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There are total 20 matches and the outcome can either be win, lose or tie. We have to find the number of ways in which exactly 10 predictions are correct which can be shown by <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 20 subscript 10" width="44" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»10«/mn»«none/»«mprescripts/»«none/»«mn»20«/mn»«/mmultiscripts»«/math»'/> ways in which his prediction is correct. And in the remaining 10 matches, he makes wrong predictions i.e. out of 3 outcomes (win, lose, tie) he can pick 2 outcomes out of 3 , which can be done in <img src="data:image/png;base64,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" class="Wirisformula" alt="2 to the power of 10" width="26" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mn»10«/mn»«/msup»«/math»'/> ways. Thus, total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 20 subscript 10" width="44" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»10«/mn»«none/»«mprescripts/»«none/»«mn»20«/mn»«/mmultiscripts»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==" class="Wirisformula" alt="cross times" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#215;«/mo»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAARCAYAAADDjbwNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAANBJREFUeNpjYCAdqAFxLRBfwCHvA8Q3oNiHgQKwGIjTgPg/FjlLID4IxMJQvB8qRhHAZtEGILZH4tsC8SZaWPQJiJmQ+ExQMTiwBuI1UMFf0PCPJsMibGK/kDmgcI0EYh4oXwuIj0LFKPERC7qPsAF5IL5EYRyB2FuIiYcfJFpkCU1pgkAsCg0pL0KWWEKDD5sF6Bg9H90C4ndAnEfIEg4gPglNJDQDgtCwdqOlJUpQS1RoaYkGEM8GYi5aWiIOxKug6Z6mYAvURzQH//HgoQUAEB02yr6Q1qIAAABhdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1uPjI8L21uPjxtbj4xMDwvbW4+PC9tc3VwPjwvbWF0aD5mg81tAAAAAElFTkSuQmCC" class="Wirisformula" alt="2 to the power of 10" width="26" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mn»10«/mn»«/msup»«/math»'/>

A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :

Solution for the question - a person predicts the outcome of 20 cricket matches of his home team. eachmatch can result either in a win, loss or tie for the home

A person predicts the outcome of 20 cricket matches of his home-Turito

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The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

Solution for the question - the sum of all the numbers that can be formed with the digits 2, 3, 4, 5taken all at a time is (repetition is not allowed) : none of these

The sum of all the numbers that can be formed with the digits 2-Turito

Total number of divisors of 480, that are of the form 4n + 2, n <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAALCAYAAAB24g05AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAKIPF7gAAAADFJREFUeNpjYMAE+4HYkoECANK8d3gaVATE/8l1wX6oKywHt0YY2EtpYFEMfhDAKAAAkv8WtNOHnC8AAABQdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDIyNjU7PC9tbz48L21hdGg+tOdhZwAAAABJRU5ErkJggg==" class="Wirisformula" alt="greater or equal than" width="16" height="11" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math»'/> 0, is equal to :

Solution for the question - total number of divisors of 480, that are of the form 4n + 2, n 0, isequal to : none of these4

Total number of divisors of 480, that are of the form 4n + 2, n-Turito

If 9P5 + 5 9P4 = <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAVCAYAAADID4fUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAQpJREFUeNpjYEAANSCuBeILDNiBDxDfgGIfBhqBxUCcBsT/schZAvFBIBaG4v1QMZoBbI7YAMT2SHxbIN5Eb0d8AmImJD4TVIyujsAm9guH/h9Q9SD8BYhXAbEjLUKCBUdIqKAlbDYgdgHi+0CsRe00AWJvwaIuAIiXYhFPBuISSh1hCc0RgkAsCs0pXljU1eOwrAOIc4i1HB2jlxO3gPgdEOfhMAMU/35oYqJQfcIMdAIgyySR+MZAfJSchEkuACXcP9AQfAe1vBnNUTQH5tB0M6AgEojnD7QjJkHrngEF63BkW3QAq4X3Q0tXaWo6ApQYOYhMvLOhpeuAAHNorhlNvEMq8dIUYE28AMGMQqnGyHAPAAAAn3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbXVsdGlzY3JpcHRzPjxtc3ViPjxtaT5QPC9taT48bWk+cjwvbWk+PC9tc3ViPjxtcHJlc2NyaXB0cy8+PG5vbmUvPjxtbj4xMDwvbW4+PC9tbXVsdGlzY3JpcHRzPjwvbWF0aD41RwYWAAAAAElFTkSuQmCC" class="Wirisformula" alt="scriptbase P subscript r end scriptbase presuperscript 10" width="33" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«msub»«mi»P«/mi»«mi»r«/mi»«/msub»«mprescripts/»«none/»«mn»10«/mn»«/mmultiscripts»«/math»'/>, then r =

