HSC Commerce (Marathi Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the rate of change of demand (x) of a commodity with respect to its price (y) if 

y = `12 + 10x + 25x^2`

Evaluate the following.

`int "x"^3/sqrt(1 + "x"^4)` dx

Evaluate the following.

`int 1/ (x^2 + 4x - 5) dx`

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

If x + y = 3 show that the maximum value of x²y is 4.

Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx

An annuity immediate is to be paid for some years at 12% p.a. The present value of the annuity is ₹ 10,000 and the accumulated value is ₹ 20,000. Find the amount of each annuity payment

A person sets up a sinking fund in order to have ₹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given (1.025)²⁰ = 1.675]

Four new machines M₁, M₂, M₃ and M₄ are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M₂ cannot be placed at C and M₃ cannot be placed at A. The cost matrix is given below:

Find the optimal assignment schedule.

Solve the following problem :

Solve the following assignment problem to maximize sales:

Use quantifiers to convert the given open sentence defined on N into a true statement

n² ≥ 1

Use quantifiers to convert the given open sentence defined on N into a true statement.

3x – 4 < 9

Use quantifiers to convert the given open sentence defined on N into a true statement.

Y + 4 > 6

Choose the correct alternative:

If y = (x )^x + (10)^x, then `("d"y)/("d"x)` = ?

If x^y = 2^{x – y}, then `("d"y)/("d"x)` = ______

If y = `"a"^((1 + log"x"))`, then `("d"y)/("d"x)` is ______

If u = 5^x and v = log x, then `("du")/("dv")` is ______

If u = e^x and v = log_e x, then `("du")/("dv")` is ______

State whether the following statement is True or False:

If y = log(log x), then `("d"y)/("d"x)` = logx

State whether the following statement is True or False:

If y = 4^x, then `("d"y)/("d"x)` = 4^x