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Cases : i) If d = 6 then seven digit numbers possible are = 5C3. 3C3 [as a,b,c can be choosen from 1,2,3,4 or 5 &amp; similarly e,f,g can be choosen from the unused 2 digit which are less than 6 &amp; 0 can be used] ii) If d = 7 then numbers possible =,<img src="data:image/png;base64,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" class="Wirisformula" alt="6 straight C subscript 3 times to the power of 4 straight C subscript 3" width="68" height="22" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«msub»«mi mathvariant=¨normal¨»C«/mi»«mn»3«/mn»«/msub»«msup»«mo»§#8901;«/mo»«mn»4«/mn»«/msup»«msub»«mi mathvariant=¨normal¨»C«/mi»«mn»3«/mn»«/msub»«/math»'/> iii) If d = 8 then numbers possible = <img src="data:image/png;base64,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" class="Wirisformula" alt="7 C subscript 3 times to the power of 5 C subscript 3" width="70" height="22" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«msub»«mi»C«/mi»«mn»3«/mn»«/msub»«msup»«mo»§#8901;«/mo»«mn»5«/mn»«/msup»«msub»«mi»C«/mi»«mn»3«/mn»«/msub»«/math»'/> iv) If d = 9 then numbers possible = <img src="data:image/png;base64,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" class="Wirisformula" alt="8 straight C subscript 3 times to the power of 6 straight C subscript 3" width="68" height="22" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»8«/mn»«msub»«mi mathvariant=¨normal¨»C«/mi»«mn»3«/mn»«/msub»«msup»«mo»§#8901;«/mo»«mn»6«/mn»«/msup»«msub»«mi mathvariant=¨normal¨»C«/mi»«mn»3«/mn»«/msub»«/math»'/> Add all cases

A seven digit number is in form of abcdefg (g, f, e, etc. are digits at units, tens, hundred place etc.) where a &lt; b &lt; c &lt; d &gt; e &gt; f &gt; g. The number of such numbers are

Solution for the question - a seven digit number is in form of abcdefg (g, f, e, etc. are digits atunits, tens, hundred place etc.) where a e > f

A seven digit number is in form of abcdefg (g, f, e, etc. are d-Turito

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First of all select 1 + 2 + 3 + 4 = 10 balls out of 25 identical balls and distribute them as desired. It can happen only in one way. Now let x1, x2, x3 and x4 balls are given to them respectively. (where x1, x2, x3, x4 <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) Its now one can get any number of balls <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACBJREFUeNpjYCAM/kMxRYAqhowC/AEZAJVbThdDBgYAAO75C+VyngYIAAAAUHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyMjM0OzwvbW8+PC9tYXRoPhpvPpoAAAAASUVORK5CYII=" class="Wirisformula" alt="therefore" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8756;«/mo»«/math»'/> non negative integral solution of x1 + x2 + x3 + x4 = 15 will be the number of ways so 15 + 4 –1C4–1 = 18C3

Number of ways in which 25 identical balls can be distributed among Ram, Shyam, Sunder and Ghanshyam such that atleast 1, 2, 3, and 4 balls are given to Ram, Shyam, Sunder and Ghanshyam respectively, is-

Solution for the question - number of ways in which 25 identical balls can be distributed among ram,shyam, sunder and ghanshyam such that atleast 1, 2, 3, and 4

Number of ways in which 25 identical balls can be distributed a-Turito

Let the children be A,B.C A   B   C  <img src="data:image/png;base64,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" class="Wirisformula" alt="open table attributes columnalign right end attributes row 202159 row 3941 end table close curly brackets" width="80" height="45" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mn»202159«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3941«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»'/>→19 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAAFCAYAAAD7VZRuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAEx0lWhwAAABdJREFUeNpjYBgFIwv8h+LhwB717LAHAIjrQ70//jg5AAAAa3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtdGV4dD4mI3hBMDsuLi4uLi4uLi4uLi4uLi4uLiYjeEEwOzwvbXRleHQ+PC9tYXRoPhzV0ZkAAAAASUVORK5CYII=" class="Wirisformula" alt="text  .................  end text" width="59" height="5" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtext»§#160;.................§#160;«/mtext»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="323335 right curly bracket not stretchy rightwards arrow 1" width="95" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»323335«/mn»«mo»}«/mo»«mo stretchy=¨false¨»§#8594;«/mo»«mn»1«/mn»«/math»'/> Total number of ways <img src="data:image/png;base64,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" class="Wirisformula" alt="equals 1 plus 2 plus midline horizontal ellipsis.. plus 19 minus left parenthesis 17 plus 14 plus 11 plus 8 plus 5 plus 2 right parenthesis" width="332" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mn»1«/mn»«mo»+«/mo»«mn»2«/mn»«mo»+«/mo»«mo»§#8943;«/mo»«mo».«/mo»«mo».«/mo»«mo»+«/mo»«mn»19«/mn»«mo»§#8722;«/mo»«mo»(«/mo»«mn»17«/mn»«mo»+«/mo»«mn»14«/mn»«mo»+«/mo»«mn»11«/mn»«mo»+«/mo»«mn»8«/mn»«mo»+«/mo»«mn»5«/mn»«mo»+«/mo»«mn»2«/mn»«mo»)«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="equals 190 minus 57 equals 133" width="131" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mn»190«/mn»«mo»§#8722;«/mo»«mn»57«/mn»«mo»=«/mo»«mn»133«/mn»«/math»'/> By termination Permutation <img src="data:image/png;base64,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" class="Wirisformula" alt="133 cross times 3 factorial equals 798" width="109" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»133«/mn»«mo»§#215;«/mo»«mn»3«/mn»«mo»!«/mo»«mo»=«/mo»«mn»798«/mn»«/math»'/>

One hundred identical marbles are to be distributed to three children so that each gets atlest 20 and no two get equal number. The number of ways  of doing this is -

Solution for the question - one hundred identical marbles are to be distributed to three children sothat each gets atlest 20 and no two get equal number. the nu

One hundred identical marbles are to be distributed to three ch-Turito

The number of five-digit telephone numbers which can be formed using the digits 0, 1, 2 ….9 is 105 . The number of five-digit telephone number which have none of their digits repeated is 10P5 = 30240. Thus, the required number of telephone number is 105 – 30240 = 69760.

The number of five-digit telephone numbers having at least one of their digits repeated is

Solution for the question - the number of five-digit telephone numbers having at least one of theirdigits repeated is 697603024010000090000

