Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

Find one-parameter families of solution curves of the following differential equation:-

\[e^{- y} \sec^2 y dy = dx + x dy\]

Find one-parameter families of solution curves of the following differential equation:-

\[x \log x\frac{dy}{dx} + y = 2 \log x\]

Find one-parameter families of solution curves of the following differential equation:-

\[x\frac{dy}{dx} + 2y = x^2 \log x\]

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) ?