Turito Academy

Test Prep

Global form fields

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/863960/1/925115/Picture34.png" alt="" width="63" height="" /> <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator table row 12 end table over denominator table row 4 end table table row 4 end table table row 4 end table end fraction" width="62" height="39" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mtable»«mtr»«mtd»«mn»12«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«mrow»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«/mfrac»«/math»'/>×<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator table row 3 end table over denominator table row 3 end table end fraction" width="26" height="39" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«mrow»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«/mfrac»«/math»'/> = <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator table row 12 end table over denominator left parenthesis table row 4 end table right parenthesis to the power of 3 end exponent end fraction" width="44" height="41" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mtable»«mtr»«mtd»«mn»12«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«mrow»«mo»(«/mo»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«msup»«mrow»«mo»)«/mo»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/>

The set S : = { 1, 2, 3 .........12} is to be partitioned into three sets A, B, C of equal size. Thus A <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAOCAYAAADJ7fe0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAFRJREFUeNpjYMAE/xnwA0Lyo4aMDEP+EJD/RYwhn4CYDYccG1SeINgCxD445Lyg8gRBABDfAmJHIGaCijFB+deg8kSBUCDeD8TfoAH5DcoPZ6AVAADphR3A4vuiTwAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIyQTs8L21vPjwvbWF0aD7NWDhaAAAAAElFTkSuQmCC" class="Wirisformula" alt="union" width="17" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8746;«/mo»«/math»'/> B <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAOCAYAAADJ7fe0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAFRJREFUeNpjYMAE/xnwA0Lyo4aMDEP+EJD/RYwhn4CYDYccG1SeINgCxD445Lyg8gRBABDfAmJHIGaCijFB+deg8kSBUCDeD8TfoAH5DcoPZ6AVAADphR3A4vuiTwAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIyQTs8L21vPjwvbWF0aD7NWDhaAAAAAElFTkSuQmCC" class="Wirisformula" alt="union" width="17" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8746;«/mo»«/math»'/> C = S, A <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAOCAYAAADJ7fe0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAFdJREFUeNpjYMAOQoF4LxB/A+JfUHo/VJwoEATEt4DYHojZoGIsQOwIxDeAOIAYQ7YAsRcOOZD4JmIM+YTkAnTABpUnCP4QkP9FjCH/KZQfNWRkGEIyAAD9bx27irKb/AAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIyOTs8L21vPjwvbWF0aD4UbpUpAAAAAElFTkSuQmCC" class="Wirisformula" alt="intersection" width="17" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8745;«/mo»«/math»'/> B = B  C = A <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAOCAYAAADJ7fe0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAFdJREFUeNpjYMAOQoF4LxB/A+JfUHo/VJwoEATEt4DYHojZoGIsQOwIxDeAOIAYQ7YAsRcOOZD4JmIM+YTkAnTABpUnCP4QkP9FjCH/KZQfNWRkGEIyAAD9bx27irKb/AAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIyOTs8L21vPjwvbWF0aD4UbpUpAAAAAElFTkSuQmCC" class="Wirisformula" alt="intersection" width="17" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8745;«/mo»«/math»'/> C = <img src="data:image/png;base64,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" class="Wirisformula" alt="ϕ" width="13" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#981;«/mi»«/math»'/>. The number of ways to partition S is -

Solution for the question - the set s : = { 1, 2, 3 .........12} is to be partitioned into three setsa, b, c of equal size. thus ad bd c = s, a? b = b  c = a? c

The set s : = { 1, 2, 3 .........12} is to be partitioned into -Turito

PSAT

One-On-One Tutoring

Your gateway to the top global universities

Coding

Discover traits & skills, get a clear pathway to academic success.

Discovery Program

A one kilowatt motor is used to pump water from a well 10 m deep. The quantity of water pumped out per second is nearly

Solution for the question - a one kilowatt motor is used to pump water from a well 10 m deep. thequantity of water pumped out per second is nearly 1000 kg

