multiple choice questions for discrete structure

The same principle can be generalized to three or more events occurring in succession as follows: If n operations can be performed in m 1 ,m 2 ,m 3 ,...m n ways respectively, then all n operations in succession can be performed exactly in m 1 ,m 2 ,m 3 ,...m n ways. The above principle is called..

Matrix multiplication is not commutative in general. Matrix multiplication is associative i.e., (AB)C = A(BC), whenever both sides are defined. Matrix multiplication is distributive over matrix addition i.e., (i) A(B + C) = AB + BC (ii) (A + B)C = AB + AC wh..

Question: A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, and he is not permitted to attempt more than 4 from each group. In how many ways can he make his choice? Answer: ..

Equality of Matrices, Addition of Matrices, Matrix Addition is commutative, Matrix addition is associative, Subtraction of Matrices, Multiplication of a matrix by a scalar, Multiplication of Matrices, Properties of Matrix Multiplication, Transpose of a Matrix, Pr..

Question: A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? Answer: Let the two ladies who refuse to work on the same comm..

Elementary transformations are of the following three types: Interchange of any two rows (or columns) The multiplication of the elements of a row (or column) by a non-zero number. The addition to the elements of any row (or column) the corresponding elements of any other row (or ..

If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..

Summary - A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be comparable..

Summary - The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. ..

Which of the choices represents the associative property of multiplication? => p × ( q × r ) = ( p × q ) × r or p × ( q + r ) = p q + p r or p × q × 1 = p × q or p × q × r × 0 = 0..