Combinations problems and word problems
Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..
Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..Types of Matrices
Row Matrix - A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..
Example:
(i) Note that the entries in a given matrix need not be distinct. (ii) The entries in this matrix are function of x. A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements. In general, an mxn matrix is in the form Where a i j represen..
(i) Note that the entries in a given matrix need not be distinct. (ii) The entries in this matrix are function of x. A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements. In general, an mxn matrix is in the form Where a i j represen..Proof:
The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one of the n ..
The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one of the n ..Skew-Symmetric Matrix:
A square matrix A = [a i j ] is said to be skew-symmetric if the (i,j) t h element of A is the negative of the (j,i) t h element of A i.e., if a i j = -a j i for all i, j. In particular, for i = j, we have Thus the diagonal elements of a skew symmetric matrix are all zero. ..
A square matrix A = [a i j ] is said to be skew-symmetric if the (i,j) t h element of A is the negative of the (j,i) t h element of A i.e., if a i j = -a j i for all i, j. In particular, for i = j, we have Thus the diagonal elements of a skew symmetric matrix are all zero. ..Question 1 Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we get ..
Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we get ..Suggested answer:
i) 1.2 + 2.4 + 3.8 +.... to n terms The n t h term of (1,2,3,....n) is n. The n t h term of (2,4,8,...) is The n t h term of the given series is n2 n Subtracting (ii) from (i), we have ..
i) 1.2 + 2.4 + 3.8 +.... to n terms The n t h term of (1,2,3,....n) is n. The n t h term of (2,4,8,...) is The n t h term of the given series is n2 n Subtracting (ii) from (i), we have ..Summary
(iii) If 'a' and 'd' be the first term and common difference of the A.P. {T n }, then the sum of first n terms, S n is given by The form (a) is used when common difference 'd' is known and the form (b) is used when the last term 'l' is known. (iv) T 1 = S 1 and for n > 1, we have T n = S n - S n..
(iii) If 'a' and 'd' be the first term and common difference of the A.P. {T n }, then the sum of first n terms, S n is given by The form (a) is used when common difference 'd' is known and the form (b) is used when the last term 'l' is known. (iv) T 1 = S 1 and for n > 1, we have T n = S n - S n..Discrete Mathematics - Test Questions I
Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..
Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..Verification by numerical problems
then show that (A+B)+C = A+(B..
then show that (A+B)+C = A+(B..See what our Users say :
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