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

Choose the correct alternative:

An overall upward or downward pattern in an annual time series would be contained in which component of the times series?

______ components of time series is indicated by a smooth line

______ component of time series is indicated by periodic variation year after year.

State whether the following statement is True or False: 

Seasonal variation can be observed over several years

Cyclical variation can occur several times in a year.

Choose the correct alternative: 

The Cost of Living Index Number by Aggregate Expenditure Method is same as

The Cost of Living Index Number by Aggregate Expenditure Method is given by ______

Calculate the Cost of Living Index Number for the following data.

Given the following table, find the Cost of living Index Number using Aggregate Expenditure Method by completing the activity.

Therefore, Cost of Living Index using Aggregate Expenditure method is

CLI = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx square`

= `square/square xx 100`

= `square`

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If LPP has optimal solution at two point, then

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The maximum value of Z = 3x + 5y subjected to the constraints x + y ≤ 2, 4x + 3y ≤ 12, x ≥ 0, y ≥ 0 is

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The minimum value of Z = 4x + 5y subjected to the constraints x + y ≥ 6, 5x + y ≥ 10, x, y ≥ 0 is

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The point at which the minimum value of Z = 8x + 12y subject to the constraints 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0 is obtained at the point

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The point at which the maximum value of Z = 4x + 6y subject to the constraints 3x + 2y ≤ 12, x + y ≥ 4, x ≥ 0, y ≥ 0 is obtained at the point

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The corner points of feasible region for the inequations, x + y ≤ 5, x + 2y ≤ 6, x ≥ 0, y ≥ 0 are

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The corner points of the feasible region are (0, 3), (3, 0), (8, 0), `(12/5, 38/5)` and (0, 10), then the point of maximum Z = 6x + 4y = 48 is at

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The corner points of the feasible region are (4, 2), (5, 0), (4, 1) and (6, 0), then the point of minimum Z = 3.5x + 2y = 16 is at

State whether the following statement is True or False:

The maximum value of Z = 5x + 3y subjected to constraints 3x + y ≤ 12, 2x + 3y ≤ 18, 0 ≤ x, y is 20

State whether the following statement is True or False:

If LPP has two optimal solutions, then the LPP has infinitely many solutions

State whether the following statement is True or False:

A convex set includes the points but not the segment joining the points