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The general solution of the differential equation

is :

( where c is a constant of integration)

• Option 1)

• Option 2)

• Option 3)

• Option 4)

general solution of the differential equation  Option 1) Option 2) Option 3) Option 4)

Consider the differential equation,  If value of y is 1 when  then the value of x for which  is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

IF=                when  Option 1) Option 2) Option 3)   Option 4)

If  the ordered pair  at  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Again differentiate w.r.t.   x Option 1) Option 2)   Option 3)      Option 4)

Let  be the solution of the fifferential equation,

such that . Then :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

C

If y = y(x) is the solution of the differential equation

, such that y(0) = 0 , then

is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Given differential eqn I.F. = =  Solution of given differential eqn                                  Given that  =>  put  So, correct option is (1) Option 1) Option 2) Option 3) Option 4)

If

and   , then    is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3)   Option 4)

The solution of the differential equation   with  is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

This D.E in the form of Linear D.E. Solution, given       Option 1)          Option 2) Option 3)        Option 4)

Given that the slope of the tangent to a curve  at any point  is . If the curve passes through the centre of the circle , then its equation is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

given slope of tangent  Integrate but side. It passes through centre of circle    Eq. of curve is  Option 1) Option 2) Option 3)   Option 4)

Let be the solution of the differential equation, such that If , then the value of 'a' is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

this is a linear differential equation with We have   Option 1) Option 2) Option 3)   Option 4)

The solution of the differential equation,

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Solution of Differential Equation - put       - wherein Equation with convert to   let  y(1) = 1 or      Option 1)Option 2)Option 3)Option 4)

If      is the solution of the differential equation  where , then :

• Option 1)

• Option 2)

is decreasing in

• Option 3)

• Option 4)

is decreasing in (0,1)

Linear Differential Equation - - wherein P, Q are functions of x alone.     Linear Differential Equation - Multiply by   which is the Integrating factor - wherein P is the function of x alone   Solution of a differential equation, Hence,   if   is decreasing in       Option 1)  Option 2)    is decreasing in Option 3)  Option 4)  is decreasing in (0,1)

Let f: be a function such that ,. Then f(2) equals :

• Option 1)

-4

• Option 2)

30

• Option 3)

-2

• Option 4)

8

Differential Equations - An equation involving independent variable (x), dependent variable (y) and derivative of dependent variable with respect to independent variable  - wherein eg:        Order of a Differential Equation - The order of a differential equation is order of highest order occuring in differential equation - wherein order of    is...

If   ,and

then  equals

• Option 1)

• Option 2)

1/3

• Option 3)

-4/3

• Option 4)

Linear Differential Equation - - wherein P, Q are functions of x alone.     Linear Differential Equation - Multiply by   which is the Integrating factor - wherein P is the function of x alone From the concept I.F. = or Now put  Option 1)  Option 2)  1/3Option 3)  -4/3Option 4)

The curve amongst the family of curves responded by the differential equation,  which passes through (1,1), is:

• Option 1)

A hyperbola with the transverse axis along the x-axis

• Option 2)

A circle with centre on the x-axis

• Option 3)

an ellipse with the major axis along the y-axis.

• Option 4)

A circle with centre on the y-axis

Homogeneous Differential Equation - A function   is called homogeneous function of  degree n, if - wherein eg:     Homogeneous Differential Equation - Put - The D.E. can be written as  from the concept  put  On Integrating Passes through (1,1)        Option 1)A hyperbola with the transverse axis along the x-axisOption 2)A circle with centre on the x-axisOption 3)an ellipse with...

For  if ,  then   is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Differential Equations - An equation involving independent variable (x), dependent variable (y) and derivative of dependent variable with respect to independent variable  - wherein eg:      Using   both sides     Option 1)       Option 2)Option 3)Option 4)

Let  be the solution of the differential equation,  If  then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Linear Differential Equation - - wherein P, Q are functions of x alone.     Linear Differential Equation - Multiply by   which is the Integrating factor - wherein P is the function of x alone   Putting x = 2 we get C = 0 Option 1)      Option 2)Option 3)Option 4)

If  and y = 3sect, then the value of  at ,is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

1/6

Second Order Differential Equation - - wherein  Option 1)Option 2)Option 3)  Option 4)  1/6

Let  be such that , for all ,and . If y = y(x) satisfies the differential equation,  with y(0) = 1, then is equal to :

• Option 1)

3

• Option 2)

2

• Option 3)

5

• Option 4)

4

Differential Equations - An equation involving independent variable (x), dependent variable (y) and derivative of dependent variable with respect to independent variable  - wherein eg:      Given that At  Option 1)  3Option 2)  2Option 3)  5Option 4)  4

If  is the solution of the differential equation,  satisfying  then  is equal to

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Linear Differential Equation - - wherein P, Q are functions of x alone.     Linear Differential Equation - Multiply by   which is the Integrating factor - wherein P is the function of x alone Differential Equation can be written as. from the concept we have learnt  If =  Solution of this d.e is  So,  given  We need to find  Put   Option 1)Option 2)Option 3)Option 4)
Engineering
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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 is given by . If the firm employs 25 more workers,then the new level of production of items is :

• Option 1)

4500

• Option 2)

2500

• Option 3)

3000

• Option 4)

3500

As we have learned Variable Separation Method - integrating, we get -   and    We have              Option 1) 4500 Option 2) 2500 Option 3) 3000 Option 4) 3500
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