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

Fill in the blank :

In Hungarian Method, only _______ task can be assigned to each facility.

State whether the following is True or False :

The Hungarian method operates on the principle of matrix reduction, whereby the cost table is reduced to a set of opportunity costs.

State whether the following is True or False :

Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a zero.

State whether the following is True or False :

Using the Hungarian method, the optimal solution to an assignment problem is found when the minimum number of lines required to cover the zero cells in the reduced matrix equals the no of persons.

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements

State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p

Negation of “Some men are animal” is ______.

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra

Choose the correct alternative:

The function f(x) = x³ – 3x² + 3x – 100, x ∈ R is

The price P for the demand D is given as P = 183 + 120D − 3D², then the value of D for which price is increasing, is ______.

The slope of tangent at any point (a, b) is also called as ______.

If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______

The total cost function for production of articles is given as C = 100 + 600x – 3x², then the values of x for which the total cost is decreasing is  ______

State whether the following statement is True or False: 

The function f(x) = `3/x` + 10, x ≠ 0 is decreasing

The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing

State whether the following statement is True or False: 

If the function f(x) = x² + 2x – 5 is an increasing function, then x < – 1

Find the values of x such that f(x) = 2x³ – 15x² + 36x + 1 is increasing function

Find the values of x such that f(x) = 2x³ – 15x² – 144x – 7 is decreasing function