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

Choose the correct alternative:

Z = 9x + 13y subjected to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, 0 ≤ x, y was found to be maximum at the point

State whether the following statement is True or False:

Objective function of LPP is a relation between the decision variables

State whether the following statement is True or False:

LPP is related to efficient use of limited resources

The variables involved in LPP are called ______

Constraints are always in the form of ______ or ______.

The constraint that in a particular XII class, number of boys (y) are less than number of girls (x) is given by ______

Choose the correct alternative:

The assignment problem is solved by ______

The Hungarian method is an ______ algorithm that solves an assignment problem

State whether the following statement 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 statement is True or False: 

The Hungarian method is used to assign n jobs on 2 machines to get the optimal sequence

The order and degree of the differential equation `[1 + ((dy)/(dx))^3]^(2/3) = 8((d^3y)/(dx^3))` are respectively ______.

State whether the following statement is true or false.

If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).

y² = (x + c)³ is the general solution of the differential equation ______.

Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."

Solve the following LP.P.

Maximize z = 13x + 9y,

Subject to 3x + 2y ≤ 12,

x + y ≥ 4,

x ≥ 0,

y ≥ 0.

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

Evaluated the following

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

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

Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`

if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`