87640
Assertion (A) : Order of the differential equations of a family of circles with constant radius is two. Reason (R) : An algebraic equation having two arbitrary constants is general solution of 2nd order differential equation.
1 (A) and (R) are true, (R) is the correct explanation to (A)
2 is true, (R) is false
3 (A) and (R) are false, (R) is not the correct explanation to (A)
4 (A) is false, (R) is true
Explanation:
(A) : Any circle with given radius can be written as \((\mathrm{x}-\mathrm{h})^{2}+(\mathrm{y}-\mathrm{k})^{2}=\mathrm{a}^{2}\) Where \((\mathrm{h}, \mathrm{k})\) be the centre of the circle which is variable. So in above algebraic equation, there are two arbitrary constant \(\mathrm{h}\) and \(\mathrm{k}\). So, order of differential equation will be second order. Hence, assertion and reason are true and reason is the correct explanation to assertion.
AP EAMCET-05.07.2022
Differential Equation
87641
The solution of \(\frac{d^{2} y}{d x^{2}}=0\) represents
1 straight lines
2 a circle
3 a parabola
4 \((9,6 \sqrt{3})\)
Explanation:
(A) : Given differential equation - \(\frac{d^{2} y}{d x^{2}}=0\) \(\frac{d y}{d x}=a\) \(d y=a d x\) \(\int d y=a \int d x\) \(y=a x+b\) is a equation of straight line.
87640
Assertion (A) : Order of the differential equations of a family of circles with constant radius is two. Reason (R) : An algebraic equation having two arbitrary constants is general solution of 2nd order differential equation.
1 (A) and (R) are true, (R) is the correct explanation to (A)
2 is true, (R) is false
3 (A) and (R) are false, (R) is not the correct explanation to (A)
4 (A) is false, (R) is true
Explanation:
(A) : Any circle with given radius can be written as \((\mathrm{x}-\mathrm{h})^{2}+(\mathrm{y}-\mathrm{k})^{2}=\mathrm{a}^{2}\) Where \((\mathrm{h}, \mathrm{k})\) be the centre of the circle which is variable. So in above algebraic equation, there are two arbitrary constant \(\mathrm{h}\) and \(\mathrm{k}\). So, order of differential equation will be second order. Hence, assertion and reason are true and reason is the correct explanation to assertion.
AP EAMCET-05.07.2022
Differential Equation
87641
The solution of \(\frac{d^{2} y}{d x^{2}}=0\) represents
1 straight lines
2 a circle
3 a parabola
4 \((9,6 \sqrt{3})\)
Explanation:
(A) : Given differential equation - \(\frac{d^{2} y}{d x^{2}}=0\) \(\frac{d y}{d x}=a\) \(d y=a d x\) \(\int d y=a \int d x\) \(y=a x+b\) is a equation of straight line.
87640
Assertion (A) : Order of the differential equations of a family of circles with constant radius is two. Reason (R) : An algebraic equation having two arbitrary constants is general solution of 2nd order differential equation.
1 (A) and (R) are true, (R) is the correct explanation to (A)
2 is true, (R) is false
3 (A) and (R) are false, (R) is not the correct explanation to (A)
4 (A) is false, (R) is true
Explanation:
(A) : Any circle with given radius can be written as \((\mathrm{x}-\mathrm{h})^{2}+(\mathrm{y}-\mathrm{k})^{2}=\mathrm{a}^{2}\) Where \((\mathrm{h}, \mathrm{k})\) be the centre of the circle which is variable. So in above algebraic equation, there are two arbitrary constant \(\mathrm{h}\) and \(\mathrm{k}\). So, order of differential equation will be second order. Hence, assertion and reason are true and reason is the correct explanation to assertion.
AP EAMCET-05.07.2022
Differential Equation
87641
The solution of \(\frac{d^{2} y}{d x^{2}}=0\) represents
1 straight lines
2 a circle
3 a parabola
4 \((9,6 \sqrt{3})\)
Explanation:
(A) : Given differential equation - \(\frac{d^{2} y}{d x^{2}}=0\) \(\frac{d y}{d x}=a\) \(d y=a d x\) \(\int d y=a \int d x\) \(y=a x+b\) is a equation of straight line.
87640
Assertion (A) : Order of the differential equations of a family of circles with constant radius is two. Reason (R) : An algebraic equation having two arbitrary constants is general solution of 2nd order differential equation.
1 (A) and (R) are true, (R) is the correct explanation to (A)
2 is true, (R) is false
3 (A) and (R) are false, (R) is not the correct explanation to (A)
4 (A) is false, (R) is true
Explanation:
(A) : Any circle with given radius can be written as \((\mathrm{x}-\mathrm{h})^{2}+(\mathrm{y}-\mathrm{k})^{2}=\mathrm{a}^{2}\) Where \((\mathrm{h}, \mathrm{k})\) be the centre of the circle which is variable. So in above algebraic equation, there are two arbitrary constant \(\mathrm{h}\) and \(\mathrm{k}\). So, order of differential equation will be second order. Hence, assertion and reason are true and reason is the correct explanation to assertion.
AP EAMCET-05.07.2022
Differential Equation
87641
The solution of \(\frac{d^{2} y}{d x^{2}}=0\) represents
1 straight lines
2 a circle
3 a parabola
4 \((9,6 \sqrt{3})\)
Explanation:
(A) : Given differential equation - \(\frac{d^{2} y}{d x^{2}}=0\) \(\frac{d y}{d x}=a\) \(d y=a d x\) \(\int d y=a \int d x\) \(y=a x+b\) is a equation of straight line.
