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Inserting n Harmonic Means between two quantities
To insert n Harmonic Means between two given quantities - Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h 2..
To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and ..
Question 2
Question: A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees? Answer: Here, there are two events E 1 and E 2 . E 1 = Selection of ..
Question 2
Question: vi) (n! + 1) is not divisible by any natural number between 2 and n. vii) Simplify Answer: ..
Example 2:
How many numbers are there between 100 and 1000 such that every digit is either 2 or ..
Question 2
Question: Answer: i. The value of C(n, 25) = C(25, 25) = 1 ii..
Note 2:
From the definition, it is clear that if B is the inverse of A, then A is the inverse of ..
Combinations problems and word problems
or n < 2n Multiplying the above terms of both sides respectively, we get Multiplying both sides by n!, we get From (1) and (2), we g..
Cramer's rule for the solution of a system of equations in 2 variables
We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..
Examples:
1. 2 and 3 are two digits and with these digits, the numbers 32 and 23 are formed. Although both numbers viz., 32 and 23 consist of the digits 2 and 3, the order of digits is different. Each of the above arrangements is called a 'permutation'. Thus, the number of arra..
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