NEET Test Series from KOTA - 10 Papers In MS WORD
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Differential Equation
87165
The differential equation representing the family of curve \(y^{2}=2 c\left(x+c^{3}\right)\), where \(c\) is a positive parameters, is of
1 order 1, degree 1
2 order 1, degree 2
3 order 1, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(D) : We have, \(y^{2}=2 c\left(x+c^{3}\right)\) On differentiating with respect to \(\mathrm{x}\), we have \(2 y \frac{d y}{d x}=2 c \Rightarrow c=y \frac{d y}{d x}\) \(\therefore \quad y^{2}=2 y x \frac{d y}{d x}+2\left[\frac{y d y}{d x}\right]^{4}\) Hence, order is 1 and degree is 4
Kerala CEE-2008
Differential Equation
87166
The order and degree of the differential equation \(\sqrt{\sin x}(d x+d y)=\sqrt{\cos x}(d x-d y)\) is
87077
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : Given that, differential equation \(2 \mathrm{x}^{2} \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}-3 \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0\) It is clear that order is 2.
SRM JEEE-2018
Differential Equation
87078
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(C_{1} y=\left(C_{2}+C_{3}\right) e^{x+c_{4}}\) is
1 2
2 3
3 4
4 1
Explanation:
(D) : Given that family of curve \(\mathrm{C}_{1} \mathrm{y}=\left(\mathrm{C}_{2}+\mathrm{C}_{3}\right) \mathrm{e}^{\mathrm{x}+\mathrm{c}_{4}}\) \(y=\left(\frac{C_{2}+C_{3}}{C_{1}}\right) e^{x} \cdot e^{C_{4}} \Rightarrow y=C \cdot e^{x}\) Hence order is one.
87165
The differential equation representing the family of curve \(y^{2}=2 c\left(x+c^{3}\right)\), where \(c\) is a positive parameters, is of
1 order 1, degree 1
2 order 1, degree 2
3 order 1, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(D) : We have, \(y^{2}=2 c\left(x+c^{3}\right)\) On differentiating with respect to \(\mathrm{x}\), we have \(2 y \frac{d y}{d x}=2 c \Rightarrow c=y \frac{d y}{d x}\) \(\therefore \quad y^{2}=2 y x \frac{d y}{d x}+2\left[\frac{y d y}{d x}\right]^{4}\) Hence, order is 1 and degree is 4
Kerala CEE-2008
Differential Equation
87166
The order and degree of the differential equation \(\sqrt{\sin x}(d x+d y)=\sqrt{\cos x}(d x-d y)\) is
87077
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : Given that, differential equation \(2 \mathrm{x}^{2} \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}-3 \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0\) It is clear that order is 2.
SRM JEEE-2018
Differential Equation
87078
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(C_{1} y=\left(C_{2}+C_{3}\right) e^{x+c_{4}}\) is
1 2
2 3
3 4
4 1
Explanation:
(D) : Given that family of curve \(\mathrm{C}_{1} \mathrm{y}=\left(\mathrm{C}_{2}+\mathrm{C}_{3}\right) \mathrm{e}^{\mathrm{x}+\mathrm{c}_{4}}\) \(y=\left(\frac{C_{2}+C_{3}}{C_{1}}\right) e^{x} \cdot e^{C_{4}} \Rightarrow y=C \cdot e^{x}\) Hence order is one.
87165
The differential equation representing the family of curve \(y^{2}=2 c\left(x+c^{3}\right)\), where \(c\) is a positive parameters, is of
1 order 1, degree 1
2 order 1, degree 2
3 order 1, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(D) : We have, \(y^{2}=2 c\left(x+c^{3}\right)\) On differentiating with respect to \(\mathrm{x}\), we have \(2 y \frac{d y}{d x}=2 c \Rightarrow c=y \frac{d y}{d x}\) \(\therefore \quad y^{2}=2 y x \frac{d y}{d x}+2\left[\frac{y d y}{d x}\right]^{4}\) Hence, order is 1 and degree is 4
Kerala CEE-2008
Differential Equation
87166
The order and degree of the differential equation \(\sqrt{\sin x}(d x+d y)=\sqrt{\cos x}(d x-d y)\) is
87077
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : Given that, differential equation \(2 \mathrm{x}^{2} \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}-3 \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0\) It is clear that order is 2.
SRM JEEE-2018
Differential Equation
87078
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(C_{1} y=\left(C_{2}+C_{3}\right) e^{x+c_{4}}\) is
1 2
2 3
3 4
4 1
Explanation:
(D) : Given that family of curve \(\mathrm{C}_{1} \mathrm{y}=\left(\mathrm{C}_{2}+\mathrm{C}_{3}\right) \mathrm{e}^{\mathrm{x}+\mathrm{c}_{4}}\) \(y=\left(\frac{C_{2}+C_{3}}{C_{1}}\right) e^{x} \cdot e^{C_{4}} \Rightarrow y=C \cdot e^{x}\) Hence order is one.
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
Differential Equation
87165
The differential equation representing the family of curve \(y^{2}=2 c\left(x+c^{3}\right)\), where \(c\) is a positive parameters, is of
1 order 1, degree 1
2 order 1, degree 2
3 order 1, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(D) : We have, \(y^{2}=2 c\left(x+c^{3}\right)\) On differentiating with respect to \(\mathrm{x}\), we have \(2 y \frac{d y}{d x}=2 c \Rightarrow c=y \frac{d y}{d x}\) \(\therefore \quad y^{2}=2 y x \frac{d y}{d x}+2\left[\frac{y d y}{d x}\right]^{4}\) Hence, order is 1 and degree is 4
Kerala CEE-2008
Differential Equation
87166
The order and degree of the differential equation \(\sqrt{\sin x}(d x+d y)=\sqrt{\cos x}(d x-d y)\) is
87077
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : Given that, differential equation \(2 \mathrm{x}^{2} \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}-3 \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0\) It is clear that order is 2.
SRM JEEE-2018
Differential Equation
87078
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(C_{1} y=\left(C_{2}+C_{3}\right) e^{x+c_{4}}\) is
1 2
2 3
3 4
4 1
Explanation:
(D) : Given that family of curve \(\mathrm{C}_{1} \mathrm{y}=\left(\mathrm{C}_{2}+\mathrm{C}_{3}\right) \mathrm{e}^{\mathrm{x}+\mathrm{c}_{4}}\) \(y=\left(\frac{C_{2}+C_{3}}{C_{1}}\right) e^{x} \cdot e^{C_{4}} \Rightarrow y=C \cdot e^{x}\) Hence order is one.