The number of five-digit telephone numbers having at least one -Turito

99 × 97 × 95 ×....× 51 <img src="data:image/png;base64,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" class="Wirisformula" alt="equals times fraction numerator 100 factorial over denominator left parenthesis 100 cross times 98 cross times 96 cross times horizontal ellipsis cross times 52 right parenthesis end fraction cross times fraction numerator 1 over denominator 50 factorial end fraction times fraction numerator 100 factorial over denominator 2 to the power of 25 cross times 50 factorial cross times 50 factorial end fraction" width="397" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mo»§#8901;«/mo»«mfrac»«mrow»«mn»100«/mn»«mo»!«/mo»«/mrow»«mrow»«mo»(«/mo»«mn»100«/mn»«mo»§#215;«/mo»«mn»98«/mn»«mo»§#215;«/mo»«mn»96«/mn»«mo»§#215;«/mo»«mo»§#8230;«/mo»«mo»§#215;«/mo»«mn»52«/mn»«mo»)«/mo»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»50«/mn»«mo»!«/mo»«/mrow»«/mfrac»«mo»§#8901;«/mo»«mfrac»«mrow»«mn»100«/mn»«mo»!«/mo»«/mrow»«mrow»«msup»«mn»2«/mn»«mn»25«/mn»«/msup»«mo»§#215;«/mo»«mn»50«/mn»«mo»!«/mo»«mo»§#215;«/mo»«mn»50«/mn»«mo»!«/mo»«/mrow»«/mfrac»«/math»'/> maximum power of 3 in 100 ! <img src="data:image/png;base64,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" class="Wirisformula" alt="equals times open square brackets 100 over 3 close square brackets plus open square brackets 100 over 9 close square brackets plus open square brackets 100 over 27 close square brackets plus open square brackets 100 over 81 close square brackets" width="288" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mo»§#8901;«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mfrac»«mn»100«/mn»«mn»3«/mn»«/mfrac»«/mfenced»«mo»+«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mfrac»«mn»100«/mn»«mn»9«/mn»«/mfrac»«/mfenced»«mo»+«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mfrac»«mn»100«/mn»«mn»27«/mn»«/mfrac»«/mfenced»«mo»+«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mfrac»«mn»100«/mn»«mn»81«/mn»«/mfrac»«/mfenced»«/math»'/> = 33 + 11 + 3 + 1 = 48. maximum power of 3 in 50! = <img src="data:image/png;base64,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" class="Wirisformula" alt="open ceil 50 over 3 close ceil plus open ceil 50 over 9 close ceil plus open ceil 50 over 27 close ceil" width="160" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨§#8968;¨ close=¨§#8969;¨ separators=¨|¨»«mfrac»«mn»50«/mn»«mn»3«/mn»«/mfrac»«/mfenced»«mo»+«/mo»«mfenced open=¨§#8968;¨ close=¨§#8969;¨ separators=¨|¨»«mfrac»«mn»50«/mn»«mn»9«/mn»«/mfrac»«/mfenced»«mo»+«/mo»«mfenced open=¨§#8968;¨ close=¨§#8969;¨ separators=¨|¨»«mfrac»«mn»50«/mn»«mn»27«/mn»«/mfrac»«/mfenced»«/math»'/> = 16 + 5 + 1 = 22 maximum power of 3 in 25! = <img src="data:image/png;base64,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" class="Wirisformula" alt="open square brackets 25 over 3 close square brackets plus open ceil 25 over 9 close square brackets" width="101" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mfrac»«mn»25«/mn»«mn»3«/mn»«/mfrac»«/mfenced»«mo»+«/mo»«mfenced open=¨§#8968;¨ close=¨]¨ separators=¨|¨»«mfrac»«mn»25«/mn»«mn»9«/mn»«/mfrac»«/mfenced»«/math»'/> = 8 + 2 = 10 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACBJREFUeNpjYCAM/kMxRYAqhowC/AEZAJVbThdDBgYAAO75C+VyngYIAAAAUHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyMjM0OzwvbW8+PC9tYXRoPhpvPpoAAAAASUVORK5CYII=" class="Wirisformula" alt="therefore" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8756;«/mo»«/math»'/>exponent of 3 = 48 + 10 – (22 × 2) = 14

The maximum value of P such that 3P divides 99 × 97 × 95 × .... × 51 is-

Solution for the question - the maximum value of p such that 3p divides 99  97  95  ....  51is- 12131411

