Question

Match List - I with List - II.

List - I	List -II
(A) Null Matrix	(I)\(P(A)+P(B)\)
(B) Scaler Matrix	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) Skew-symmetric matrix	(III)\(P(B)-P(A\cap B)\)
(D)Symmetric Matrix	(IV)\(P(B)-P(A\cap B)\)

Choose the correct answer from the options given below:

• A. (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
• B. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
• C. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
• D. (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

Answer 1

The Correct Option is A

Solution: To correctly match the terms from List-I with List-II, we need to understand each definition or property of the matrices described in List-I and associate it with the corresponding characteristic or formula from List-II. Let's analyze each one:

(A) Null Matrix: A null matrix is a matrix in which all the elements are zero. It generally represents the absence of any data or interaction, thus relating to the result where any operation returns zero. The correct match from List-II is (IV) \(P(B)-P(A\cap B)\), representing no additional intersecting components connected to it.

(B) Scaler Matrix: A scalar matrix is a \((n \times n)\) matrix where all off-diagonal elements are zero and all diagonal elements are equal. It essentially acts like constant multiplication. The matching operation in probability that behaves similarly (not adding complexity, just scaling) is (I) \(P(A)+P(B)\).

(C) Skew-symmetric Matrix: This type of matrix has the property that its transpose is also its negative (i.e., \(-A = A^T\)). Such matrices usually model oppositional properties. Thus, the match with probability involves subtracting overlaps multiple times: (II) \(P(A)+P(B)-2P(A\cap B)\).

(D) Symmetric Matrix: A symmetric matrix is equal to its transpose (i.e., \(A = A^T\)), implying a balance or equivalence characteristic. The correct match in the context of probability is (III) \(P(B)-P(A\cap B)\), indicating a balance by removing overlap once.

Final Matching: Thus, the correct matching of List-I with List-II according to the problem are: (A)-(IV), (B)-(I), (C)-(II), (D)-(III).

Correct Option: (A)-(IV), (B)-(I), (C)-(II), (D)-(III).