HSC Commerce (Marathi Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

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

Three cars were sold through an agent for ₹ 2,40,000, ₹ 2,22,000 and ₹ 2,25,000 respectively. The rates of commission were 17.5% on the first, 12.5% on the second. If the agent overall received 14% commission on the total sales, find the rate of commission paid on the third car.

Solution: Total selling Price of three cars = 2,40,000 + 2,22,000 + 2,25,000

= `square`

Commision on total sale = 14%

= `14/100 xx square`

Selling price of First car = ₹ 2,40,000

Rate of commission = 17.5% 

= `17.5/100 xx 2,40,000 = square`

∴ Commission on first car = ₹ `square`

Selling price of Second car = ₹ 2,22,000

Rate of commission = 12.5%

= `12.5/100 xx 2,22,000 = square`

∴ Commission on second car = ₹ `square`

Selling price of third car = ₹ 2,25,000

Let the rate of commission be x

Commission on third car = `x/100 xx 2,25,000`

∴ Commission on third car = Total commission − (commission on first car + commission on second car)

∴ `x/100 xx 2,25,000 = square - {square + square}`

∴ x = `square`

Multiple choice questions:

If for an immediate annuity r = 10% p.a., P = ₹ 12,679.46 and A = ₹ 18,564, then the amount of each annuity paid is ______

Multiple choice questions:

The present value of an immediate annuity of ₹ 10,000 paid each quarter for four quarters at 16% p.a. compounded quarterly is ______

A 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?

Find the amount of an ordinary annuity if a payment of ₹ 500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly. [Given (1.03)²⁰ = 1.8061]