Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Find the equation of the normal at a point on the curve x² = 4y which passes through the point (1, 2). Also find the equation of the corresponding tangent.

The equation of tangent at (2, 3) on the curve y² = ax³ + b is y = 4x – 5. Find the values of a and b.

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

Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)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`

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

Find the equation of tangents to the curve y= x³ + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.

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`

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

Show that the equation of normal at any point t on the curve x = 3 cos t – cos³t and y = 3 sin t – sin³t is 4 (y cos³t – sin³t) = 3 sin 4t

Show that the equation of normal at any point t on the curve x = 3 cos t – cos³t and y = 3 sin t – sin³t is 4 (y cos³t – sin³t) = 3 sin 4t

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

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