Question
Statement-I : If
then A=![7 over 4](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJ9JREFUeNpjYMAO/hPAFINQIJ5NqSHiQHwYiDkoNWgTEBtQakgGENdSaog8EJ8EYhZKDToIxI7UiKVtlBrCBMQ3qBHAAVBvUQyWA3EiNQx6CcSCDKNgcIP/ZOJRMFiBDzViiAeIr1HDoJlAnEypQdZAvBcpwZIF2ID4ErQWocigDiDOQctCJAM9ID6KJS+SDEAVogo1DKJpjqdakUEfgwCGRTp0g/2KWQAAAGJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjc8L21uPjxtbj40PC9tbj48L21mcmFjPjwvbWF0aD7kU9SNAAAAAElFTkSuQmCC)
Statement-II : If
then ![p equals 2 comma q equals 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAPCAYAAACcCyOxAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAepJREFUeNrVl7FLw0AUxkORIlIK4lCkg1AcxEEKDiIiIohDcQiCgziULs7i4iAi/gMixc3BwSEgIg4iLiIOIm4iIlIQBxG3Ih1KEUG/B9+Qhou9SC6JH/ygueaS9+69d+9iWfFoAhyBBvgEd2DJSqamwRloghaogR3QF7dhV2ARZHg9DK45ljRdgnmQdo0VwXkSIz4A7q3/o4ZqcBOsgy3wztSVKPRHaFgrwL2SxVXwwXmyPeyCtQjsLIAn1R+H4JlG9IIU2AbOLw/71kBX4yxpHaUY4Ap/Z5kE8j7boK05vlP2xZLqhhr3JreyfmkbsrrBLRuOjjZ8Mk58yBuwz7vYK36Rbfo4Z3oRJetPwGyAOa+uptTJh7BttRnwKe+fYywPVYldGCznAhdwMIAjRXZ3XR9MbD0ZLmSb5Gixr7h5laVjQkNgD/QEnCfHjQPFuJ8PkTXBKjdMt9I8cpjozjk2sq4/zLU51ytZ2OWIFnCE+2+bjjk4w+s8xyqGjDhlJnaSo+i4krmPLGvRKJ/35tcxQ/gwWGDAU/yCeQFl7411GioL+cXPMNtgJHX3Jcfn2JJjkKWkbuhYnY0wbE0ySC3X2XnOUpRtPcFfBo5GhqV56I5NJUY1iZKSfdDYO2P3oczGkkTlWbqJ9uEHLUyOob+pMncAAACFdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnA8L21pPjxtbz49PC9tbz48bW4+MjwvbW4+PG1vPiw8L21vPjxtaT5xPC9taT48bW8+PTwvbW8+PG1uPjM8L21uPjwvbWF0aD7FLdr5AAAAAElFTkSuQmCC)
Which of the above statements is true
- Only I is true
- Only II is true
- both I & II are true
- Neither I nor II true
Hint:
In this question we will solve both the questions to know whether they are true or not. In both statements we will first solve the fractions in RHS. Then we will find the coefficients of
, x and constant term after that we will compare both sides to get the value of A,B,C and p and q.
The correct answer is: Only I is true
Statement-I : If
then A=![7 over 4](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJ9JREFUeNpjYMAO/hPAFINQIJ5NqSHiQHwYiDkoNWgTEBtQakgGENdSaog8EJ8EYhZKDToIxI7UiKVtlBrCBMQ3qBHAAVBvUQyWA3EiNQx6CcSCDKNgcIP/ZOJRMFiBDzViiAeIr1HDoJlAnEypQdZAvBcpwZIF2ID4ErQWocigDiDOQctCJAM9ID6KJS+SDEAVogo1DKJpjqdakUEfgwCGRTp0g/2KWQAAAGJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjc8L21uPjxtbj40PC9tbj48L21mcmFjPjwvbWF0aD7kU9SNAAAAAElFTkSuQmCC)
![fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A left parenthesis x plus 1 right parenthesis squared plus B left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus C left parenthesis x minus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A left parenthesis x squared plus 2 x plus 1 right parenthesis plus B left parenthesis x squared minus 1 right parenthesis plus C x minus C over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A x squared plus A 2 x plus A plus B x squared minus B plus C x minus C over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator x squared left parenthesis A plus B right parenthesis plus x left parenthesis 2 A plus C right parenthesis plus 1 left parenthesis A minus B minus C right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
N o w comma space o n space c o m p a r i n g space b o t h space s i d e s space comma space
A plus B equals 0 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 A plus C equals 3 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A minus B minus C equals 4
rightwards double arrow A equals negative B space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B plus C equals 3 space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative B minus B minus C equals 4
p u t t i n g space B equals fraction numerator negative 7 over denominator 4 end fraction space space space space space space space space space space space space space space space space rightwards double arrow space minus 2 B equals 3 minus C space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B minus C equals 4
rightwards double arrow A equals 7 over 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space p u t t i n g C equals fraction numerator negative 1 over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space 3 minus C minus C equals 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B equals 3 plus 1 half space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space 3 minus 2 C equals 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow B equals fraction numerator negative 7 over denominator 4 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space C equals fraction numerator negative 1 over denominator 2 end fraction space space space space space space space 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)
statement 1 is true.
