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

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.

Maximize Z = 60x + 50y Subject to x + 2y ≤ 40, 3x + 2y ≤ 60, x ≥ 0, y ≥ 0

Choose the correct alternative:

The feasible region is

Choose the correct alternative:

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

Choose the correct alternative:

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

State whether the following statement is True or False:

If the corner points of the feasible region are `(0, 7/3)`, (2, 1), (3, 0) and (0, 0), then the maximum value of Z = 4x + 5y is 12

A doctor prescribed 2 types of vitamin tablets, T₁ and T₂ for Mr. Dhawan. The tablet T₁ contains 400 units of vitamin and T₂ contains 250 units of vitamin. If his requirement of vitamin is at least 4000 units, then the inequation for his requirement will be ______

Heramb requires at most 400 calories from his breakfast. Every morning he likes to take oats and milk. If each bowl of oats and a glass of milk provides him 80 calories and 50 calories respectively, then as a constraint this information can be expressed as ______

Smita is a diet conscious house wife, wishes to ensure certain minimum intake of vitamins A, B and C for the family. The minimum daily needs of vitamins A, B, and C for the family are 30, 20, and 16 units respectively. For the supply of the minimum vitamin requirements Smita relies on 2 types of foods F₁ and F₂. F₁ provides 7, 5 and 2 units of A, B, C vitamins per 10 grams and F₂ provides 2, 4 and 8 units of A, B and C vitamins per 10 grams. F₁ costs ₹ 3 and F₂ costs ₹ 2 per 10 grams. How many grams of each F₁ and F₂ should buy every day to keep her food bill minimum