HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Important Questions for Mathematics and Statistics

Find the area between the two curves (parabolas)

y² = 7x and x² = 7y.

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

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:

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 ______.

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

State whether the following statement is True or False:

Order and degree of differential equation `x ("d"^3y)/("d"x^3) + 6(("d"^2y)/("d"x^2))^2 + y` = 0 is (2, 2)

Find the differential equation by eliminating arbitrary constants from the relation y = (c₁ + c₂x)e^x 

The order and degree of the differential equation `[1 + ((dy)/(dx))^3]^(2/3) = 8((d^3y)/(dx^3))` are respectively ______.

y² = (x + c)³ is the general solution of the differential equation ______.

A retailer sold a suit for ₹ 8,832 after allowing 8% discount on marked price and further 4% cash discount. If he made 38% profit, find the cost price and the marked price of the suit.

Choose the correct alternative:

The present worth of ₹ 11,660 due 9 months hence is ₹ 11,000. The True discount is ______

State whether the following statement is True or False:

The trade discount is first calculated on the catalogue (list) price

State whether the following statement is True or False: 

A factor is an agent who is given the possession of goods and enters a contract for sale in his/her own name