Arts (English Medium) Class 12 - CBSE Important Questions

Find the particular solution of the differential equation `(x - y) dy/dx = (x + 2y)` given that y = 0 when x = 1.

Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where C is parameter

Solve the differential equation `x dy/dx + y = x cos x + sin x`,  given that y = 1 when `x = pi/2`

The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.

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

Solve the differential equation:  ` (dy)/(dx) = (x + y )/ (x - y )`

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

Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.

Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.

Find the general solution of the differential equation:

`log((dy)/(dx)) = ax + by`.

Degree of the differential equation `sinx + cos(dy/dx)` = y² is ______.

Find the general solution of the differential equation:

(xy – x²) dy = y² dx

Find the general solution of the differential equation:

`(x^2 + 1) dy/dx + 2xy = sqrt(x^2 + 4)`

The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.

Prove that, for any three vector `veca,vecb,vecc [vec a+vec b,vec b+vec c,vecc+veca]=2[veca vecb vecc]`

Show that the points A, B, C with position vectors `2hati- hatj + hatk`, `hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle

If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, find the angle which `veca + vecb + vecc`make with `veca or vecb or vecc`

Using vectors find the area of triangle ABC with vertices A(1, 2, 3), B(2, −1, 4) and C(4, 5, −1).

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is `sqrt(3)`.