Statement-II : If
then
![fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space equals fraction numerator left parenthesis 2 x minus 3 right parenthesis plus 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space equals fraction numerator 2 x over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
N o w comma space o n space c o m p a r i n g space b o t h space s i d e s space comma space
p equals 2 space a n d space q equals 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statement 2 is false.
Related Questions to study
If b > a , then the equation, (x - a) (x - b) - 1 = 0, has:
Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of (−α,a) and the other root will be in the interval (b,α).
If b > a , then the equation, (x - a) (x - b) - 1 = 0, has:
Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of (−α,a) and the other root will be in the interval (b,α).
If
be that roots
where
, such that
and
then the number of integral solutions of λ is
Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between
If
be that roots
where
, such that
and
then the number of integral solutions of λ is
Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between
If α,β then the equation
with roots
will be
Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore, will be the equation for the roots
.
If α,β then the equation
with roots
will be
Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore, will be the equation for the roots
.
The equation of the directrix of the conic
is
The equation of the directrix of the conic
is
The conic with length of latus rectum 6 and eccentricity is
The conic with length of latus rectum 6 and eccentricity is
For the circle
centre and radius are
For the circle
centre and radius are
The polar equation of the circle of radius 5 and touching the initial line at the pole is
The polar equation of the circle of radius 5 and touching the initial line at the pole is
The circle with centre at and radius 2 is
The circle with centre at and radius 2 is
Statement-I : If ![fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text then end text bold italic A plus bold italic B plus bold italic C equals bold 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZYAAAArCAYAAABb266JAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAACKJJREFUeNrtnXGEVXkUx4+RZySRMZKRSJL9YwxrjSSJrJWsRDKyRoaRjGRF1koylrGSpH+SrCSRNVZGIkkyEhnJSoaxkpVE1kjGM8z+vt1ze7fbfe/d9+7vd9/93ff9cMzMvW/uve93f+d3fuf8zj1XJDsrKlUjs0a2CCGEEGKBHiPHjMyxKQghhNhkiU1ACCHEFruMPGQzEEIIscEGCdZYNjs49m4jd4x8VI9o3sgFI30F+e5bjZw28ozdoC0Pd9nIKyMLRm5rXyIB0KfftW991HaaNLKOTUPKDgbWGYcDwgMjB4xUItuGjNwtyPe/bmRcgiQGkp4tCcYYg+YfbJpPnFS92inBGibYaOQE24h0g6cCb2JtG/+bdSBedPSdVnL+v25lv5EbsW0HErZ1I6eMXGEzkLIxZmQqYfuk7guBUdnWgYEYIYKXGa6bhqXznNEBNMo1Iz8wAvApLLiKXYSUEaQOr4/8fcTIpYTBNC4uB+L1eh1YZ9mb4bppWDrPLfVaEOZBaPOqBGGebucc24GUGcwcz+vve4zct3z8Vo1QVE44vG4alnyYj9zPD/RUPvNC+KAxKTn3JEgjxiJr1iyslRTSjHU6y32i12Xjum1cFw1La/SoMQEVnQA8liAM1O3twmfBSOmBZ4ByLYMOjp1lIF6jxsXFddNjcc9wgid5WILU2m4GRnaR3YOUmR1G/pQgrDRSMMMiDWZ2Wa+bhsU9uC9XY9t+EmZCiXpyq9kMpIwg6+q2dnB4B0/F/gOJWQZieCLzjq6bhsU9FyVIqohy1dEExjfQDifZDKRs9EuQRhwdkPdJ8CBgJwwLysQclCD9EjFoPIn/j5FRR9dNw+Keaakt1vfr/cV6WIVNI5uMvDfyi9SesO/Vvgyjs4dNRHyjoko/kLDvpnQmcwdPHuMJ5CWVB6pkRbnuLCnXtvElTfV9pK2W9B4NUP0+g6wwPNOzqG30nwTh3b0Fv+4iTq4wNvyr17YstSoGrliKjQU451v10tc4PC/05zcJojQo/4M15tcSVGkYsnwueNQLeo4Fetjl5pDeaD5YR/KYGPhiWE7FBvphxxOCRtmlU47OO5Zg0KJis47hpTrn4PpoCUHI5LkEadb7SzDL7OYZts/tVrT2XKNGEBOuOb2+Qw77yH79/M3Itg3qbWL7dQd98qj+D7wUVLMICwHDM9uhXsxFS+25Xc8FD/Bb3Yafb3T7TqpGubgswcL3qLRWZYCGhbTTZvXCvuHfCNk91lk01kg3JhwH/fW1fgbhmt46x8L620KTY9XjrB4H1QyuRX531UfO6OfjpYqmdPuo5fNtlNoSwXAO9/6GXl+8PNaRBINKCqSk7azXYBYxo7+vVyXk4Mrv3imPBYNOtIbgEfn6PU0YBF/qwIiZNaqDn084FowKnm3a1OBY9UBSyAeVPqlVIJ922Edu6efDqAGu+1cJ1lluOzhfaLAmcxp3Xum+/tj2vognQ0oA1lOexmZxc9JaYVAaFmLTsMSrU8NwVGPbpuXr1PI3CcfaneJY9Tinxzgd8aJW1Ety1UfmEwboF5K+AG6r53uun8+rYkW1yb2vtmPBKO2LK+B6xzMyEFM95shL8r29u+G759FnGw0uvSk+/0G+LBQLFls4R5oQEQa5d1LLxFob+W4VB32kRz2T+GffaWisx9H5qpIfzQwLyxGVIBS2Tb2TOLtacLvpsRDbHkua7Wn6ehbDcqWJTu1y0EeG9bMPIgM/dPRnCRIIHtYxuu2eryLtp1C7CoW9pmr4z6MGnaKVtGMaFpK3YcFAu9ryOUK21vEconLYQR8Z0c8mvd1zQvcdt9wnQw9iNKf7Hi7ex6tmhIv3fEmf52Ah8kKD/cjO2GtZcWhYSHRA68lgDDD4jrV5b5rds3ABfSJh30Xdd9lBHwmPPR7Z1qt6+FLcZIWFA/1H9Yz6I94SUn+xuH/Q4n2PphsPRTy1MN14B1XDX5AXj0W7Rk/xjjUxPBxc+d2z8EyS67qlNQZ4kBDZi9/r38ieumbBsAzq/vk6hi/0KqYd9JHpJl7S32I3FAYGpFZVoJ7YrjpyWXJ4QDIaepkVvqAoDzAj25eiw82zqYgjvUW21lvJti7ynZ57WQfdHy0Ylru6v14x0x2638WrCd5Lckgak8Cz4q6cC9Y3zqlXVNX2fCVuS1mdklpJF4wzzkq6YHaATKQ56ixxDGLop8VumYp2OSbuynTYYEoaZwhSb4kXMN2MuAZlMcal82EshF0ee9Bes9L8hXfUW1JYkML3kM1AWsTX1xRgwB4qQPs18+BQy+kR9Zb4yAZVtM0Ojh2+ERJx0aoq0OECffcihWbyBkkCSaGgSUn/tLGPhmVI+7svHtwjqRUNzEtvCck8sM5oJ3UBZlNYjAsXv75RZRjxSLHLDOLz0aeokdPeSiFMHw0L6ldNeOTBHU+YALjWW0IyeSooOLc254EB6YnPPVLsMoPMk7CAIN5ueL8L2hvZRzs98uC2x+5LFr0lpG3SKki0imneA8OSR4pddvAeGMTqEQ7sS9FONmqrdbK9EZateOTBVeTLFNssekuI8xBHloKLWQYGzMBmPVLssoNXImP9azDHdutkey976MFVLektIR0NcbhSIDy9+kTqlw/oxtBMJwmTK9DmIzm2W1ENS1E9uKoQ4mGIQ3JQILyC9y+plYLwSbHLCLKJUEkZBQWRXPG0jX7io2FpFAorogcXD4UR4m2Iw7YCbVajssXxddNjSQcK3t2JGRKUmrneBe19r4HHXEQPbruDiAMhHQlx2FQgLDRekealtouq2GUDM2AU3RtI2OeyRpFIMdYH6qUbF9