Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

If θ is the angle between two vectors `veca` and `vecb`, then `veca . vecb >= 0` only when ______.

Let `veca` and `vecb` be two unit vectors, and θ is the angle between them. Then `veca + vecb` is a unit vector if ______.

Determine the order and degree (if defined) of the differential equation:

`(d^4y)/(dx^4) + sin(y^("')) = 0`

Determine the order and degree (if defined) of the differential equation:

y' + 5y = 0

Determine the order and degree (if defined) of the differential equation:

`((ds)/(dt))^4 + 3s  (d^2s)/(dt^2) = 0`

Determine the order and degree (if defined) of the differential equation:

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

Determine the order and degree (if defined) of the differential equation:

`(d^2y)/(dx^2)` = cos 3x + sin 3x

Determine the order and degree (if defined) of the differential equation:

( y′′′) + (y″)³ + (y′)⁴ + y⁵ = 0

Determine the order and degree (if defined) of the differential equation:

y′′′ + 2y″ + y′ = 0

Determine the order and degree (if defined) of the differential equation:

y′ + y = e^x

Determine the order and degree (if defined) of the differential equation:

y″ + (y′)² + 2y = 0

Determine the order and degree (if defined) of the differential equation:

y″ + 2y′ + sin y = 0

The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.

The order of the differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y = 0` is ______.

For the differential equation given below, indicate its order and degree (if defined).

`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`

For the differential equation given below, indicate its order and degree (if defined).

`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`

For the differential equation given below, indicate its order and degree (if defined).

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

xy = a e^x + b e^-x + x² : `x (d^2y)/(dx^2) + 2 dy/dx - xy + x^2 - 2 = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = e^x (acos x + b sin x)  :  (d^2y)/(dx^2) - 2 dy/dx + 2y = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = xsin 3x   :   (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`