HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Important Questions for Mathematics and Statistics

If a body cools from 80°C to 50°C at room temperature of 25°C in 30 minutes, find the temperature of the body after 1 hour.

Find the differential equation whose general solution is

x³ + y³ = 35ax.

Solve the following differential equation.

`dy/dx + y` = 3

The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.

The solution of `dy/ dx` = 1 is ______

The integrating factor of `(dy)/(dx) + y` = e^–x is ______.

A solution of a differential equation which can be obtained from the general solution by giving particular values to the arbitrary constants is called ___________ solution.

The rate of growth of population is proportional to the number present. If the population doubled in the last 25 years and the present population is 1 lac, when will the city have population 4,00,000?

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

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

Solve: `("d"y)/("d"x) + 2/xy` = x² 

Choose the correct alternative:

The integrating factor of `("d"^2y)/("d"x^2) - y` = e^x, is e^–x, then its solution is

Choose the correct alternative:

General solution of `y - x ("d"y)/("d"x)` = 0 is

The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.

Choose the correct alternative:

The solution of `dy/dx` = 1 is ______.

A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution

The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation

Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______

State whether the following statement is True or False: 

The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any

State whether the following statement is True or False:  

The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined