 2 is True; Statement – 2 is NOT a 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 a correct explanation for Statement – 1

$table row cell text end text text A end text text r end text text e end text text a end text text end text open parentheses A C subscript 1 end subscript C subscript 2 end subscript close parentheses equals fraction numerator 1 over denominator 2 end fraction cross times square root of 3 cross times 1 equals fraction numerator square root of 3 over denominator 2 end fraction end cell row cell t a n invisible function application theta equals square root of 3 rightwards double arrow theta equals fraction numerator pi over denominator 3 end fraction text end text text s end text text o end text text end text beta equals fraction numerator pi over denominator 6 end fraction end cell end table$
$table row cell text end text text A end text text r end text text e end text text a end text text end text text o end text text f end text text end text text a end text text r end text text c end text text end text text s end text text e end text text g end text text m end text text e end text text n end text text t end text text end text A D C subscript 2 end subscript equals fraction numerator theta r to the power of 2 end exponent over denominator 2 end fraction equals fraction numerator fraction numerator pi over denominator 3 end fraction over denominator 2 end fraction equals fraction numerator pi over denominator 6 end fraction equals A subscript 1 end subscript end cell row cell text end text text S end text text i end text text m end text text i end text text l end text text a end text text r end text text l end text text y end text text end text text a end text text r end text text e end text text end text text o end text text f end text text end text text a end text text r end text text c end text text end text text s end text text e end text text g end text text m end text text e end text text n end text text t end text text end text C subscript 1 end subscript E A equals fraction numerator pi over denominator 6 end fraction cross times fraction numerator 3 over denominator 2 end fraction equals fraction numerator pi over denominator 4 end fraction equals A subscript 2 end subscript end cell row cell text end text text S end text text o end text text end text text a end text text r end text text e end text text a end text text end text text o end text text f end text text end text text c end text text o end text text m end text text m end text text o end text text n end text text end text text r end text text e end text text g end text text i end text text o end text text n end text text end text equals A subscript 1 end subscript plus A subscript 2 end subscript minus fraction numerator square root of 3 over denominator 2 end fraction equals fraction numerator pi over denominator 6 end fraction plus fraction numerator pi over denominator 4 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction equals fraction numerator 5 pi minus 6 square root of 3 over denominator 12 end fraction end cell row cell text end text text S end text text o end text text end text text t end text text o end text text t end text text a end text text l end text text end text text a end text text r end text text e end text text a end text text end text text o end text text f end text text end text text c end text text o end text text m end text text m end text text o end text text n end text text end text text r end text text e end text text g end text text i end text text o end text text n end text text end text equals 2 open parentheses fraction numerator 5 pi minus 6 square root of 3 over denominator 12 end fraction close parentheses equals open parentheses fraction numerator 5 pi minus 6 square root of 3 over denominator 6 end fraction close parentheses end cell end table$

Related Questions to study

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

The value of $blank to the power of n end exponent C subscript 1 end subscript minus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses blank to the power of n end exponent C subscript 2 end subscript plus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction close parentheses blank to the power of n end exponent C subscript 3 end subscript minus horizontal ellipsis horizontal ellipsis horizontal ellipsis. plus left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis times fraction numerator 1 over denominator n end fraction close parentheses blank to the power of n end exponent C subscript n end subscript text is end text$

The value of $blank to the power of n end exponent C subscript 1 end subscript minus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses blank to the power of n end exponent C subscript 2 end subscript plus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction close parentheses blank to the power of n end exponent C subscript 3 end subscript minus horizontal ellipsis horizontal ellipsis horizontal ellipsis. plus left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis times fraction numerator 1 over denominator n end fraction close parentheses blank to the power of n end exponent C subscript n end subscript text is end text$

If $text end text open parentheses 1 plus x plus x to the power of 2 end exponent close parentheses to the power of n end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus horizontal ellipsis plus a subscript 2 n end subscript x to the power of 2 n end exponent comma text then end text a subscript 0 end subscript a subscript 1 end subscript minus a subscript 1 end subscript a subscript 2 end subscript plus a subscript 2 end subscript a subscript 3 end subscript minus a subscript 3 end subscript a subscript 4 end subscript plus horizontal ellipsis$ is equal to

