HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find A⁻¹ using column transformations:

A = `[(2, -3),(-1, 2)]`

If A = `[(1, 2, -1),(3, -2, 5)]`, apply R₁ ↔ R₂ and then C₁ → C₁ + 2C₃ on A

Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`

Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.

If A = `[(2, 3),(1, 2)]`, B = `[(1, 0),(3, 1)]`, find AB and (AB)⁻¹ 

Select and write the correct alternative from the given option for the question

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in

Select and write the correct alternative from the given option for the question

The differential equation of y = Ae^5x + Be^–5x is

Select and write the correct alternative from the given option for the question 

Differential equation of the function c + 4yx = 0 is

Solve the differential equation sec²y tan x dy + sec²x tan y dx = 0

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`

Solve the differential equation xdx + 2ydy = 0

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Solve the following differential equation `("d"y)/("d"x)` = x²y + y

Solve: `("d"y)/("d"x) + 2/xy` = x² 

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Solve the following differential equation

`yx ("d"y)/("d"x)` = x² + 2y² 

Solve the following differential equation y log y = `(log  y - x) ("d"y)/("d"x)`

For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0

Solve the following differential equation y²dx + (xy + x²) dy = 0