The core vision behind the School Learning initiative of GeeksforGeeks is to provide the school students with quality learning resources and to make the learning… Read More

# Category Archives: Class 12

Separable equations is an equation where dy/dx=f(x, y) is called separable provided algebraic operations, usually multiplication, division, and factorization, allow it to be written in… Read More

Matrix is an array of real numbers(or other suitable entities), arranged in rows and columns where entities are referred to elements present in the Matrix.… Read More

A quantity that is characterized not only by magnitude but also by its direction, is called a vector. Velocity, force, acceleration, momentum, etc. are vectors.… Read More

Straight Lines in 3D space are generally represented in two forms Cartesian Form and Vector Form. Hence the angles between any two straight lines in… Read More

A Point in three-dimensional geometry is defined as a location in 3D space that is uniquely defined by an ordered triplet (x, y, z) where… Read More

In the study of algebra and matrices, a system of linear equations is usually expressed in the form of matrices. For example, a1x + b1y… Read More

Question 1. In the matrix A = , write: (i)The order of the matrix Solution: We can see that matrix contains 3 rows and 4 columns… Read More

Inverse trigonometric functions are the inverse functions of the trigonometric functions. There are inverses of the sine, cosine, cosecant, tangent, cotangent, and secant functions. They… Read More

Determine the order and degree of the following differential equation. State also whether it is linear or non-linear(Question 14-26) Question 14. Solution: We have,… Read More

Determine the order and degree of the following differential equation. State also whether it is linear or non-linear(Question 1-13) Question 1. Solution: We have, Order… Read More

Question 14. sin4x(dy/dx) = cosx Solution: We have, sin4x(dy/dx) = cosx dy = (cosx/sin4x)dx Let, sinx = z On differentiating… Read More

Solve the following differential equations: Question 1. (dy/dx) = x2 + x – (1/x) Solution: We have, (dy/dx) = x2 + x – (1/x) dy… Read More

Question 1. Find the value of Solution: We know that Here, Now, can be written as : , where Hence, the value of = π/6 Question 2.… Read More

Question 1. If O is a point in space, ABC is a triangle, and D, E, F are the mid-points of the sides BC, CA,… Read More