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

Find the equations of the tangent and normal to the curve `x^2/a^2−y^2/b^2=1` at the point `(sqrt2a,b)` .

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.

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = 2at², y = at⁴

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a cos θ, y = b cos θ

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = sin t, y = cos 2t

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = 4t, y = `4/y`

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = cos θ – cos 2θ, y = sin θ – sin 2θ

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a (θ – sin θ), y = a (1 + cos θ)

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

`x = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = `a(cos t + log tan  t/2)`, y = a sin t

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a sec θ, y = b tan θ

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

If x = `sqrt(a^(sin^(-1)t))`, y = `sqrt(a^(cos^(-1)t))` show that `dy/dx = - y/x`.

Find the scalar components and magnitude of the vector joining the points `P(x_1, y_1, z_1) and Q (x_2, y_2, z_2).`

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.

Which of the following differential equations has y = c₁ e^x + c₂ e^–x as the general solution?

(A) `(d^2y)/(dx^2) + y = 0`

(B) `(d^2y)/(dx^2) - y = 0`

(C) `(d^2y)/(dx^2) + 1 = 0`

(D) `(d^2y)/(dx^2)  - 1 = 0`