WDm9BrJsT7EIctBcJCPAovrsrpumlYSDOSHpAssgdX7wFJQrwLcdhSoBlJlxrZzaEZkj+oEzbogQfXrKQLIaUOcbSiOHEF6vbQDMmfMhWhJIQQUhCOSrHL5mNdZZy3ieTJ/yWTMS7ClQSRAAACr3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjM8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWk+QTwvbWk+PG1vPis8L21vPjxtZnJhYz48bWk+QjwvbWk+PG1yb3c+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPis8L21vPjxtZnJhYz48bWk+QzwvbWk+PG1yb3c+PG1vPig8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjxtdGV4dD4mI3hBMDt0aGVuJiN4QTA7PC9tdGV4dD48bWkgbWF0aHZhcmlhbnQ9ImJvbGQtaXRhbGljIj5BPC9taT48bW8+KzwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+QjwvbWk+PG1vPis8L21vPjxtaSBtYXRodmFyaWFudD0iYm9sZC1pdGFsaWMiPkM8L21pPjxtbz49PC9tbz48bW4gbWF0aHZhcmlhbnQ9ImJvbGQiPjA8L21uPjwvbWF0aD54/yeqAAAAAElFTkSuQmCC)
Statement-II :If ![fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text then end text A plus B minus C equals 0](data:image/png;base64,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)
Which of the above statements is true
Statement-I : If ![fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text then end text bold italic A plus bold italic B plus bold italic C equals bold 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZYAAAArCAYAAABb266JAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAACKJJREFUeNrtnXGEVXkUx4+RZySRMZKRSJL9YwxrjSSJrJWsRDKyRoaRjGRF1koylrGSpH+SrCSRNVZGIkkyEhnJSoaxkpVE1kjGM8z+vt1ze7fbfe/d9+7vd9/93ff9cMzMvW/uve93f+d3fuf8zj1XJDsrKlUjs0a2CCGEEGKBHiPHjMyxKQghhNhkiU1ACCHEFruMPGQzEEIIscEGCdZYNjs49m4jd4x8VI9o3sgFI30F+e5bjZw28ozdoC0Pd9nIKyMLRm5rXyIB0KfftW991HaaNLKOTUPKDgbWGYcDwgMjB4xUItuGjNwtyPe/bmRcgiQGkp4tCcYYg+YfbJpPnFS92inBGibYaOQE24h0g6cCb2JtG/+bdSBedPSdVnL+v25lv5EbsW0HErZ1I6eMXGEzkLIxZmQqYfuk7guBUdnWgYEYIYKXGa6bhqXznNEBNMo1Iz8wAvApLLiKXYSUEaQOr4/8fcTIpYTBNC4uB+L1eh1YZ9mb4bppWDrPLfVaEOZBaPOqBGGebucc24GUGcwcz+vve4zct3z8Vo1QVE44vG4alnyYj9zPD/RUPvNC+KAxKTn3JEgjxiJr1iyslRTSjHU6y32i12Xjum1cFw1La/SoMQEVnQA8liAM1O3twmfBSOmBZ4ByLYMOjp1lIF6jxsXFddNjcc9wgid5WILU2m4GRnaR3YOUmR1G/pQgrDRSMMMiDWZ2Wa+bhsU9uC9XY9t+EmZCiXpyq9kMpIwg6+q2dnB4B0/F/gOJWQZieCLzjq6bhsU9FyVIqohy1dEExjfQDifZDKRs9EuQRhwdkPdJ8CBgJwwLysQclCD9EjFoPIn/j5FRR9dNw+Keaakt1vfr/cV6WIVNI5uMvDfyi9SesO/Vvgyjs4dNRHyjoko/kLDvpnQmcwdPHuMJ5CWVB6pkRbnuLCnXtvElTfV9pK2W9B4NUP0+g6wwPNOzqG30nwTh3b0Fv+4iTq4wNvyr17YstSoGrliKjQU451v10tc4PC/05zcJojQo/4M15tcSVGkYsnwueNQLeo4Fetjl5pDeaD5YR/KYGPhiWE7FBvphxxOCRtmlU47OO5Zg0KJis47hpTrn4PpoCUHI5LkEadb7SzDL7OYZts/tVrT2XKNGEBOuOb2+Qw77yH79/M3Itg3qbWL7dQd98qj+D7wUVLMICwHDM9uhXsxFS+25Xc8FD/Bb3Yafb3T7TqpGubgswcL3qLRWZYCGhbTTZvXCvuHfCNk91lk01kg3JhwH/fW