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<img src="data:image/png;base64,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" class="Wirisformula" alt="0 less or equal than a less or equal than 3 comma 0 less or equal than b less or equal than 3" width="130" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo»§#8804;«/mo»«mi»a«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«mo»,«/mo»«mn»0«/mn»«mo»§#8804;«/mo»«mi»b«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«/math»'/> and the equation <img src="data:image/png;base64,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" class="Wirisformula" alt="x squared plus 4 plus 3 cos space left parenthesis a x plus b right parenthesis equals 2 x" width="199" height="18" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»4«/mn»«mo»+«/mo»«mn»3«/mn»«mi»cos«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»a«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«mi»x«/mi»«/math»'/> has at least one solution then the value of (a+b)

Solution for the question - 0 3 '/> (pi)/(3) '/> (pi)/(4) '/> (pi)/(2) '/>

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Carbocation stability increased by mesomeric effect and by + I effect, decreased by I effect

Correct order for stability of carbocation is <img src="data:image/png;base64,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" 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Solution for the question - correct order for stability of carbocation is ii > iii > iii > i > iiiiii > ii > ii > ii > iii

Correct order for stability of carbocation is-Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text  then  end text y equals" width="339" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mi»sec«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»+«/mo»«mi»tan«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mi»cosec«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»§#8722;«/mo»«mi»cot«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mtext»§#160;then§#160;«/mtext»«mi»y«/mi»«mo»=«/mo»«/math»'/>

Solution for the question - if x=sec theta+tan theta,y=cosec theta-cot theta then y= (x-1)/(x+1) (x+1)/(x-1) (1-x)/(1+x) (1+x)/(1-x)

If x=sec theta+tan theta,y=cosec theta-cot theta then y= -Turito

For all values of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/>, the values of <img src="data:image/png;base64,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" class="Wirisformula" alt="3 minus cos space theta plus cos space open parentheses theta plus pi over 3 close parentheses" width="178" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§#8722;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mfenced separators=¨|¨»«mrow»«mi»§#952;«/mi»«mo»+«/mo»«mfrac»«mi»§#960;«/mi»«mn»3«/mn»«/mfrac»«/mrow»«/mfenced»«/math»'/> lie in the interval

Solution for the question - for all values of, the values oflie in the interval '/> '/> '/> '/>

For all values of, the values oflie in the interval  -Turito

Solution for the question - General '/> '/> '/> '/>

General-Turito

does not exist Extreme Values; <img src="data:image/png;base64,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" class="Wirisformula" alt="cos space invisible function application x plus sin to the power of 4 space x element of" width="120" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»§#160;«/mo»«mo»§#8289;«/mo»«mi»x«/mi»«mo»+«/mo»«msup»«mi»sin«/mi»«mn»4«/mn»«/msup»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8712;«/mo»«/math»'/>

Solution for the question - does not exist extreme values; cos x+sin^(4)x in [(3)/(4),1] [(3)/(2),2] [1,(3)/(2)] [(1)/(2),1]

Does not exist extreme values; cos x+sin^(4)x in -Turito

Solution for the question - (sin x+cos x)^(2)+cos^(2)((pi)/(4)+x)in [0,3] [1,2] [0,2] [0,1]

(sin x+cos x)^(2)+cos^(2)((pi)/(4)+x)in -Turito

The minimum and maximum values of <img src="data:image/png;base64,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" class="Wirisformula" alt="cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6" width="211" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«mi»sin«/mi»«mo»§#160;«/mo»«mfenced separators=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«/mrow»«/mfenced»«mo»+«/mo»«mn»6«/mn»«/math»'/> are

Solution for the question - the minimum and maximum values ofare 5,66,511,-11,11

The minimum and maximum values ofare -Turito

The minimum and maximum values of <img src="data:image/png;base64,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" class="Wirisformula" alt="sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses" width="180" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mo»§#160;«/mo»«mfenced separators=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«/mrow»«/mfenced»«mi»sin«/mi»«mo»§#160;«/mo»«mfenced separators=¨|¨»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«/mrow»«/mfenced»«/math»'/> are

