HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.

Given P₀₁(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320, Find P₀₁(L)

Find the missing wage if the Cost of Living Index for the following data is 150.

The Cost of Living Index Numbers for years 2003 and 2008 are 150 and 200 respectively. A person earned ₹ 18,000 per month in year 2003. What should be his earning per month in year 2008, so as to maintain same standard of living as 2003?

State whether the following statement is true or false:

Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.

If P₀₁ (L) = 121, P₀₁ (P) = 100, then P₀₁ (F) = ______.

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

`sqrt((sump_1q_0)/(sump_0q_0)) xx sqrt((sump_1q_1)/(sump_0q_1)) xx 100`

Laspeyre’s Price Index Number uses current year’s quantities as weights.

Calculate Marshall – Edgeworth’s price index number for the following data:

The cost of living index number using Weighted Relative Method is given by ______.

The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs ₹ 20 per kg and sand costs of ₹ 6 per kg. Strength consideration dictates that a concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand. Form the L.P.P. for the cost to be minimum.

Feasible region is the set of points which satisfy ______.

A firm manufactures two products A and B on which profit earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M₁ and M₂. The product A requires one minute of processing time on M₁ and two minutes of processing time on M₂, B requires one minute of processing time on M₁ and one minute of processing time on M₂. Machine M₁ is available for use for 450 minutes while M₂ is available for 600 minutes during any working day. Find the number of units of products A and B to be manufactured to get the maximum profit.

Solve the following L.P.P. by graphical method:

Maximize: Z = 10x + 25y
subject to 0 ≤ x ≤ 3,
0 ≤ y ≤ 3,
x + y ≤ 5.
Also find the maximum value of z.

Solve the following L.P.P. by graphical method:

Minimize: Z = 6x + 2y subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0.

Objective function of LPP is ______.

The optimal value of the objective function is attained at the ______ points of the feasible region.

A train carries at least twice as many first class passengers (y) as second class passengers (x). The constraint is given by ______.

Graphical solution set of x ≤ 0, y ≥ 0 in xy system lies in second quadrant.