JEE Main & Advanced Mathematics Applications of Derivatives Question Bank

done Numerical Value Type Questions - Application of Derivatives Total Questions - 15

• question_answer1)
  If the maximum volume (in cu.m) of the right circular cone having slant height 3 m is equal to \[k\sqrt{3}\,\pi {{m}^{3}},\] then k is equal to
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• question_answer2)
  If a curve passes through the point \[(1,-2)\] and has slope of the tangent at any point \[(x,y)\] on it as  also the curve passes through the point \[\left( \sqrt{3}\,a,0 \right),\] then value of a is
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• question_answer3)
  The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is equal to \[m\sqrt{3},\] then the value of m is
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• question_answer4)
  The function  has a local minimum at
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• question_answer5)
  If \[y=4x-5\] is tangent to the curve \[{{y}^{2}}=p{{x}^{3}}+q\] at \[(2,3)\] then find \[\left| \frac{q}{p} \right|\]
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• question_answer6)
  If the curves \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{12}=1\]and \[{{y}^{3}}=8x\] intersect at right angles, then the value of \[{{a}^{2}}\] is equal to
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• question_answer7)
  A stone moving vertically upwards has its equation of \[s=490\,t-4.9{{t}^{2}}.\] The maximum height reached by the stone is
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• question_answer8)
  The minimum value of \[4{{e}^{2x}}+9{{e}^{-2x}}\] is
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• question_answer9)
  The minimum value of  is
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• question_answer10)
  On the interval \[[0,1],\]the function \[{{x}^{25}}{{(1-x)}^{75}}\] takes its maximum value at the point      
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• question_answer11)
  A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]. Water is poured into it at a constant rate of 5 cubic meter per minute. Then the rate (in m/min.), at which the level of water is rising at the instant when the depth of water in the tank is \[10m;\] is equal to \[\frac{k}{\pi },\] then k is
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• question_answer12)
  If the tangent to the curve \[y=\frac{x}{{{x}^{2}}-3},\] \[x\in R,\] \[\left( x\ne \pm \sqrt{3} \right),\] at a point \[(\alpha ,\beta )\ne (0,0)\] on it is parallel to the line \[2x+6y-11=0,\] then calculate \[|6\alpha +2\beta |.\]
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• question_answer13)
  If m is the minimum value of A: for which the function \[f(x)=x\sqrt{kx-{{x}^{2}}}\] increasing in the interval \[[0,3]\] and M is the maximum value of f in \[[0,3],\] when \[k=m,\] find
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• question_answer14)
  If the function \[f(x)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1,\] where \[a>0,\] attains its maximum and minimum at p and q respectively such that \[{{p}^{2}}=q\text{ },\]then a equals
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• question_answer15)
  If the normal to the curve \[y=f\left( x \right)\] at the point \[(3,4)\] makes an angle \[\frac{3\pi }{4}\] with the positives-axis, then \[f'(3)\] is equal to
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