Solution for the question - if 9p5 + 59p4 = , then r = 10954

If 9p5 + 59p4 = , then r = -Turito

Assertion (A) :If <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 5 x plus 1 over denominator left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x plus 2 end fraction plus fraction numerator B over denominator x minus 1 end fraction" width="230" height="37" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mi»A«/mi»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mi»B«/mi»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math»'/>, then <img src="data:image/png;base64,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" class="Wirisformula" alt="A equals 3 comma B equals 2" width="81" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mn»3«/mn»«mo»,«/mo»«mi»B«/mi»«mo»=«/mo»«mn»2«/mn»«/math»'/> Reason (R) :<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator P x plus q over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end fraction equals fraction numerator P a plus q over denominator left parenthesis x minus a right parenthesis left parenthesis a minus b right parenthesis end fraction plus fraction numerator P b plus q over denominator left parenthesis x minus b right parenthesis left parenthesis b minus a right parenthesis end fraction" width="348" height="37" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»P«/mi»«mi»x«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mi»a«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mi»b«/mi»«mo»)«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»P«/mi»«mi»a«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mi»a«/mi»«mo»)«/mo»«mo»(«/mo»«mi»a«/mi»«mo»§#8722;«/mo»«mi»b«/mi»«mo»)«/mo»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»P«/mi»«mi»b«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mi»b«/mi»«mo»)«/mo»«mo»(«/mo»«mi»b«/mi»«mo»§#8722;«/mo»«mi»a«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/math»'/>

Solution for the question - assertion (a) :if (5x+1)/((x+2)(x-1))=(a)/(x+2)+(b)/(x-1) , thena=3,b=2 reason (r) :(p_(x)+q)/((x-a)(x-b))=(pa+q)/((x-a)(a-b))+(pb+q

Assertion (a) :if (5x+1)/((x+2)(x-1))=(a)/(x+2)+(b)/(x-1) , t-Turito

Velocity at  when dropped from  where Or  (i) Potential energy at  (ii)  Kinetic energy  potential energy

A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

Solution for the question - a particle is released from a height. at certain height its kinetic energyis three times its potential energy. the height and speed

A particle is released from a height. at certain height its kin-Turito

If x is real, then maximum value of <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 3 x to the power of 2 end exponent plus 9 x plus 17 over denominator 3 x to the power of 2 end exponent plus 9 x plus 7 end fraction" width="112" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»3«/mn»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mn»9«/mn»«mi»x«/mi»«mo»+«/mo»«mn»17«/mn»«/mrow»«mrow»«mn»3«/mn»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mn»9«/mn»«mi»x«/mi»«mo»+«/mo»«mn»7«/mn»«/mrow»«/mfrac»«/math»'/> is

Solution for the question - if x is real, then maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7) is 41(1)/(4)   (17)/(7)  1

If x is real, then maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7-Turito

The value of 'c' of Lagrange's mean value theorem for <img src="data:image/png;base64,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" class="Wirisformula" alt="f space left parenthesis x right parenthesis equals x squared minus 3 x minus 2 text  for  end text x element of left square bracket negative 1 , 2 right square bracket" width="244" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«mtext»§#160;for§#160;«/mtext»«mi»x«/mi»«mo»§#8712;«/mo»«mo»[«/mo»«mo»-«/mo»«mn»1,2«/mn»«mo»]«/mo»«/math»'/> is

