HSC Science (Electronics) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Solve the following equation by the method of inversion:

5x − y + 4z = 5, 2x + 3y + 5z = 2 and 5x − 2y + 6z = −1

Solve the following equations by the method of inversion:

x + y + z = - 1, y + z = 2, x + y - z = 3

Express the following equations in matrix form and solve them by the method of reduction:

x − y + z = 1, 2x − y = 1, 3x + 3y − 4z = 2

Express the following equations in matrix form and solve them by the method of reduction:

`x + y = 1, y + z = 5/3, z + x 4/33`.

Express the following equations in matrix form and solve them by the method of reduction:

2x - y + z = 1, x + 2y + 3z = 8, 3x + y - 4z = 1.

Express the following equations in matrix form and solve them by the method of reduction:

x + 2y + z = 8, 2x + 3y – z = 11, 3x – y – 2z = 5.

The cost of 4 pencils, 3 pens, and 2 books is ₹ 150. The cost of 1 pencil, 2 pens, and 3 books is ₹ 125. The cost of 6 pencils, 2 pens, and 3 books is ₹ 175. Find the cost of each item by using matrices.

The sum of three numbers is 6. Thrice the third number when added to the first number, gives 7. On adding three times the first number to the sum of second and third numbers, we get 12. Find the three number by using matrices.

An amount of ₹ 5000 is invested in three types of investments, at interest rates 6%, 7%, 8% per annum respectively. The total annual income from these investments is ₹ 350. If the total annual income from the first two investments is ₹ 70 more than the income from the third, find the amount of each investment using matrix method.

Solve the following equations by the method of inversion:

2x + 3y = - 5, 3x + y = 3

Express the following equations in matrix form and solve them by the method of reduction:

x + 3y + 2z = 6,

3x − 2y + 5z = 5,

2x − 3y + 6z = 7

Find the feasible solution of the following inequation:

3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Find the feasible solution of the following inequation:

2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0

Find the feasible solution of the following inequation:

3x + 4y ≥ 12, 4x + 7y ≤ 28, y ≥ 1, x ≥ 0.

Find the feasible solution of the following inequation:

x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9,  x ≥ 0, y ≥ 0.

Find the feasible solution of the following inequations:

x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0

A company produces two types of articles A and B which requires silver and gold. Each unit of A requires 3 gm of silver and 1 gm of gold, while each unit of B requires 2 gm of silver and 2 gm of gold. The company has 6 gm of silver and 4 gm of gold. Construct the inequations and find feasible solution graphically.

A furniture dealer deals in tables and chairs. He has ₹ 1,50,000 to invest and a space to store at most 60 pieces. A table costs him ₹ 1500 and a chair ₹ 750. Construct the inequations and find the feasible solution.

A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to the machine shop for finishing. The number of man-hours of labour required in each shop for production of A and B per unit and the number of man-hours available for the firm is as follows:

Profit on the sale of A is ₹ 30 and B is ₹ 20 per units. Formulate the L.P.P. to have maximum profit.

In a cattle breading firm, it is prescribed that the food ration for one animal must contain 14. 22 and 1 units of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit of these two contains the following amounts of these three nutrients: 

The cost of fodder 1 is ₹ 3 per unit and that of fodder 2 ₹ 2. Formulate the LPP to minimize the cost.