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

Z = 20x₁ + 20x₂, subject to x₁ ≥ 0, x₂ ≥ 0, x₁ + 2x₂ ≥ 8, 3x₁ + 2x₂ ≥ 15, 5x₁ + 2x₂ ≥ 20. The minimum value of Z occurs at ____________.

In linear programming feasible region (or solution region) for the problem is ____________.

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,

Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then ____________.

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

In Corner point method for solving a linear programming problem the first step is to ____________.

In the Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is ____________.

A feasible solution to a linear programming problem

The corner points of the bounded feasible region of a LPP are A(0,50), B(20, 40), C(50, 100) and D(0, 200) and the objective function is Z = x + 2y. Then the maximum value is ____________.

The feasible region (shaded) for a L.P.P is shown in the figure. The maximum Z = 5x + 7y is ____________.

The maximum value of Z = 3x + 4y subjected to contraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is ____________.

If A is a square matrix such that A² = A, then (I + A)² - 3A is ____________.

If a matrix A is both symmetric and skew symmetric then matrix A is ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.).

Based on the information given above, answer the following questions:

• The equations in terms x and y are ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.).

Based on the information given above, answer the following questions:

• Which of the following matrix equations represent the information given above?

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

Based on the information given above, answer the following questions:

• The number of children who were given some money by Seema, is ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

Based on the information given above, answer the following questions:

• How much amount is given to each child by Seema?

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

Based on the information given above, answer the following questions:

• How much amount Seema spends in distributing the money to all the students of the Orphanage?

If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.

A function is said to be continuous for x ∈ R, if ____________.