Test: 35 Year JEE Previous Year Questions: Differential Equations - JEE MCQ

The degree and order of the differential equation of the family of all parabolas whose axis is x - axis, are respectively.

The solution of the differential equation 

The differential equation for the family of circle x² + y² - 2ay = 0, where a is anarbitrary constant is

Solution of the differential equation ydx + (x + x² y)dy = 0 is

The differential equation representing the family of curves   is a parameter, is of order and degree as follows :

then the solution of theequation is

The differential equation whose solution is Ax² + By² = 1 where A and B are arbitrary constants is of

The differential equation of all circles passing through the origin and having their centres on the x-axis is

The soluton of the differential equation  satisfying the condition y(1) =1 is

The differential equation which represents the family of curves are arbitrary constants, is

Solution of the differential equation 

then y (ln 2) is equal to :

Let I be the purchase value of an equipment and V (t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation  where k > 0 is a constant and T is thetotal life in years of the equipment. Then the scrap value V(T) of the equipment is

The population p (t) at time t of a certain mouse species satisfies the differential equation  If p (0) = 850, then the time at which the population becomes zero is :

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by If thefirm employs 25 more workers, then the new level of production of items is

Let the population of rabbits surviving at time t be governed by the differential equation  If p(0) = 100, then p(t) equals:

Let y(x) be the solution of the differential equation  Then y (e) is equal to:

If a curve y = f(x) passes through the point (1, –1) and satisfies the differential equation, y(1 + xy) dx = x dy, then