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

Find the assignments of salesman to various district which will yield maximum profit

For the following assignment problem minimize total man hours:

Subtract the `square` element of each `square` from every element of that `square`

Subtract the smallest element in each column from `square` of that column.

The lines covering all zeros is `square` to the order of matrix `square`

The assignment is made as follows:

Optimum solution is shown as follows:

A → `square, square` → III, C → `square, square` → IV

Minimum hours required is `square` hours

`int 1/sqrt(x^2 - 9) dx` = ______.

The slope of a tangent to the curve y = 3x² – x + 1 at (1, 3) is ______.

The area of the region bounded by the curve y = x², x = 0, x = 3, and the X-axis is ______.

State whether the following statement is true or false.

If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2e^x – 5| + c, where c is the constant of integration, then A = 5.

`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`

Find the area between the two curves (parabolas)

y² = 7x and x² = 7y.

Divide 20 into two ports, so that their product is maximum.

State whether the following statement is true or false:

To convert a maximization-type assignment problem into a minimization problem, the smallest element in the matrix is deducted from all elements of the matrix.

Calculate the cost of living index number for the following data by aggregative expenditure method:

Solve the following

`int_0^1 e^(x^2) x^3 dx`

Three new machines M1, M2, M3 are to be installed in a machine shop. There are four vacant places A, B, C, D. Due to limited space, machine M2 can not be placed at B. The cost matrix (in hundred rupees) is as follows:

Determine the optimum assignment schedule and find the minimum cost.

Determine the minimum value of the function.

f(x) = 2x³ – 21x² + 36x – 20

Evaluate the following:

`intx^3e^(x^2)dx` 

Evaluate the following.

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

Evaluate the following.

`intx^3 e^(x^2) dx`

Evaluate the following.

`intx^3/sqrt(1+x^4)  dx`

Evaluate the following.

`intx^3e^(x^2) dx`

Evaluate `int (1 + x + x^2/(2!))dx`