The maximum value of p such that 3p divides 99  97  95  .-Turito

If <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAAAkCAYAAABlhn+2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAAAhtJREFUeNrtWjFLw0AULiJFxE3EQVwcHByk4CBSxMVBxKmbowgiUsTNSRxcSgcRcXfo4CIODiKIOBTpIuLg4B8QNwcHkVI4v8AbQrwkd7kmuYvvg4+2d8lreV/v3buvLZUYcdgEG5LxI5pjWIBncNz3egM847TYgxXwmJ4vg/ecEvtwBy6BL+Aop8M+7IFdcJZTYR+q4CWVuXWbP+hOSEcThQbd5yqmwGtwGBwBn2wocQOBrqVES7uTMN6jo6VhDLwJCLIGtvLuWD6Jr+CgL8mVhDHnwLZj4pTBK3BCMndBecocnhjvPiFm6LFCApmgTUIxDFCjb0cQTbBuGHs3wf7FCOAQ3JeM34KLknEdG2SBD3hm8Oqt8NHfTn5RTZZB1QYpUxwZhAIZwBs4KRnv9ckG6XKKzVrr75C5Xp9skDQEEgXlH8yDDyFJiCpxqjYIlzhDeHvOecQKqRraINwkGOIU3AqZC2uzdWyQOsVhGHRxqyFzsoOqrg1S1IOqyCqGZ+0MRcx3fHuMrg3iotVjlUDeaviIucYls3QaPKCu0nmBTuj8o2LDbCewa5oRe1taaNF7iiII5JWfGpefxPcIS0RmgTSv1/EpWaCcVpCqT8kC5SSQqk/JAsVcY2Izxc2r+JQsUI5NgopPyQLlJJCqT8kC5SCQjk/JAmUskK5PKf6jMFn9nhSMneTvWvx7l2WrlAVigRgskCP4STPGLyr+8WayUYyQAAAAyXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1mcmFjPjxtaT54PC9taT48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtbz58PC9tbz48bWk+eDwvbWk+PG1vPnw8L21vPjwvbXJvdz48L21mcmFjPjwvbWF0aD7rEXGwAAAAAElFTkSuQmCC" class="Wirisformula" alt="f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction" width="104" height="36" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mi»x«/mi»«mrow»«mn»1«/mn»«mo»+«/mo»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«/mrow»«/mfrac»«/math»'/> for <img src="data:image/png;base64,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" class="Wirisformula" alt="x element of R" width="38" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8712;«/mo»«mi»R«/mi»«/math»'/>, then <img src="data:image/png;base64,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" class="Wirisformula" alt="f to the power of straight prime left parenthesis 0 right parenthesis equals" width="48" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»f«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«mo»(«/mo»«mn»0«/mn»«mo»)«/mo»«mo»=«/mo»«/math»'/>

Solution for the question - if f(x)=(x)/(1+|x|) for x in r , then f(0)= 311 if for then 3210

If f(x)=(x)/(1+|x|) for x in r , then f(0)= 311 if f-Turito

The largest value of r satisfying inequality 20Cr <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAANCAYAAAC3mX7tAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAKNJREFUeNpjYKAOcATibUD8DYh/APEtIJ4AxMIMVAb7gTgIiNmQxAyAeAchTZZUcsAnfJIgS/ZSwUIlIL5BjEJyLRQH4kRoPHmR4jJiLfyPhgvIDYoiqAGEgCAQBwDxSSC2J9VH+6G+IiUIeaCW0cwCZPCD1haAgB40QeAE5FhwEIhDgZgFiJmgJcV9II6ndslgC8RboEH1AxoiPsSEKz5MFgAAzhAvzl0r/jMAAABadEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDIyNjU7PC9tbz48bW4+MzwvbW4+PC9tYXRoPvsCfT0AAAAASUVORK5CYII=" class="Wirisformula" alt="greater or equal than 3" width="26" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«mn»3«/mn»«/math»'/>20Cr – 1 is -

Solution for the question - the largest value of r satisfying inequality 20cr >= 3 20cr  1 is - 765

The largest value of r satisfying inequality 20cr >= 3 20cr -Turito

A double decker bus can accommodate (u + <img src="data:image/png;base64,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" class="Wirisformula" alt="ell" width="12" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#8467;«/mi»«/math»'/>) passengers, u in the upper deck and <img src="data:image/png;base64,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" class="Wirisformula" alt="ell" width="12" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#8467;«/mi»«/math»'/> in the lower deck. The number of ways in which the (u + <img src="data:image/png;base64,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" class="Wirisformula" alt="ell" width="12" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#8467;«/mi»«/math»'/>) passengers can be distributed in the two decks, if r (<img src="data:image/png;base64,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" class="Wirisformula" alt="less or equal than ell" width="28" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8804;«/mo»«mi»§#8467;«/mi»«/math»'/>) particular passengers refuse to go in the upper deck and S(<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAALCAYAAAB24g05AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAKIPF7gAAAADlJREFUeNpjYCAeWALxfgYyAEzjXiibfhr3k6oRBv4DcREDBYBiF9DMIFBgmlNq0G4GeoAfBDAKAACLixa2LHq2kwAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjI2NDs8L21vPjwvbWF0aD4p6IARAAAAAElFTkSuQmCC" class="Wirisformula" alt="less 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»§#8804;«/mo»«/math»'/>u) refuse to sit in the lower deck, is -

