Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Form the differential equation representing the family of curves `y² = m(a² - x²) by eliminating the arbitrary constants 'm' and 'a'. 

Find the equation of a tangent and the normal to the curve `"y" = (("x" - 7))/(("x"-2)("x"-3)` at the point where it cuts the x-axis

Find the area of the region bounded by the curves (x -1)² + y² = 1 and x² + y² = 1, using integration.

Form the differential equation representing the family of curves y = e²x (a + bx), where 'a' and 'b' are arbitrary constants.

Find the equation of the tangent line to the curve `"y" = sqrt(5"x" -3) -5`, which is parallel to the line  `4"x" - 2"y" + 5 = 0`.

Find the equation of tangent to the curve `y = sqrt(3x -2)` which is parallel to the line 4x − 2y + 5 = 0. Also, write the equation of normal to the curve at the point of contact.

x = `"t" + 1/"t"`, y = `"t" - 1/"t"`

x = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`

x = 3cosθ – 2cos³θ, y = 3sinθ – 2sin³θ

sin x = `(2"t")/(1 + "t"^2)`, tan y = `(2"t")/(1 - "t"^2)`

x = `(1 + log "t")/"t"^2`, y = `(3 + 2 log "t")/"t"`

If x = e^cos2t and y = e^sin2t, prove that `"dy"/"dx" = (-y log x)/(xlogy)`

If x = asin2t (1 + cos2t) and y = b cos2t (1–cos2t), show that `("dy"/"dx")_("at  t" = pi/4) = "b"/"a"`

If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`

Differentiate `x/sinx` w.r.t. sin x

Differentiate `tan^-1 ((sqrt(1 + x^2) - 1)/x)` w.r.t. tan^–1x, when x ≠ 0

If x = sint and y = sin pt, prove that `(1 - x^2) ("d"^2"y")/("dx"^2) - x "dy"/"dx" + "p"^2y` = 0

If x = t², y = t³, then `("d"^2"y")/("dx"^2)` is ______.

Derivative of x² w.r.t. x³ is ______.

Find the angle of intersection of the curves y² = x and x² = y.