A one kilowatt motor is used to pump water from a well 10 m dee-Turito

Assertion (A) : The Remainder obtained when the polynomial <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAARCAYAAAAv+NkbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAepJREFUeNpjYCAPmAPxQSD+AcT/oXiwA5g7fwHxUSBWYRhmQAuIzwGxzhB1PxMQZ0H9MKzAQiC2HQb++DHcIuY1EEcD8UMgvgXEoUPQD/bQonhYgT9APBuI+YCYDcpOxKPeZ5DVQZLQOkYJRx2EC9MCqAFxLRBfoIZht6DlNAzwQHMPNgCSuzaIIgYUEFugkUMsCIUmPlqAxUCcRq3wATlSEIkPyjVncKidCcTJZFj8n0Y5ZRs0pxMLxIH4MBBz0NjdePWBArADi3gzVA4G9KANAJAHWYB4ChB7YNFnDcR7yXQwKeqJdTcoUjRIdMcmIDagQ4IiqO8cNJXAQCI04NEBqPK/C8QvcVT+oFx0CYjl6RAxxLqb1HojA1r+MwyGiAGl/D4o2wUpxZMKQCk4hwIHk6qeWu6GAVCCOgktEQZFxIDAbmhzEtRSECbDEj1oq4cUi/8zUN4qotTdyADUlHYkYTSB0tYcUeoKoMMWemR66iSW4Q56VP6Uuhu5FbaNlimfHH2gCnsNtFiIpMASuqQgKrsbNlxzg8QKn+YRowRthXBB+x9nqFAk0CPHUNPdARSOCFA9YkSh2VcYrce+eJBHDLXdvZzAKAZdIwbUtF0HxNI4HOoxABFDDKCFu1+idZ5pDeg19DMKqAUA3XqjImDVqtQAAACzdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj42PC9tbj48L21zdXA+PG1uPjQ8L21uPjxtbz4rPC9tbz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW4+NzwvbW4+PG1vPis8L21vPjxtbj4xPC9tbj48L21hdGg+hu6SBwAAAABJRU5ErkJggg==" class="Wirisformula" alt="x to the power of 6 4 plus x squared 7 plus 1" width="102" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mn»4«/mn»«mo»+«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mn»7«/mn»«mo»+«/mo»«mn»1«/mn»«/math»'/> is divided by <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAANCAYAAADFVhxbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYBhYoAbEtUB8gWGQgcVAnAbE/2lt0X9a6EsG4g4s4s1QuQFzGAicA2JxJH4iEE8Z6BADAQ8g7oOyXYB472CIShjYDcT20JwiTISBhDDVHFYAxL+AWG+wJH4QsAbiNdDojBwsDlMC4k1AzAXEPEB8hoiopLnDRIF4G5pDfKAF4IA5jA2I1wGxNBa55dCcSssCmZzMMnAAAExeMnZLoJj8AAAAXXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbWF0aD4PWQOIAAAAAElFTkSuQmCC" class="Wirisformula" alt="x plus 1" 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»+«/mo»«mn»1«/mn»«/math»'/> Is 1 Reason (R): If <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis" width="29" 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»«/math»'/> is divided by <img src="data:image/png;base64,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" class="Wirisformula" alt="x minus a" width="38" height="10" 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»«/math»'/> then the remainder is f(a)

Solution for the question - assertion (a) : the remainder obtained when the polynomialx^(6)4+x^(2)7+1 is divided by x+1 is 1 reason (r): if f(x) isdivided by x-

Assertion (a) : the remainder obtained when the polynomial x^-Turito

By the conservation of momentum in the absence of external force total momentum of the system (ball + earth) remains constant

A ball hits the floor and rebounds after inelastic collision. In this case

Solution for the question - a ball hits the floor and rebounds after inelastic collision. in this case the total energy of the ball and the earth is conserved

A ball hits the floor and rebounds after inelastic collision. i-Turito

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement II Principle of conservation of momentum holds true for all kinds of collisions.

Solution for the question - statement i two particles moving in the same direction do not lose alltheir energy in a completely inelastic collision. statement ii

Statement i two particles moving in the same direction do not l-Turito

A mass M  is lowered with the help of a string by a distance h at a constant acceleration g/2. The work done by the string will be

Solution for the question - a mass is lowered with the help of a string by a distance at a constantacceleration . the work done by the string will be (-3mgh)/(2)

A mass is lowered with the help of a string by a distance a-Turito

A particle begins at the origin and moves successively in the following manner as shown, 1 unit to the right, 1/2 unit up, 1/4 unit to the right, 1/8 unit down, 1/16 unit to the right etc. The length of each move is half the length of the previous move and movement continues in the ‘zigzag’ manner indefinitely. The co-ordinates of the point to which the ‘zigzag’ converges is – <img src="data:image/png;base64,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" alt="" />

Solution for the question - a particle begins at the origin and moves successively in the followingmanner as shown, 1 unit to the right, 1/2 unit up, 1/4 unit t