If $text end text open parentheses 1 plus x plus x to the power of 2 end exponent close parentheses to the power of n end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus horizontal ellipsis plus a subscript 2 n end subscript x to the power of 2 n end exponent comma text then end text a subscript 0 end subscript a subscript 1 end subscript minus a subscript 1 end subscript a subscript 2 end subscript plus a subscript 2 end subscript a subscript 3 end subscript minus a subscript 3 end subscript a subscript 4 end subscript plus horizontal ellipsis$ is equal to

parallel

Total number of divisors of $n equals 2 to the power of 5 end exponent times 3 to the power of 5 end exponent times 5 to the power of 10 end exponent times 7 to the power of 2 end exponent$ that are of the form $4 lambda plus 2 comma lambda greater or equal than 1$ is equal to

Total number of divisors of $n equals 2 to the power of 5 end exponent times 3 to the power of 5 end exponent times 5 to the power of 10 end exponent times 7 to the power of 2 end exponent$ that are of the form $4 lambda plus 2 comma lambda greater or equal than 1$ is equal to

If the sum of the coefficients in the expansion of $left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis 1 plus left parenthesis p minus 2 right parenthesis x right parenthesis to the power of 20 end exponent$ is equal to square of the sum of the coefficients in the expansion of $left square bracket 2 r q x minus left parenthesis r plus q right parenthesis times y right square bracket to the power of 10 end exponent text , where end text p comma r comma q$ are positive constants, then

If the sum of the coefficients in the expansion of $left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis 1 plus left parenthesis p minus 2 right parenthesis x right parenthesis to the power of 20 end exponent$ is equal to square of the sum of the coefficients in the expansion of $left square bracket 2 r q x minus left parenthesis r plus q right parenthesis times y right square bracket to the power of 10 end exponent text , where end text p comma r comma q$ are positive constants, then

If $text end text stretchy sum from r equals 0 to n of open curly brackets a subscript r end subscript left parenthesis x minus y plus 2 right parenthesis to the power of r end exponent minus b subscript r end subscript left parenthesis y minus x minus 1 right parenthesis to the power of r end exponent close curly brackets equals 0 for all n element of N comma text then end text b subscript n end subscript text end text$ is equal to

If $text end text stretchy sum from r equals 0 to n of open curly brackets a subscript r end subscript left parenthesis x minus y plus 2 right parenthesis to the power of r end exponent minus b subscript r end subscript left parenthesis y minus x minus 1 right parenthesis to the power of r end exponent close curly brackets equals 0 for all n element of N comma text then end text b subscript n end subscript text end text$ is equal to

parallel

Statement-1 : Silicones are resistant to heat, oxidation and most chemicals
Statement-2 : The silicones(a) have stable silica-like six electron owing to high bond energy of Si – O bond and (b) have high strength of Si – C

Statement-1 : Silicones are resistant to heat, oxidation and most chemicals
Statement-2 : The silicones(a) have stable silica-like six electron owing to high bond energy of Si – O bond and (b) have high strength of Si – C

chemistry-General

Statement-1 : Boron forms only covalent compounds
Statement-2 : Due to small size of boron, the sum of its first three ionisation enthalpies very high

Statement-1 : Boron forms only covalent compounds
Statement-2 : Due to small size of boron, the sum of its first three ionisation enthalpies very high

chemistry-General

chemistry-General

parallel

ConcH₂SO₄ cannot be used to prepare HBr from NaBr because it –

ConcH₂SO₄ cannot be used to prepare HBr from NaBr because it –

chemistry-General

Three allotropes (A), (B) and (C) of phosphorous in the following change are respectively

Three allotropes (A), (B) and (C) of phosphorous in the following change are respectively

chemistry-General

The molecular shapes of diborane is shown: Consider the following statements for diborane
1) Boron is approximately sp³ hybridised
2) B-H-B angle is 180°
3) There are two terminal B-H bonds for each boron atom
4) There are only 12 bonding electrons available Of these statements –

The molecular shapes of diborane is shown: Consider the following statements for diborane
1) Boron is approximately sp³ hybridised
2) B-H-B angle is 180°
3) There are two terminal B-H bonds for each boron atom
4) There are only 12 bonding electrons available Of these statements –

chemistry-General

parallel

Which two of the following salts are used for preparing iodized salt–
i) KIO₃
ii) KI
iii) I₂
iv) HI

Which two of the following salts are used for preparing iodized salt–
i) KIO₃
ii) KI
iii) I₂
iv) HI

chemistry-General

Which one of the following oxy acid of fluorine exists ?

Which one of the following oxy acid of fluorine exists ?

chemistry-General

Thermite is a mixture of –

Thermite is a mixture of –

chemistry-General

parallel

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