Solved papers for JEE Main & Advanced AIEEE Solved Paper-2005

done AIEEE Solved Paper-2005 Total Questions - 6

• question_answer1) Area of the greatest rectangle that can be inscribed in the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]is     AIEEE  Solved  Paper-2005
  A)
  \[\frac{a}{b}\]   
  done clear
  B)
                                         \[\sqrt{ab}\]                     
  done clear
  C)
  \[ab\]                   
  done clear
  D)
         \[2ab\]
  done clear
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• question_answer2) If\[f\]is a real-valued differentiable function satisfying\[|f(x)-f(y)|\le {{(x-y)}^{2}},x,y\in R\]and \[f(0)=0,\]then\[f(1)\]equals     AIEEE  Solved  Paper-2005
  A)
  1             
  done clear
  B)
         2             
  done clear
  C)
         0             
  done clear
  D)
         -1
  done clear
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• question_answer3) The normal to the curve \[x=a(\cos \theta +\theta \sin \theta ),y=a(\sin \theta -\theta \cos \theta )\]at any point\['\theta '\]is such that     AIEEE  Solved  Paper-2005
  A)
  it is at a constant distance from the origin
  done clear
  B)
  it passes through\[(a\text{ }\pi /2,-a)\]
  done clear
  C)
  it makes angle\[\pi /2+\theta \]with the X-axis
  done clear
  D)
  it passes through the origin
  done clear
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• question_answer4) A function is matched below against an interval, where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval                Function     AIEEE  Solved  Paper-2005
  A)
  \[(-\infty ,\,\,-4]\]           \[{{x}^{3}}+6{{x}^{2}}+6\]
  done clear
  B)
  \[\left( -\infty ,\frac{1}{3} \right]\]           \[3{{x}^{2}}-2x+1\]
  done clear
  C)
  \[[2,\,\infty )\]                  \[2{{x}^{3}}-3{{x}^{2}}-12{{x}^{4}}-6\]
  done clear
  D)
  \[(-\infty ,\infty )\]                          \[{{x}^{3}}-3{{x}^{2}}+3x+3\]
  done clear
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• question_answer5) A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of\[50\text{ }c{{m}^{3}}/\min \]. When the thickness of ice is 15 cm, then the rate at which the thickness of ice decreases, is     AIEEE  Solved  Paper-2005
  A)
  \[\frac{5}{6\pi }cm/\min \]      
  done clear
  B)
         \[\frac{1}{54\pi }cm/\min \]
  done clear
  C)
         \[\frac{1}{18\pi }cm/\min \]      
  done clear
  D)
  \[\frac{1}{36\pi }cm/\min \]
  done clear
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• question_answer6) If the equation \[{{a}_{n}}{{X}^{n}}+{{a}_{n-1}}{{X}^{n-1}}+....+{{a}_{1}}x=0,\] \[{{a}_{1}}\ne 0,n\ge 2,\]has a positive root \[x=\alpha ,\] then the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{X}^{n-2}}+....+{{a}_{1}}=0\] has a positive root, which is     AIEEE  Solved  Paper-2005
  A)
  equal to\[\alpha \]
  done clear
  B)
  greater than or equal to\[\alpha \]
  done clear
  C)
  smaller than\[\alpha \]
  done clear
  D)
  greater than \[\alpha \]
  done clear
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