A particle begins at the origin and moves successively in the f-Turito

Detailed Solution The number point of intersection between two circles can be counted by finding the number of ways in which one circle and one line can be selected out of the lot multiplied by 2 as one circle and one line can intersect at most two points. For selecting r objects from n objects can be done by using the formula as follows <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript n subscript r space equals space fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction" width="123" height="37" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mi»r«/mi»«none/»«mprescripts/»«none/»«mi»n«/mi»«/mmultiscripts»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»n«/mi»«mo»!«/mo»«/mrow»«mrow»«mi»r«/mi»«mo»!«/mo»«mo»(«/mo»«mi»n«/mi»«mo»-«/mo»«mi»r«/mi»«mo»)«/mo»«mo»!«/mo»«/mrow»«/mfrac»«/math»'/>  As mentioned in the question, we have to find the total number of intersection points. For calculating the points of intersection between two lines, we can use the formula which is mentioned in the hint as follows = <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 8 subscript 2 space cross times 1 space equals space 28" width="104" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»2«/mn»«none/»«mprescripts/»«none/»«mn»8«/mn»«/mmultiscripts»«mo»§#160;«/mo»«mo»§#215;«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»28«/mn»«/math»'/>  For calculating the points of intersection between two circles, we can use the formula which is mentioned in the hint as follows = <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 4 subscript 2 space cross times 2 space equals space 12" width="104" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»2«/mn»«none/»«mprescripts/»«none/»«mn»4«/mn»«/mmultiscripts»«mo»§#160;«/mo»«mo»§#215;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»12«/mn»«/math»'/>  For calculating the points of intersection between one line and one circle, we can use the formula which is mentioned in the hint as follows = <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 4 subscript 1 space cross times C presuperscript 8 subscript 1 cross times 2 space equals space 64" width="149" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»4«/mn»«/mmultiscripts»«mo»§#160;«/mo»«mo»§#215;«/mo»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»8«/mn»«/mmultiscripts»«mo»§#215;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»64«/mn»«/math»'/>  Hence, the total number of points of intersection is = 28 + 64 + 12 = 104

The greatest possible number of points of intersections of 8 straight line and 4 circles is :

Solution for the question - the greatest possible number of points of intersections of 8 straight lineand 4 circles is : 10476