Solution for the question - the minimum and maximum values ofare '/> '/> '/>-1,1

Solution for the question - sin^(2)x+cos^(4)x in [-(3)/(4),(3)/(4)] [-1,-(3)/(4)] [(3)/(4),1] [(1)/(4),(1)/(2)]

Sin^(2)x+cos^(4)x in -Turito

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at <img src="data:image/png;base64,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" class="Wirisformula" alt="lambda divided by 4" width="31" height="15" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»λ«/mi»«mo»/«/mo»«mn»4«/mn»«/math»'/> and second resonance occurs at <img src="data:image/png;base64,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" class="Wirisformula" alt="3 lambda divided by 4." width="46" height="15" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»3«/mn»«mi»λ«/mi»«mo»/«/mo»«mn»4«/mn»«mo».«/mo»«/math»'/> Thus, at first resonance <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses" width="88" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»λ«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»13«/mn»«mi» «/mi»«mo»…«/mo»«mfenced separators=¨|¨»«mrow»«mi»i«/mi»«/mrow»«/mfenced»«/math»'/> And a second resonance <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAAjCAYAAACJiBSDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAmtJREFUeNrtmTFLA0EQhY8gwSKNWFhYCCKWErCQICJ2IilEsLASESSIiIVgIWJhE1KJnYWIiI2IWIgEgoiEENKIWIjY+A8sUoQgQpyFKc5k93Zvk927XOaDB2ZuT86Z3Ozs03H4zIEeQDVQHfQJOgYNctbG8PqMQ1jhCbQEirtiSVBesL4PdCUoHmGJqse1edABpSgYRkEfHtdZe3uhNNllCLSG+8qCZG2J9h47NJq0I1mfAe2Czih19hgALYIqoFnBmjHQHf78DEpQ2uySwALx9poCtj/GPmiD0mWfOid2BFpxfZ4EFSlVdpnAocBNCnTDWfvV42eeTVDW5z1ZvE8K2zeW8XAZQ8eAJXyV0+Z4Rcj1cGtjX+Ky5r0lvN8TNg7fYxuro2OQblpzgS5Cpx9QlzROlSLG8ZD8avg5WIKTgms1/LKLYpHcEthb/C4pziW+zQ2Dz5HE4ogm2jeFWBGLFBlOQeuKiTdZHNbOt9r8Hdsa+1VomQY9+ki8yeLkPRySQ9CeQizl+ntC50TwJCKObWEkJMWpOv+dfDfXeJiXxeKOt8HcNWSb2kjQxfn1uMaOIcMKMcaPzje4HZkYWUsaiQ+iODGcymQxYXG6ra1VcNoJU3FEbW0KjyOyWGTamu6barI4BRxQmmH21rlCLHQDQacLFsZR+gRHfVnMwftzVBz1t1P1s+gQeuu0/qOSF4vkIVQl8TpDit/iMMpOqz/2DepXiHXMvkkbbhHdinHjU4aKl9XLZDQsmI45+X68LMIifr0swhI6XhZhCR0vi7A0heh4WYQFdL0swtIBz6brTBg8kRNUHIKKEwB/ZfHYnVlZLsEAAAD3dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbj4zPC9tbj48bWk+JiN4M0JCOzwvbWk+PC9tcm93Pjxtbj40PC9tbj48L21mcmFjPjxtbz49PC9tbz48bW4+NDE8L21uPjxtaT4mI3hBMDs8L21pPjxtbz4mI3gyMDI2OzwvbW8+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1pPmk8L21pPjxtaT5pPC9taT48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD6VqI3XAAAAAElFTkSuQmCC" class="Wirisformula" alt="fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses" width="103" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»3«/mn»«mi»λ«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»41«/mn»«mi» «/mi»«mo»…«/mo»«mfenced separators=¨|¨»«mrow»«mi»i«/mi»«mi»i«/mi»«/mrow»«/mfenced»«/math»'/> <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/487208/1/940053/Picture3.png" alt="" width="261" height="140" /> <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/487208/1/940053/Picture2.png" alt="" width="278" height="152" /> Subtracting Eq.(i) from Eq.(ii), we have <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13" width="137" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»3«/mn»«mi»λ«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mi»λ«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»41«/mn»«mo»-«/mo»«mn»13«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="⟹ fraction numerator lambda over denominator 2 end fraction equals 28" width="75" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⟹«/mo»«mfrac»«mrow»«mi»λ«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»28«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="therefore blank lambda equals 56 blank c m" width="96" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∴«/mo»«mi» «/mi»«mi»λ«/mi»«mo»=«/mo»«mn»56«/mn»«mi» «/mi»«mi»c«/mi»«mi»m«/mi»«/math»'/> Hence, frequency of tuning fork <img src="data:image/png;base64,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" class="Wirisformula" alt="v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z" width="218" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»v«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»v«/mi»«/mrow»«mrow»«mi»λ«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»350«/mn»«/mrow»«mrow»«mn»56«/mn»«mo»×«/mo»«msup»«mrow»«mn»10«/mn»«/mrow»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»=«/mo»«mn»365«/mn»«mi» «/mi»«mi»H«/mi»«mi»z«/mi»«/math»'/>

