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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
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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
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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
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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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