The greatest possible number of points of intersections of 8 st-Turito

Assertion (A):If<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPkAAAAoCAYAAAA8LVwaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABI1JREFUeNrtndFnVnEYx38mkyQyyUzilZkuMrrITHaTzHSRSF6TZEwy08VIF+liYpIk3SSvmSQmk5lEdpGZiUx20UV00T8wmWReYz2P88xOp/O+57zvOb9zfs853w8P23m92/M75/uc3/P7nd/vOcYUl16y+2RfDcibO4p93ybbIftJ9oNskazbAb8qZI9E33/Ev2myo2US1iuycbJdxFiuXCOrkx1Q6PupkE6CA2k2Z7+myJbIzpN1yLETcjOdLaPIEOT5wb3KBtlHsssK/WefXweOXQk5lqU+75K9hLQQ5K7wgqxKdoPsuUL/H0hQ+ZkjG5afx8hmQr43LZ+lrc9eGTIcgLQQ5C4wICklc1zEqY156c05Je4nq4XML6xL+/a42eINrRV9PlY+v4EgLxDc03yRcaI/GPqUteO76Iftt68H98PHnsjPF8iWLerzm8wTAAS5E2nuVODYQ7LbitrQIYHNdEoAr0nKHITnHIaMN0nXFUOPUdbIn21IC0HuAn3SawfhIFhU1I5zIb3yqPEeWwXhFJqfIJyxqE++0WxBXghyF1hp0kNpepRWlTG4n+vm/5ntQbK3krJXLeuTM4tDkBiCPE94XcLTJp+/IRtR0pZnxptE81MLBHJFshMOvMMyD9FlUZ+1kGEQQJBnBq8C2xCxN2Is4ibgEgtmf6LtGNlVGXN3+o69DwT1JeMtwrKlz5Nkm2T3zP7KtoPyf2syb1C64I4zoQHSYV7E1owe481Ya2DTp5ttyUJ6fOPjBd/vwWxl2KJfPLs+J+Nz9u2XDBdGIEEAAAAYqgEAEOQAOCHsdhZbIMgBAAjyMvQAMHeszBqwkcVAIwDpOnpyAACCHACAIAcAIMhBhuNa3jW1arBRH0AzhYU36nOhg3WcCuvsbdnckkDhzSCj0Ix92NkZh/2bMc2rjaTl/7aj7SsSn4y3jXNvF9tp6RGrStujoooLV7lYU+DnqgmvyJGW/0MiQNfaVwZ4a+WGQr/z1kxL4upXkL6dNV41Ehv+d8vfqVhsZ9SbXhq1LwvSKDlcih7RMc3Eol8c1ZK+rUgwpOk/n8glY/+VOHHe9BJsX5YkLTmchAEHdKhVM5FwsboJRenbZKDHSeo/XySu+nGkje+2e+KbfW8yx7mRpCWH24UrnnyWjE5LD+6SZiL5YLz3LGlJ3wYC4kvqP1+svoxP/G5Ej7aco4CzKDnsh0sbvSO76EDwatVMJDwO7lSUvgXL1Sb1P8l6bxsXLO9yvElKDrdKRQLcpefMGjUTyY7C9K3uiP+2Llg9J4EnLTncCtwTcslj18oOa9VM20HuavpWt+S/yaB9rgZ5GiWH48I9JReDdLUuu0bNtJ2uu5i+tZKu2/a/KOl6WiWH47Jk3H5XmjbNxLprDSpK34ITU3n6X4SJtzxKDru8/12jZiJp9AjK1fRtwvz7jqo8/bdxwYLtA8UasuQS5GGLSVxO3+IshsnKfxsXLM/FMGVGs2ZiseYbf7icvjVa9pm3/0naGad9oHhDlrQ0ExtsUHG7fQCkwi3j9lZTHqeOK/Y/afsAiOQvY1CPFvKynaoAAAHndEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bXJvdz48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjI8L21uPjxtbz4pPC9tbz48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21mZW5jZWQ+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bWk+QTwvbWk+PG1yb3c+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21mcmFjPjxtbz4rPC9tbz48bWZyYWM+PG1yb3c+PG1pPkI8L21pPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPkM8L21pPjwvbXJvdz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21mcmFjPjwvbWF0aD6fTb1TAAAAAElFTkSuQmCC" class="Wirisformula" alt="fraction numerator 1 over denominator left parenthesis x minus 2 right parenthesis open parentheses x squared plus 1 close parentheses end fraction equals fraction numerator A over denominator x minus 2 end fraction plus fraction numerator B x plus C over denominator x squared plus 1 end fraction" width="249" height="40" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«mo»)«/mo»«mfenced separators=¨|¨»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mi»A«/mi»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»B«/mi»«mi»x«/mi»«mo»+«/mo»«mi»C«/mi»«/mrow»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math»'/> ,then A<img src="data:image/png;base64,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" class="Wirisformula" alt="equals 1 fifth comma B equals 1 fifth comma C equals negative 2 over 5" width="154" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»5«/mn»«/mfrac»«mo»,«/mo»«mi»B«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»5«/mn»«/mfrac»«mo»,«/mo»«mi»C«/mi»«mo»=«/mo»«mo»§#8722;«/mo»«mfrac»«mn»2«/mn»«mn»5«/mn»«/mfrac»«/math»'/> Reason (R) : <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 1 over denominator left parenthesis x minus a right parenthesis open parentheses x squared plus b close parentheses end fraction equals fraction numerator 1 over denominator a squared plus b end fraction open square brackets fraction numerator 1 over denominator x minus a end fraction minus fraction numerator x plus a over denominator x squared plus b end fraction close square brackets" width="316" height="42" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mi»a«/mi»«mo»)«/mo»«mfenced separators=¨|¨»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mfrac»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mi»a«/mi»«/mrow»«/mfrac»«mo»§#8722;«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mi»a«/mi»«/mrow»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«/math»'/>

Solution for the question - assertion (a):if,then a reason (r) : a is false but r is trueboth a & r are true and r is not correct explanation of a

Assertion (a):if,then a reason (r) : -Turito

As the area above the time axis is numerically equal to area below the time axis therefore net momentum gained by body will be zero because momentum is a vector quantity

A force–time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and  is <img src="data:image/png;base64,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" alt="" width="196" height="124" />

Solution for the question - a forcetime graph for a linear motion is shown in figure where thesegments are circular. the linear momentum gained between zero and

A forcetime graph for a linear motion is shown in figure whe-Turito

How many different nine digit numbers can be formed from the number 2,2,3,3,5,5,8,8,8 by rearranging its digits so that the odd digits occupy even position ?

Solution for the question - how many different nine digit numbers can be formed from the number2,2,3,3,5,5,8,8,8 by rearranging its digits so that the odd digit

How many different nine digit numbers can be formed from the nu-Turito

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,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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»'/>

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

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,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" 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