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is <img src="data:image/png;base64,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" class="Wirisformula" alt="350 m s to the power of negative 1 end exponent" width="73" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»350«/mn»«mi»m«/mi»«msup»«mrow»«mi»s«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»'/> is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a piston fitted in cylindrical pipe is pulled as shown in the figure. atuning fork is sounded at open end and loudest sound is heard

A piston fitted in cylindrical pipe is pulled as shown in the f-Turito

In a sine wave, position of different particles at time <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAANCAYAAADMvbwhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAANZJREFUeNpjYKAf4APiaUB8EopnQsUwgAoQH6WhQ/YCsR8S3wcqhgGCgHgpjRwRCsSTsIhPAOJIZIF6IP6PhMup7JA1QOyGRdwRKocCVgFxAAED/xOBsYF3QMyGRRwk9hJd8AYQy9Moav7gkfuFzGEC4m80TKj4HPIDmWMOxAeJMJDcqHmJI2o40KMGlHIX0jBEQAnSA4u4G3piBWWjHBo6BFQ0zMYiPh89+04B4rk0Lln3A3EBELNAo6kaW3LQAuKn0Dhmo5FDBKGe/QHNGKAinodhsAEATrg6rA9XPdMAAABddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnQ8L21pPjxtbz49PC9tbz48bW4+MDwvbW4+PC9tYXRoPolY7C4AAAAASUVORK5CYII=" class="Wirisformula" alt="t equals 0" width="34" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»t«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/> is shown in figure. The equation for this wave travelling along positive <img src="data:image/png;base64,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" class="Wirisformula" alt="x minus a x i s" width="61" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»-«/mo»«mi»a«/mi»«mi»x«/mi»«mi»i«/mi»«mi»s«/mi»«/math»'/> can be <img src="data:image/png;base64,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" alt="" />

Solution for the question - in a sine wave, position of different particles at time t=0 is shown infigure. the equation for this wave travelling along positive

In a sine wave, position of different particles at time t=0 is -Turito

The function <img src="data:image/png;base64,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" class="Wirisformula" alt="sin space open parentheses x squared close parentheses" width="56" height="18" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mo»§#160;«/mo»«mfenced separators=¨|¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/mfenced»«/math»'/><img src="data:image/png;base64,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" class="Wirisformula" alt="plus cos space square root of x" width="70" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«msqrt»«mi»x«/mi»«/msqrt»«/math»'/> is

Solution for the question - the functionis not a periodic function extreme values:periodic with period 0periodic with period 2'/> periodic with period'/>

The functionis -Turito

The period of the function <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus 6 x" width="212" height="17" style="vertical-align:-3px" 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»«mo»[«/mo»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mn»7«/mn»«mo»]«/mo»«mo»+«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mi»§#960;«/mi»«mi»x«/mi»«mo»§#8722;«/mo»«mn»6«/mn»«mi»x«/mi»«/math»'/> where [.] de-notes the greatest integer function, is

Solution for the question - the period of the functionwhere [.]de-notes the greatest integerfunction, is '/>2'/>3