Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20225 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

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 a second order differential equation.

Options

  1. A( A ) and ( R ) are true, ( R ) is the correct explanation to (A)
  2. B(A) is true, (R) is false
  3. C(A) and (R) are false, (R) is not the correct explanation to (A)
  4. D(A) is false, (R) is true

Correct answer

A. ( A ) and ( R ) are true, ( R ) is the correct explanation to (A)

Step-by-step solution

Any circle with given radius can be written as, (x-h)^2+(y-k)^2=a^2 where (h, k) be the centre of the circle which is variable. So, in above algebraic equation, there are two arbitrary constant h and k . Hence, order of differential equation will be second order. Hence, assertion and reason are true and reason is the correct explanation to assertion.

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is 2025The general solution of the differential equation (x+y) d y=d x is 2025If Ax ^3+ Bxy =4 (A and B are arbitrary constants) is the general solution of the differential equation F(x) d^2 y d x^2 +G(x) d y d x -2 y=0 , then F(1)+G(1)= 2025If y=A t^2+ B t (A,B are parameters) is general solution of the differential equation f(t) y^ (t)+g(t) y^ (t)+h(t) y=0 then 2 f(t)+t^2 h(t)= 2025The general solution of the differential equation (2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0 is 2025The general solution of the differential equation x x d y=(x x-y) d x is 2025If a and b are arbitrary constants, then the differential equation corresponding to the family of curves y= (a x+b) is 2025The general solution of the differential equation x y(y+2) d y+ (y^3-1 ) d x=0 is 2025 Full Differential Equations list All AP EAMCET PYQs