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

Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.

Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P(x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.

Family y = Ax + A³ of curves is represented by the differential equation of degree ______.

The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.

The differential equation of the family of curves x² + y² – 2ay = 0, where a is arbitrary constant, is ______.

Family y = Ax + A³ of curves will correspond to a differential equation of order ______.

The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is ______.

At (0, 0) the curve y = x³ + x

The differential equation of the family of curves y² = 4a(x + a) is ______.

The differential equation representing the family of circles x² + (y – a)² = a² will be of order two.

Differential equation representing the family of curves y = e^x (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0

The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4), respectively is ______.

If `abs (("a - b - c", 2"a", 2"a"),(2"b", "b - c - a", 2"b"),(2"c", 2"c", "c - a - b")) = "k" ("a + b + c")^3,` then k is ____________.

If `"x = a sin"  theta  "and  y = b cos"  theta, "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

The points on the curve `"x"^2/9 + "y"^2/16` = 1 at which the tangents are parallel to the y-axis are:

If A = `[(0, 2),(3, −4)]` and kA = `[(0, 3"a"),(2"b", 24)]`, then the values of k, a and b respectively are:

For which value of m is the line y = mx + 1 a tangent to the curve y² = 4x?

If y `= "Ae"^(5"x") + "Be"^(-5"x") "x"  "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

`"sin"^"p" theta  "cos"^"q" theta` attains a maximum, when `theta` = ____________.

The point on the curves y = (x – 3)² where the tangent is parallel to the chord joining (3, 0) and (4, 1) is ____________.