Solution for the question - a double decker bus can accommodate (u + in ) passengers, u in the upperdeck and in in the lower deck. the number of ways in which t

A double decker bus can accommodate (u + in ) passengers, u in -Turito

<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC" class="Wirisformula" alt="because" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8757;«/mo»«/math»'/> log10 (1 + x3) &gt; 0 Take antilog 1+ x3 &gt; 1 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAGF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3gyMUQyOzwvbW8+PC9tYXRoPkdgprsAAAAASUVORK5CYII=" class="Wirisformula" alt="not stretchy rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo stretchy=¨false¨»§#8658;«/mo»«/math»'/> x3 &gt; 0 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACBJREFUeNpjYCAM/kMxRYAqhowC/AEZAJVbThdDBgYAAO75C+VyngYIAAAAUHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyMjM0OzwvbW8+PC9tYXRoPhpvPpoAAAAASUVORK5CYII=" class="Wirisformula" alt="therefore" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8756;«/mo»«/math»'/> x &gt; 0 x <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAMCAYAAABr5z2BAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAALV/ZLFgAAAGNJREFUeNpjYMANNIB4AhCfA+JvQPwLiP8zEAmCgPgKEGcAsTEQszGQAGShtnIxkAkmAXEAAwXgKRAzUWIALLBwYdq7YAKlYQCKhTNAzEOJIeFI6cAAiFnIMQQ9Jf4hJSUSDQC2pRnou82QIwAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIwODs8L21vPjwvbWF0aD4h58XOAAAAAElFTkSuQmCC" class="Wirisformula" alt="element of" width="16" height="12" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«/math»'/> (0, <img src="data:image/png;base64,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" class="Wirisformula" alt="straight infinity" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8734;«/mi»«/math»'/>) or x <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAMCAYAAABr5z2BAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAALV/ZLFgAAAGNJREFUeNpjYMANNIB4AhCfA+JvQPwLiP8zEAmCgPgKEGcAsTEQszGQAGShtnIxkAkmAXEAAwXgKRAzUWIALLBwYdq7YAKlYQCKhTNAzEOJIeFI6cAAiFnIMQQ9Jf4hJSUSDQC2pRnou82QIwAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIwODs8L21vPjwvbWF0aD4h58XOAAAAAElFTkSuQmCC" class="Wirisformula" alt="element of" width="16" height="12" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«/math»'/> R+

Domain of f(x) = log10(log10(1 + x3)) is -

Solution for the question - domain of f(x) = log10(log10(1 + x3)) is - none of theser+r

Domain of f(x) = log10(log10(1 + x3)) is --Turito

Solution for the question - the correct orders about compounds i and ii are: melting point vec(r) ii > i   acid strength vec(r) i ii

The correct orders about compounds i and ii are:-Turito

Solution for the question - which of the following is correct method for separating a mixture offollowing compounds?

Which of the following is correct method for separating a mixtu-Turito

Solution for the question - the order in which the reagent must be used to separate the compound i - ivis: naoh, hcl, nahco3

The order in which the reagent must be used to separate the com-Turito

Solution for the question - decreasing order of solubility of following compounds is: iv > iii > ii > iii > iii > i > iv

Decreasing order of solubility of following compounds is:-Turito

Which of the following statement is correct about tropolone? <img src="data:image/png;base64,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" 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Solution for the question - which of the following statement is correct about tropolone? tropolone has lower boiling point than tropone

Which of the following statement is correct about tropolone?-Turito

Solution for the question - in which case first has higher solubility than second? i) phenol, benzeneii) nitrobenzene, phenol iii) ohydroxybenzaldehyde, phydrox

In which case first has higher solubility than second? i) pheno-Turito

Solution for the question - arrange the following in decreasing order of their solubility in water iv > iii > ii > iiv > iii > i > ii