JEE Main & Advanced Mathematics Differential Equations Question Bank

done Order and degree of differential equations Total Questions - 36

• question_answer1)
  The order and degree of the differential equation \[y=x\frac{dy}{dx}+\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] are
  A)
                  1, 2 done clear
  B)
                  2, 1 done clear
  C)
                  1, 1          done clear
  D)
                  2, 2 done clear
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• question_answer2)
  The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants, will be
  A)
                  2              done clear
  B)
                  4 done clear
  C)
                  6              done clear
  D)
                  None of these done clear
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• question_answer3)
  The order and degree of the differential equation \[{{\left[ 4+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{2/3}}=\frac{{{d}^{2}}y}{d{{x}^{2}}}\] are
  A)
                  2, 2          done clear
  B)
                  3, 3 done clear
  C)
                  2, 3          done clear
  D)
                  3, 2 done clear
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• question_answer4)
  A differential equation of first order and first degree is 
  A)
                  \[x{{\left( \frac{dy}{dx} \right)}^{2}}-x+a=0\]       done clear
  B)
                  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+xy=0\] done clear
  C)
                  \[dy+dx=0\]             done clear
  D)
                  None of these done clear
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• question_answer5)
  The order and degree of the differential equation \[\sqrt{\frac{dy}{dx}}-4\frac{dy}{dx}-7x=0\]are                                   [MP PET 1993]
  A)
                  1 and 1/2 done clear
  B)
                  2 and 1 done clear
  C)
                  1 and 1    done clear
  D)
                  1 and 2 done clear
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• question_answer6)
  The order and degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\]is                                   [DCE 2002]
  A)
                  4, 2          done clear
  B)
                  1, 2 done clear
  C)
                  2, 2          done clear
  D)
                  \[2,\frac{1}{2}\] done clear
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• question_answer7)
  The order and the degree of the differential equation \[{{\left( \frac{{{d}^{2}}s}{d{{t}^{2}}} \right)}^{2}}+3{{\left( \frac{ds}{dt} \right)}^{3}}+4=0\]are
  A)
                  \[2,\,2\]  done clear
  B)
                  \[2,\,3\] done clear
  C)
                  \[3,2\]     done clear
  D)
                  None of these done clear
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• question_answer8)
  The order and the degree of differential equation \[\frac{{{d}^{4}}y}{d{{x}^{4}}}-4\frac{{{d}^{3}}y}{d{{x}^{3}}}+8\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+4y=0\] are respectively
  A)
                  4, 1          done clear
  B)
                  1, 4 done clear
  C)
                  1, 1          done clear
  D)
                  None of these done clear
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• question_answer9)
  The order of the differential equation \[{{{y\left( \frac{dy}{dx} \right)=x}/{\frac{dy}{dx}+\left( \frac{dy}{dx} \right)}\;}^{3}}\] is   [MP PET 1994]
  A)
                  1              done clear
  B)
                  2 done clear
  C)
                  3              done clear
  D)
                  4 done clear
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• question_answer10)
  The order of the differential equation whose solution is \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\], is      [MP PET 1995]
  A)
                  1              done clear
  B)
                  2 done clear
  C)
                  3              done clear
  D)
                  4 done clear
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• question_answer11)
  The order of the differential equation of all circles of radius r, having centre on y-axis and passing through the origin is
  A)
                  1              done clear
  B)
                  2 done clear
  C)
                  3              done clear
  D)
                  4 done clear
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• question_answer12)
  The order of the differential equation whose solution is \[y=a\cos x+b\sin x+c{{e}^{-x}}\]is
  A)
                  3              done clear
  B)
                  2 done clear
  C)
                  1              done clear
  D)
                  None of these done clear
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• question_answer13)
  The differential equation of all circles of radius a is of order
  A)
                  2              done clear
  B)
                  3 done clear
  C)
                  4              done clear
  D)
                  None of these done clear
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• question_answer14)
  The differential equation of all circles in the first quadrant which touch the coordinate axes is of order
  A)
                  1              done clear
  B)
                  2 done clear
  C)
                  3              done clear
  D)
                  None of these done clear
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• question_answer15)
  Order and degree of differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ y+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{1/4}}\]are [MP PET 1996]
  A)
                  4 and 2    done clear
  B)
                  1 and 2 done clear
  C)
                  1 and 4    done clear
  D)
                  2 and 4 done clear
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• question_answer16)
  The degree of the differential equation \[\left( \frac{2+\sin x}{1+y} \right)\frac{dy}{dx}=-\cos ,x\ y(0)=1,\] is                [Pb. CET 2003]
  A)
                  1              done clear
  B)
                  2 done clear
  C)
                  3              done clear
  D)
                  6 done clear
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• question_answer17)
  Degree of the given differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}={{\left( 1+\frac{dy}{dx} \right)}^{1/2}}\], is    [MP PET 1997]
  A)
                  2              done clear
  B)
                  3 done clear
  C)
                  \[\frac{1}{2}\]         done clear
  D)
                  6 done clear
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• question_answer18)
  The order and degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{\frac{1}{3}}}+{{x}^{\frac{1}{4}}}=0\] are respectively      [MP PET 1998]
  A)
                  2, 3          done clear
  B)
                  3, 3 done clear
  C)
                  2, 6          done clear
  D)
                  2, 4 done clear
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• question_answer19)
  Family \[y=Ax+{{A}^{3}}\]of curve represented by the differential equation of degree      [MP PET 1999]
  A)
                  Three       done clear
  B)
                  Two done clear
  C)
                  One done clear
  D)
                  None of these done clear
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• question_answer20)
  Which of the following differential equations has the same order and degree  [Kurukshetra CEE 1998]
  A)
                  \[\frac{{{d}^{4}}y}{d{{x}^{4}}}+8\text{ }{{\left( \frac{dy}{dx} \right)}^{6}}+5y={{e}^{x}}\] done clear
  B)
                  \[5\text{ }{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{4}}+8\text{ }{{\left( 1+\frac{dy}{dx} \right)}^{2}}+5y={{x}^{8}}\] done clear
  C)
                  \[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{2/3}}=4\frac{{{d}^{3}}y}{d{{x}^{3}}}\]          done clear
  D)
                  \[y={{x}^{2}}\frac{dy}{dx}+\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\] done clear
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• question_answer21)
  The differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}+\sin y+{{x}^{2}}=0\] is of the following type      [Roorkee 1998]
  A)
                  Linear      done clear
  B)
                  Homogeneous done clear
  C)
                  Order two               done clear
  D)
                  Degree one done clear
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• question_answer22)
  The differential equation  \[x{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{4}}+y={{x}^{2}}\] is of
  A)
                  Degree 3 and order 2              done clear
  B)
                  Degree 1 and order 1 done clear
  C)
                  Degree 4 and order 3              done clear
  D)
                  Degree 4 and order 4 done clear
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• question_answer23)
  If m and n are the order and degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\frac{{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1\], then [Karnataka CET 1999]
  A)
                  m = 3 and n = 5 done clear
  B)
                  m = 3 and n = 1 done clear
  C)
                  m = 3 and n = 3       done clear
  D)
                  m = 3 and n = 2 done clear
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• question_answer24)
  The second order differential equation is              [MP PET 2000]
  A)
                  \[{{{y}'}^{2}}+x={{y}^{2}}\]     done clear
  B)
                  \[{y}'{y}''+y=\sin x\] done clear
  C)
                  \[{y}'''+{y}''+y=0\]   done clear
  D)
                  \[{y}'=y\] done clear
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• question_answer25)
  The order and degree of the differential equation \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}+{{y}^{2}}=0\] are respectively [Karnataka CET 2001]
  A)
                  2 and 2    done clear
  B)
                  1 and 1 done clear
  C)
                  2 and 1    done clear
  D)
                  1 and 2 done clear
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• question_answer26)
  The order and degree of the differential equation \[\rho =\frac{{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{3/2}}}{{{d}^{2}}y/d{{x}^{2}}}\] are respectively [MP PET 2001; UPSEAT 2002]
  A)
                  2, 2 done clear
  B)
                  2, 3 done clear
  C)
                  2, 1 done clear
  D)
                  None of these done clear
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• question_answer27)
  Order of the differential equation of the family of all concentric circles centered at (h, k)  is           [EAMCET 2002]
  A)
                  1    done clear
  B)
                  2 done clear
  C)
                  3              done clear
  D)
                  4 done clear
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• question_answer28)
  The degree of differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{3}}+6y=0\] is              [Kerala (Engg.) 2002]
  A)
                  1              done clear
  B)
                  3 done clear
  C)
                  2              done clear
  D)
                  5 done clear
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• question_answer29)
  The order and degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{4}}-xy=0\] are respectively             [MP PET 2003]
  A)
                  2 and 4    done clear
  B)
                  3 and 2 done clear
  C)
                  4 and 5    done clear
  D)
                  2 and 3 done clear
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• question_answer30)
  \[\frac{{{d}^{3}}y}{d{{x}^{3}}}+2\,\left[ 1+\frac{{{d}^{2}}y}{d{{x}^{2}}} \right]=1\] has degree and order as [UPSEAT 2003]
  A)
                  1, 3          done clear
  B)
                  2, 3 done clear
  C)
                  3, 2          done clear
  D)
                  3, 1 done clear
  View Solution play_arrow

