The differential equation  (a is any constant) represents

Two parallel forces not having the same line of action form a couple if they are

In this question, we have to find the are two parallel forces not having the same line of action form a couple. A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance or moment.

Any two coplanar couples of equal moments

In this question, two coplanar couples of equal moments. Moments of couple is called torque. When two couples are present whose moments are equal and opposite then the forces are already balanced.

Forces of magnitudes and act at a point parallel to the sides of an equilateral triangle taken in order. The resultant of these forces, is

Here we have to find the resultant force of the given magnitude. Firstly, find the component of the force which is Fsin θ and Fcos θ.

If two forces  and  make an angle  with each other and their resultant makes an angle  with the bisector of the angle between the two forces, then  is equal to

If the square of the resultant of two equal forces is equal to  times their product, then the angle between the forces is

The maximum resultant of two forces is P and the minimum resultant is , the two forces are at right angles, the resultant is

The resultant of two forces  and  is of magnitude P. If the force is doubled, remaining unaltered, the new resultant will be

The resultant of two forces 3P and 2P is R, if the first force is doubled, the resultant is also doubled. The angle between the forces is

In this question, we have to make two equations of Resultant as per given instruction and solve the equations and find the angle. Remember the formula of Resultant is R = 

If the gradient of the tangent at any point (x, y) of a curve which passes through the point  is then equation of the curve is

If , then is

In this question, we have given ycosx + xcosy =π . Differentiate this equation with request to x and do separate second derivate and find the value of it.

The solution of the differential equation is equal to

In this question, you have to find the solution of differential equation x4  + x3 y + cosec (xy) = 0. Use variable separable method to find the solution.

A continuously differentiable function  satisfying  is

The slope of the tangent at  to a curve passing through  is given by , then the equation of the curve is

A solution of the differential equation  is

If integrating factor of  is  then P is equal to