Solution for the question - the value of 'c' of lagrange's mean value theorem for f(x)=x^(2)-3x-2 for xin[-1,2] is lmvt is not applicable

The value of 'c' of lagrange's mean value theorem for f(x)=x^(2-Turito

The value of 'c' of Rolle's mean value theorem for <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKQAAAASCAYAAADVJnUpAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAApRJREFUeNrtWjFIxDAULSKHiJuIg7iIODiI4CAi4uIg4iBujiIcIiIOgpM4uBw3iBzuDg4HIg4OIog4iNwicoiDuIvbDSIiItQf/UMJTfrTmKRe8+DBtWl+f/9/TX5yDQI9rABLin1K2M8kwozZ8dBEC7A74ZohYC2l/Rvs7wXpkYhpYAP5AGyViGo45T1GgNdekD94xwFA18/QoL8DwC1g3UBfqe9MfM8RoQ0KjAyjIHVwjcLMsyD7gff/wM9DYDHlfah9Y9vngVXCTcrAVc2HXEtRf/op262focG+se3bwE2C8XPgRMz5JYHIdrAtijHgpeXAqfhnI9F8vNnxBtbvBzidN/DlzZ0gT7j5fEHS+RVYELTdcQuiReB+zHUFtJNUV4iY9uGp/lGDqOPnEXCOO15DMU5ibdkD/AC253GEfAT2Eox/JSyKdvH3VMIo+OkgcCr+mU70EwouelyMuY6Nkp15E2QLThGBpiAZLvANrycE8tNR4Kj+mUw0H292/CZYaL7/QbJ1RnInghwFXhGNy6ZshnUUm2yv0dWUTfXPdKL5eIviP0bIS1OOkAtYu1DARphxQRs7f4zToqwOdbGoUfHPdKL5eIviT8lLUwqyIqhfVLZ9+oCnWIB3AG8lU+Iq2rEZOBX/TCe6wq3sK4KVvuh8LlbZM0TjcRvjXcAzLsGzwe/GaBxsb4yr+mc60Xy8RfGn5MW1IKvYNveXgmQruTYF52qRGqyAgesRODvNnbP916GqfzYSzcdbFH9KXkILQpTVxjJBUuvqkB89XhSd9B9XZAdZ8LOqMMNKn2Ev+N1/TPM33nKKfmWFWtULkoaPCF2AlXCyD3GUfGfT53zQXPCfn9kFK4W6fRjkb12W7HgQ8Q2OsBA/bBqiuwAAAPV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ZjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPig8L21vPjxtaT54PC9taT48bW8+KTwvbW8+PG1vPj08L21vPjxtbz58PC9tbz48bWk+eDwvbWk+PG1vPnw8L21vPjxtbz49PC9tbz48bWk+aTwvbWk+PG1pPm48L21pPjxtbz4mI3hBMDs8L21vPjxtbz5bPC9tbz48bW8+LTwvbW8+PG1uPjEsMTwvbW4+PG1vPl08L21vPjwvbWF0aD5PHjkgAAAAAElFTkSuQmCC" class="Wirisformula" alt="f space left parenthesis x right parenthesis equals vertical line x vertical line equals i n space left square bracket negative 1 , 1 right square bracket" width="164" height="18" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«mo»=«/mo»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mo»[«/mo»«mo»-«/mo»«mn»1,1«/mn»«mo»]«/mo»«/math»'/> is

Solution for the question - the value of 'c' of rolle's mean value theorem for f(x)=|x|=in[-1,1] is rolle's theorem is not applicable

