Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

A feasible region of a system of linear inequalities is said to be ______ if it can be enclosed within a circle.

A corner point of a feasible region is a point in the region which is the ______ of two boundary lines.

The feasible region for an LPP is always a ______ polygon.

If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.

Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.

In a LPP, the minimum value of the objective function Z = ax + by is always 0 if the origin is one of the corner point of the feasible region.

In a LPP, the maximum value of the objective function Z = ax + by is always finite.

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals ______.

Two cards are drawn from a well-shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is ______.

A relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?

Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:

Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?

In the given graph, the feasible region for an LPP is shaded. The objective function Z = 2x – 3y will be minimum at:

The point(s), at which the function f given by f(x) = `{("x"/|"x"|","  "x" < 0),(-1","  "x" ≥ 0):}` is continuous, is/are:

A linear programming problem is as follows:

Minimize Z = 30x + 50y

Subject to the constraints: 3x + 5y ≥ 15, 2x + 3y ≤ 18, x ≥ 0, y ≥ 0

In the feasible region, the minimum value of Z occurs at:

For an objective function Z = ax + by, where a, b > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:

In a linear programming problem, the constraints on the decision variables x and y are x − 3y ≥ 0, y ≥ 0, 0 ≤ x ≤ 3. The feasible region:

Objective function of a linear programming problem is ____________.

The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x - 2y ≥ 0, x ≥ 0, y ≥ 0 is ____________.

Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at ____________.