1fgbhmt46x8L620KTY9XjrB4H1QyuRX531UfO6OfjpYqmdPuo5fNtlNoSwXAO9/6GXl+8PNaRBINKCqSk7azXYBYxo7+vVyXk4Mrv3imPBYNOtIbgEfn6PU0YBF/qwIiZNaqDn084FowKnm3a1OBY9UBSyAeVPqlVIJ922Edu6efDqAGu+1cJ1lluOzhfaLAmcxp3Xum+/tj2vognQ0oA1lOexmZxc9JaYVAaFmLTsMSrU8NwVGPbpuXr1PI3CcfaneJY9Tinxzgd8aJW1Ety1UfmEwboF5K+AG6r53uun8+rYkW1yb2vtmPBKO2LK+B6xzMyEFM95shL8r29u+G759FnGw0uvSk+/0G+LBQLFls4R5oQEQa5d1LLxFob+W4VB32kRz2T+GffaWisx9H5qpIfzQwLyxGVIBS2Tb2TOLtacLvpsRDbHkua7Wn6ehbDcqWJTu1y0EeG9bMPIgM/dPRnCRIIHtYxuu2eryLtp1C7CoW9pmr4z6MGnaKVtGMaFpK3YcFAu9ryOUK21vEconLYQR8Z0c8mvd1zQvcdt9wnQw9iNKf7Hi7ex6tmhIv3fEmf52Ah8kKD/cjO2GtZcWhYSHRA68lgDDD4jrV5b5rds3ABfSJh30Xdd9lBHwmPPR7Z1qt6+FLcZIWFA/1H9Yz6I94SUn+xuH/Q4n2PphsPRTy1MN14B1XDX5AXj0W7Rk/xjjUxPBxc+d2z8EyS67qlNQZ4kBDZi9/r38ieumbBsAzq/vk6hi/0KqYd9JHpJl7S32I3FAYGpFZVoJ7YrjpyWXJ4QDIaepkVvqAoDzAj25eiw82zqYgjvUW21lvJti7ynZ57WQfdHy0Ylru6v14x0x2638WrCd5Lckgak8Cz4q6cC9Y3zqlXVNX2fCVuS1mdklpJF4wzzkq6YHaATKQ56ixxDGLop8VumYp2OSbuynTYYEoaZwhSb4kXMN2MuAZlMcal82EshF0ee9Bes9L8hXfUW1JYkML3kM1AWsTX1xRgwB4qQPs18+BQy+kR9Zb4yAZVtM0Ojh2+ERJx0aoq0OECffcihWbyBkkCSaGgSUn/tLGPhmVI+7svHtwjqRUNzEtvCck8sM5oJ3UBZlNYjAsXv75RZRjxSLHLDOLz0aeokdPeSiFMHw0L6ldNeOTBHU+YALjWW0IyeSooOLc254EB6YnPPVLsMoPMk7CAIN5ueL8L2hvZRzs98uC2x+5LFr0lpG3SKki0imneA8OSR4pddvAeGMTqEQ7sS9FONmqrdbK9EZateOTBVeTLFNssekuI8xBHloKLWQYGzMBmPVLssoNXImP9azDHdutkey976MFVLektIR0NcbhSIDy9+kTqlw/oxtBMJwmTK9DmIzm2W1ENS1E9uKoQ4mGIQ3JQILyC9y+plYLwSbHLCLKJUEkZBQWRXPG0jX7io2FpFAorogcXD4UR4m2Iw7YCbVajssXxddNjSQcK3t2JGRKUmrneBe19r4HHXEQPbruDiAMhHQlx2FQgLDRekealtouq2GUDM2AU3RtI2OeyRpFIMdYH6qUbF9WDm9BrJsT7EIctBcJCPAovrsrpumlYSDOSHpAssgdX7wFJQrwLcdhSoBlJlxrZzaEZkj+oEzbogQfXrKQLIaUOcbSiOHEF6vbQDMmfMhWhJIQQUhCOSrHL5mNdZZy3ieTJ/yWTMS7ClQSRAAACr3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjM8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWk+QTwvbWk+PG1vPis8L21vPjxtZnJhYz48bWk+QjwvbWk+PG1yb3c+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPis8L21vPjxtZnJhYz48bWk+QzwvbWk+PG1yb3c+PG1vPig8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjxtdGV4dD4mI3hBMDt0aGVuJiN4QTA7PC9tdGV4dD48bWkgbWF0aHZhcmlhbnQ9ImJvbGQtaXRhbGljIj5BPC9taT48bW8+KzwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+QjwvbWk+PG1vPis8L21vPjxtaSBtYXRodmFyaWFudD0iYm9sZC1pdGFsaWMiPkM8L21pPjxtbz49PC9tbz48bW4gbWF0aHZhcmlhbnQ9ImJvbGQiPjA8L21uPjwvbWF0aD54/yeqAAAAAElFTkSuQmCC)
Statement-II :If ![fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text then end text A plus B minus C equals 0](data:image/png;base64,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)
Which of the above statements is true