• question_answer31)
  The degree and order of the differential equation of the family of all parabolas whose axis is x?axis, are respectively [AIEEE 2003]
  A)
                  2, 1          done clear
  B)
                  1, 2 done clear
  C)
                  3, 2          done clear
  D)
                  2, 3 done clear
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• question_answer32)
  The degree of the differential equation \[{{\left( 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right)}^{3/4}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{1/3}}\] is [Karnataka CET 2004]
  A)
                  \[\frac{1}{3}\]         done clear
  B)
                  4 done clear
  C)
                  9              done clear
  D)
                  \[\frac{3}{4}\] done clear
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• question_answer33)
  The order and degree of the differential equation \[x\text{ }{{\left( \frac{dy}{dx} \right)}^{3}}+2\,{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+3y+x=0\] are respectively [MP PET 2004]
  A)
                  3, 2          done clear
  B)
                  2, 1 done clear
  C)
                  2, 2          done clear
  D)
                  2, 3 done clear
  View Solution play_arrow

• question_answer34)
  The degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\sqrt{\frac{dy}{dx}-3}=x\] is [Orissa JEE 2004]
  A)
                  2 done clear
  B)
                  1 done clear
  C)
                  ½ done clear
  D)
                  3 done clear
  View Solution play_arrow

• question_answer35)
  The order of differential equations of all parabolas having directrix parallel to x-axis is    [Orissa JEE 2004]
  A)
                  3              done clear
  B)
                  1 done clear
  C)
                  4              done clear
  D)
                  2 done clear
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• question_answer36)
  The degree of the differential equation \[y(x)=1+\frac{dy}{dx}+\frac{1}{1.2}{{\left( \frac{dy}{dx} \right)}^{2}}+\frac{1}{1.2.3}{{\left( \frac{dy}{dx} \right)}^{3}}+...\] is [Orissa JEE 2005]
  A)
                  2              done clear
  B)
                  3 done clear
  C)
                  1              done clear
  D)
                  None of these done clear
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