Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

The differential equation which represents the family of curves y = e^Cx is

The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by

Find the slope of the tangent and the normal to the following curve at the indicted point \[y = \sqrt{x^3} \text { at } x = 4\] ?

Find the slope of the tangent and the normal to the following curve at the indicted point \[y = \sqrt{x} \text { at }x = 9\] ?

Find the slope of the tangent and the normal to the following curve at the indicted point  y = x³ − x at x = 2 ?

Find the slope of the tangent and the normal to the following curve at the indicted point y = 2x² + 3 sin x at x = 0 ?

Find the slope of the tangent and the normal to the following curve at the indicted point x = a (θ − sin θ), y = a(1 − cos θ) at θ = −π/2 ?

Find the slope of the tangent and the normal to the following curve at the indicted point  x = a cos³ θ, y = a sin³ θ at θ = π/4 ?

Find the slope of the tangent and the normal to the following curve at the indicted point  x = a (θ − sin θ), y = a(1 − cos θ) at θ = π/2 ?

Find the slope of the tangent and the normal to the following curve at the indicted point  y = (sin 2x + cot x + 2)² at x = π/2 ?

Find the slope of the tangent and the normal to the following curve at the indicted point  x² + 3y + y² = 5 at (1, 1)  ?

Find the slope of the tangent and the normal to the following curve at the indicted point  xy = 6 at (1, 6) ?

Find a point on the curve y = x³ − 3x where the tangent is parallel to the chord joining (1, −2) and (2, 2) ?

Find the points on the curve y = x³ − 2x² − 2x at which the tangent lines are parallel to the line y = 2x− 3 ?

Find the points on the curve y² = 2x³ at which the slope of the tangent is 3 ?

Find the points on the curve xy + 4 = 0 at which the tangents are inclined at an angle of 45° with the x-axis ?

Find the point on the curve y = x² where the slope of the tangent is equal to the x-coordinate of the point ?