Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Solve the system of linear equations using the matrix method.

5x + 2y = 4

7x + 3y = 5

Solve the system of linear equations using the matrix method.

2x – y = –2

3x + 4y = 3

Solve the system of linear equations using the matrix method.

4x – 3y = 3

3x – 5y = 7

Solve the system of linear equations using the matrix method.

5x + 2y = 3

3x + 2y = 5

Solve the system of linear equations using the matrix method.

2x + y + z = 1

x – 2y – z = `3/2`

3y – 5z = 9

Solve the system of linear equations using the matrix method.

x − y + z = 4

2x + y − 3z = 0

x + y + z = 2

Solve the system of linear equations using the matrix method.

2x + 3y + 3z = 5

x − 2y + z = −4

3x − y − 2z = 3

Solve the system of linear equations using the matrix method.

x − y + 2z = 7

3x + 4y − 5z = −5

2x − y + 3z = 12

If A = `[(2,-3,5),(3,2,-4),(1,1,-2)]` find A⁻¹. Using A⁻¹ solve the system of equations:

2x – 3y + 5z = 11

3x + 2y – 4z = –5

x + y – 2z = –3

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs. 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs. 70. Find the cost of each item per kg by matrix method.

Solve the system of the following equations:

`2/x+3/y+10/z = 4`

`4/x-6/y + 5/z = 1`

`6/x + 9/y - 20/x = 2`

Solve the following Linear Programming Problems graphically:

Maximise Z = 3x + 4y

subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.

Solve the following Linear Programming Problems graphically:

Minimise Z = – 3x + 4 y

subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

Solve the following Linear Programming Problems graphically:

Maximise Z = 5x + 3y

subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0

Solve the following Linear Programming Problems graphically:

Minimise Z = 3x + 5y

such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.

Solve the following Linear Programming Problems graphically:

Maximise Z = 3x + 2y

subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

Solve the following Linear Programming Problems graphically:

Minimise Z = x + 2y

subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.

Show that the minimum of Z occurs at more than two points.

Minimise and Maximise Z = 5x + 10 y

subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.

Show that the minimum of Z occurs at more than two points.

Minimise and Maximise Z = x + 2y 

subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.

Show that the minimum of Z occurs at more than two points.

Maximise Z = – x + 2y, Subject to the constraints:

x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.