JEE Main & Advanced Mathematics Differential Equations Question Bank

done Application of differnetial equations Total Questions - 14

• question_answer1)
  The equation of the curve which passes through the point (1, 1) and whose slope is given by \[\frac{2y}{x}\], is  [Roorkee 1987]
  A)
                  \[y={{x}^{2}}\]  done clear
  B)
                  \[{{x}^{2}}-{{y}^{2}}=0\] done clear
  C)
                  \[2{{x}^{2}}+{{y}^{2}}=3\]       done clear
  D)
                  None of these done clear
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• question_answer2)
  The equation of the curve that passes through the point \[(1,\,2)\] and satisfies the differential equation \[\frac{dy}{dx}=\frac{-2xy}{({{x}^{2}}+1)}\]is
  A)
                  \[y({{x}^{2}}+1)=4\]       done clear
  B)
                  \[y({{x}^{2}}+1)+4=0\] done clear
  C)
                  \[y({{x}^{2}}-1)=4\]         done clear
  D)
                  None of these done clear
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• question_answer3)
  Equation of curve through point \[(1,\,0)\]which satisfies the differential equation \[(1+{{y}^{2}})dx-xydy=0\], is            [WB JEE 1986]
  A)
                  \[{{x}^{2}}+{{y}^{2}}=1\]          done clear
  B)
                  \[{{x}^{2}}-{{y}^{2}}=1\] done clear
  C)
                  \[2{{x}^{2}}+{{y}^{2}}=2\]       done clear
  D)
                  None of these done clear
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• question_answer4)
  Equation of curve passing through (3, 9) which satisfies the differential equation \[\frac{dy}{dx}=x+\frac{1}{{{x}^{2}}}\], is       [WB JEE 1986]
  A)
                  \[6xy=3{{x}^{2}}-6x+29\]             done clear
  B)
                  \[6xy=3{{x}^{3}}-29x+6\] done clear
  C)
                  \[6xy=3{{x}^{3}}+29x-6\]             done clear
  D)
                  None of these done clear
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• question_answer5)
  The differential equation \[y\frac{dy}{dx}+x=a\](a is any constant) represents
  A)
                  A set of circles having centre on the y-axis done clear
  B)
                  A set of circles centre on the x-axis done clear
  C)
                  A set of ellipses done clear
  D)
                  None of these done clear
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• question_answer6)
  The equation of a curve passing through \[\left( 2,\frac{7}{2} \right)\] and having gradient \[1-\frac{1}{{{x}^{2}}}\]at\[(x,\,y)\]is
  A)
                  \[y={{x}^{2}}+x+1\]       done clear
  B)
                  \[xy={{x}^{2}}+x+1\] done clear
  C)
                  \[xy=x+1\]            done clear
  D)
                  None of these done clear
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• question_answer7)
  The equation of the curve through the point (1,0) and whose slope is \[\frac{y-1}{{{x}^{2}}+x}\]is
  A)
                  \[(y-1)(x+1)+2x=0\]           done clear
  B)
                  \[2x(y-1)+x+1=0\] done clear
  C)
                  \[x(y-1)(x+1)+2=0\]           done clear
  D)
                  None of these done clear
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• question_answer8)
  The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes though the point (4, 3). The equation of the curve is
  A)
                  \[{{x}^{2}}=y+5\]            done clear
  B)
                  \[{{y}^{2}}=x-5\] done clear
  C)
                  \[{{y}^{2}}=x+5\]            done clear
  D)
                  \[{{x}^{2}}=y-5\] done clear
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• question_answer9)
  A particle moves in a straight line with a velocity given by \[\frac{dx}{dt}=x+1\](x is the distance described). The time taken by a particle to traverse a distance of 99 metre is
  A)
                  \[{{\log }_{10}}e\]               done clear
  B)
                  \[2{{\log }_{e}}10\] done clear
  C)
                  \[2{{\log }_{10}}e\]             done clear
  D)
                  \[\frac{1}{2}{{\log }_{10}}e\] done clear
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• question_answer10)
  Solution of differential equation \[x\,dy-y\,dx=0\] represents [MP PET 1996]
  A)
                  Rectangular hyperbola done clear
  B)
                  Straight line passing through origin done clear
  C)
                  Parabola whose vertex is at origin done clear
  D)
                  Circle whose centre is at origin done clear
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• question_answer11)
  Integral curve satisfying  \[y'=\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}},\ y(1)=2\] has the slope at the point (1, 0) of the curve, equal to       [MP PET 2000]
  A)
                  ? 5/3       done clear
  B)
                  ? 1 done clear
  C)
                  1              done clear
  D)
                  5/3 done clear
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• question_answer12)
  A particle starts at the origin and moves along the x?axis in such a way that its velocity at the point (x, 0) is given by the formula \[\frac{dx}{dt}={{\cos }^{2}}\pi x.\]  Then the particle never reaches the point on [AMU 2000]
  A)
                  \[x=\frac{1}{4}\]  done clear
  B)
                  \[x=\frac{3}{4}\] done clear
  C)
                  \[x=\frac{1}{2}\]  done clear
  D)
                  x = 1 done clear
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• question_answer13)
  The slope of the tangent at (x, y) to a curve passing through a point (2, 1) is \[\frac{{{x}^{2}}+{{y}^{2}}}{2xy}\], then the equation of the curve is [MP PET 2002]
  A)
                  \[2({{x}^{2}}-{{y}^{2}})=3x\]     done clear
  B)
                  \[2({{x}^{2}}-{{y}^{2}})=6y\] done clear
  C)
                  \[x({{x}^{2}}-{{y}^{2}})=6\]       done clear
  D)
                  \[x({{x}^{2}}+{{y}^{2}})=10\] done clear
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• question_answer14)
  A function \[y=f(x)\] has a second order derivatives \[{{f}'}'(x)=6(x-1)\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is \[y=3x-5\], then the function is    [AIEEE 2004]
  A)
                  \[{{(x+1)}^{3}}\]               done clear
  B)
                  \[{{(x-1)}^{3}}\] done clear
  C)
                  \[{{(x+1)}^{2}}\]               done clear
  D)
                           \[{{(x-1)}^{2}}\] done clear
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