Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals ______.

Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

If A and B are independent events, then A′ and B′ are also independent

If A and B are mutually exclusive events, then they will be independent also.

Two independent events are always mutually exclusive.

If A and B are two independent events then P(A and B) = P(A).P(B).

If A and B′ are independent events, then P(A' ∪ B) = 1 – P (A) P(B')

If A and B are independent, then P(exactly one of A, B occurs) = P(A)P(B') + P(B)P(A') 

If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then P(B|A) ≥ `1 - ("P"("B'"))/("P"("A"))`

If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P(At least two of A, B, C occur) = 3p² – 2p³ 

If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.

Let A and B be two events. If P(A | B) = P(A), then A is ______ of B.

The maximum value of `["x"("x" − 1) + 1]^(1/3)`, 0 ≤ x ≤ 1 is:

A feasible region in the set of points which satisfy ____________.

Of all the points of the feasible region for maximum or minimum of objective function the points.

A set of values of decision variables which satisfies the linear constraints and nn-negativity conditions of an L.P.P. is called its ____________.

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 ____________.