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Maths-

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Question

The centres of two circles are $5 square root of 2$ units apart. The circles are orthogonal and their radii are integers $not equal to$ 1. The area of the region, in square units, common to the two circles, is

$\frac{25}{4} (π - 2)$
$\frac{25}{2} (π - 2)$
$\frac{25}{4} (π - 3)$
$\frac{25}{2} (π - 3)$

The correct answer is: $fraction numerator 25 over denominator 2 end fraction left parenthesis pi minus 2 right parenthesis$

The radii are 5 units each. Let S be the area common to the circles $fraction numerator 25 pi over denominator 4 end fraction plus fraction numerator 25 pi over denominator 4 end fraction minus S equals 25$

Related Questions to study

If two chords, each bisected by the x - axis can be drawn to the circle, $2 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent close parentheses minus 2 a x minus b y equals 0 left parenthesis a not equal to 0 comma b not equal to 0 right parenthesis text end text$ from the point $text end text left parenthesis a comma b divided by 2 right parenthesis text end text$ then :

If two chords, each bisected by the x - axis can be drawn to the circle, $2 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent close parentheses minus 2 a x minus b y equals 0 left parenthesis a not equal to 0 comma b not equal to 0 right parenthesis text end text$ from the point $text end text left parenthesis a comma b divided by 2 right parenthesis text end text$ then :

The radius of the least circle passing through the point (8, 4) and cutting the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 40$ orthogonally is

The radius of the least circle passing through the point (8, 4) and cutting the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 40$ orthogonally is

P(3,2) is a point on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 13$ Two points A, B are on the circle such that $P A equals P B equals square root of 5$ The equation of chord AB is

P(3,2) is a point on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 13$ Two points A, B are on the circle such that $P A equals P B equals square root of 5$ The equation of chord AB is

parallel

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

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parallel

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parallel

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

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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

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Statement-2 : Due to small size of boron, the sum of its first three ionisation enthalpies very high

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parallel

chemistry-General

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

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