Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

`abs ((2"xy", "x"^2, "y"^2),("x"^2, "y"^2, 2"xy"),("y"^2, 2"xy", "x"^2)) =` ____________.

Find the angle between the lines whose direction cosines are given by the equations l + m + n = 0, l² + m² – n² = 0.

Show that the straight lines whose direction cosines are given by 2l + 2m – n = 0 and mn + nl + lm = 0 are at right angles.

If l₁, m₁, n₁; l₂, m₂, n₂; l₃, m₃, n₃ are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l₁ + l₂ + l₃, m₁ + m₂ + m₃, n₁ + n₂ + n₃ makes equal angles with them.

If the feasible region for a linear programming problem is bounded, then the objective function Z = ax + by has both a maximum and a minimum value on R.

The minimum value of the objective function Z = ax + by in a linear programming problem always occurs at only one corner point of the feasible region

Determine the maximum value of Z = 11x + 7y subject to the constraints : 2x + y ≤ 6, x ≤ 2, x ≥ 0, y ≥ 0.

Maximise Z = 3x + 4y, subject to the constraints: x + y ≤ 1, x ≥ 0, y ≥ 0

Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2, x ≥ 0, y ≥ 0.

Minimise Z = 13x – 15y subject to the constraints: x + y ≤ 7, 2x – 3y + 6 ≥ 0, x ≥ 0, y ≥ 0

Determine the maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure

Feasible region (shaded) for a LPP is shown in Figure. Maximise Z = 5x + 7y.

The feasible region for a LPP is shown in Figure. Find the minimum value of Z = 11x + 7y

Refer to Exercise 7 above. Find the maximum value of Z.

The feasible region for a LPP is shown in figure. Evaluate Z = 4x + y at each of the corner points of this region. Find the minimum value of Z, if it exists.

In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.

A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem

Refer to quastion 12. What will be the minimum cost?

Refer to question 13. Solve the linear programming problem and determine the maximum profit to the manufacturer

Refer to question 14. How many sweaters of each type should the company make in a day to get a maximum profit? What is the maximum profit.