HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

In the modification of a plant layout of a factory 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 of locating a machine at a place (in hundred rupees) is as follows.

Find the optimal assignment schedule.

Fill in the blank :

An assignment problem is said to be unbalanced when _______.

Fill in the blank :

When the number of rows is equal to the number of columns then the problem is said to be _______ assignment problem.

Fill in the blank :

If the given matrix is not a _______ matrix, the assignment problem is called an unbalanced problem.

Fill in the blank :

A dummy row(s) or column(s) with the cost elements as _______ is added to the matrix of an unbalanced assignment problem to convert into a square matrix.

Maximization assignment problem is transformed to minimization problem by subtracting each entry in the table from the _______ value in the table.

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In an assignment problem, a solution having _______ total cost is an optimum solution.

Fill in the blank :

In maximization type, all the elements in the matrix are subtracted from the _______ element in the matrix.

To convert the assignment problem into a maximization problem, the smallest element in the matrix is deducted from all other elements.

State whether the following is True or False :

The purpose of dummy row or column in an assignment problem is to obtain balance between total number of activities and total number of resources.

State whether the following is True or False

In number of lines (horizontal on vertical) > order of matrix then we get optimal solution.

Solve the following problem :

Solve the following assignment problem to maximize sales:

Solve the following problem :

The estimated sales (tons) per month in four different cities by five different managers are given below:

Find out the assignment of managers to cities in order 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 ______