PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

 If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is `6sqrt3` r.

If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`

If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of  `dy/dx `at t = `pi/4`

Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`

If x = cos t (3 – 2 cos² t) and y = sin t (3 – 2 sin² t), find the value of dx/dy at t =4/π.

Form the differential equation from the following primitive where constants are arbitrary:
y² = 4ax

Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c² + c³

Form the differential equation from the following primitive where constants are arbitrary:
xy = a²

Form the differential equation from the following primitive where constants are arbitrary:
y = ax² + bx + c

Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x + a)² + y² = a²

Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x − a)² − y² = a²

Form the differential equation of the family of curves represented by the equation (a being the parameter):
 (x − a)² + 2y² = a²