The value of 'c' of rolle's mean value theorem for f(x)=|x|=in[-Turito

The value of 'c' of Rolle's theorem for <img src="data:image/png;base64,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" class="Wirisformula" alt="f space left parenthesis x right parenthesis equals l o g space open parentheses x squared plus 2 close parentheses" width="136" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»l«/mi»«mi»o«/mi»«mi»g«/mi»«mo»§#160;«/mo»«mfenced separators=¨|¨»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/math»'/> – <img src="data:image/png;base64,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" class="Wirisformula" alt="l o g subscript 3 end subscript" width="34" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»l«/mi»«mi»o«/mi»«mi»g«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msub»«/math»'/> on [–1, 1] is

Solution for the question - the value of 'c' of rolle's theorem for f(x)=log(x^(2)+2)  log_(3) on[1, 1] is rolle's theorem is not applicable

The value of 'c' of rolle's theorem for f(x)=log(x^(2)+2)  l-Turito

For <img src="data:image/png;base64,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" class="Wirisformula" alt="f space left parenthesis x right parenthesis equals 4 minus left parenthesis 6 minus x right parenthesis to the power of 2 divided by 3 end exponent" width="150" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»4«/mn»«mo»-«/mo»«mo»(«/mo»«mn»6«/mn»«mo»-«/mo»«mi»x«/mi»«msup»«mo»)«/mo»«mrow»«mn»2«/mn»«mo»/«/mo»«mn»3«/mn»«/mrow»«/msup»«/math»'/> in [5, 7]

Solution for the question - for f(x)=4-(6-x)^(2//3) in [5, 7 both theorems are not applicablelagranges theorem is applicable but rolles theorem is not applicable

For f(x)=4-(6-x)^(2//3) in [5, 7] -Turito

The value of 'c' in Lagrange's mean value theorem for <img src="data:image/png;base64,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" class="Wirisformula" alt="f space left parenthesis x right parenthesis equals x cubed minus 2 x squared minus x plus 4" width="170" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mi»x«/mi»«mo»+«/mo»«mn»4«/mn»«/math»'/> in [0, 1] is

Solution for the question - the value of 'c' in lagrange's mean value theorem for in [0, 1] is 02/31/2

The value of 'c' in lagrange's mean value theorem for in [0, 1]-Turito

The value of 'c' in Lagrange's mean value theorem for <img src="data:image/png;base64,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" class="Wirisformula" alt="f space left parenthesis x right parenthesis equals x space left parenthesis x minus 2 right parenthesis squared" width="121" height="18" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math»'/> in [0, 2] is

Solution for the question - the value of 'c' in lagrange's mean value theorem for in [0, 2] is 3/22/31

The value of 'c' in lagrange's mean value theorem for in [0, 2]-Turito

The equation <img src="data:image/png;base64,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" class="Wirisformula" alt="r equals a c o s space theta plus b s i n space theta" width="142" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»=«/mo»«mi»a«/mi»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»+«/mo»«mi»b«/mi»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«/math»'/> represents

Solution for the question - the equation r=a cos theta+b sin theta represents a straight linea circlean ellipse

The equation r=a cos theta+b sin theta represents -Turito

The polar equation of the circle whose end points of the diameter are <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses square root of 2 comma fraction numerator pi over denominator 4 end fraction close parentheses" width="66" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«msqrt»«mn»2«/mn»«/msqrt»«mo»,«/mo»«mfrac»«mrow»«mi»π«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses square root of 2 comma fraction numerator 3 pi over denominator 4 end fraction close parentheses" width="76" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«msqrt»«mn»2«/mn»«/msqrt»«mo»,«/mo»«mfrac»«mrow»«mn»3«/mn»«mi»π«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«/math»'/> is

Solution for the question - the polar equation of the circle whose end points of the diameter are(sqrt2,(pi)/(4)) and (sqrt2,(3pi)/(4)) is none

The polar equation of the circle whose end points of the diamet-Turito

The radius of the circle <img src="data:image/png;base64,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" class="Wirisformula" alt="r equals 8 s i n space theta plus 6 c o s space theta" width="143" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»=«/mo»«mn»8«/mn»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»+«/mo»«mn»6«/mn»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«/math»'/> is

Solution for the question - the radius of the circle r=3sin theta+6cos theta is 201510