Theorem:
The number of permutations of n dissimilar things taken r ..
The number of permutations of n dissimilar things taken r ..Arithmetic Geometric Series
A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..
A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..Suggested answer:
Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..
Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..To find the sum of n terms of a GP
Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..
Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..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..
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..Suggested answer:
Subtracting (ii) from (i), we get ..
Subtracting (ii) from (i), we get ..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..Harmonic Progression (H.P.)
Harmonic Progression (H.P.) - A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..
Harmonic Progression (H.P.) - A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..Question 3
Question: Answer: i) ii) iii) ..
Question: Answer: i) ii) iii) ..Question 2
Question: A sportsteam of 11 students is to be constituted choosing at least 5 from class XI and 5 at least from XII. If there are 20 students in each of these classes, in how many ways can the team be constituted? Answer: Number of students in each class is 20. Total number of selec..
Question: A sportsteam of 11 students is to be constituted choosing at least 5 from class XI and 5 at least from XII. If there are 20 students in each of these classes, in how many ways can the team be constituted? Answer: Number of students in each class is 20. Total number of selec..See what our Users say :
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