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Find the L.C.M. of 4!, 5! and 6!....

Find the L.C.M. of 4!, 5! and 6!.

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Find the L.C.M. of the following numbers in which one number is always a multiple of 3: 6 and 5. Observe a common property in the obtained L.C.M.s. Is L.C.M. the product of two numbers in each case ?Is L.C.M. always a multiple of 3 ?

Find the L.C.M. of the following numbers in which one number is always a multiple of 3: 12 and 5. Observe a common property in the obtained L.C.M.s. Is L.C.M. the product of two numbers in each case ?Is L.C.M. always a multiple of 3 ?

Find the L.C.M. of the following numbers in which one number is always a multiple of 3: 9 and 4. Observe a common property in the obtained L.C.M.s. Is L.C.M. the product of two numbers in each case ?Is L.C.M. always a multiple of 3 ?

Find the L.C.M. of the following numbers in which one number is always a multiple of 3: 15 and 4. Observe a common property in the obtained L.C.M.s. Is L.C.M. the product of two numbers in each case ?Is L.C.M. always a multiple of 3 ?

Find the L.C.M. of the following numbers in which one number is the factor of the other : 6,18 What do you observe in the results obtained.

Find the L.C.M. of the following numbers in which one number is the factor of the other : 5,20 What do you observe in the results obtained.

Find the L.C.M. of the following numbers in which one number is the factor of the other : 9,45. What do you observe in the results obtained.

Find the L.C.M. of the following numbers in which one number is the factor of the other : 12,48 What do you observe in the results obtained.

MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. Evaluate (n!)/(r!(n-r)!) when : n=7,r= 4.

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  2. Evaluate (n!)/(r!(n-r)!) when : n= 15,r= 12.

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  3. Find the L.C.M. of 4!, 5! and 6!.

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  4. If 1/(9!)+1/(10!) =n/(11!), find n.

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  5. If 1/(8!)+1/(9!) =x/(10!), find x.

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  6. Prove that n! (n+2)=n!+(n+1)! .

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  7. If (n+1)! = 12 [(n-1)!], find n.

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  8. If (n+2)! = 60 [(n-1)!], find n.

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  9. If (n+2)! =(2550)(n!), find n.

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  10. If (n!)/(2!(n-2)!):(n!)/(4!(n-4)!) =2:1. Find the value of n.

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  11. Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!)= ((n+1)!)/ (r!(n-r+1)...

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  12. Prove that there are exactly 4! numbers between 1000 and 10000 that co...

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  13. show that 2^16 divides 32!. also, find the largest value of n for whic...

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  14. There are five colleges in a city. In how many ways can a man send 3 o...

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  15. John wants to go abroad by ship and return by air. He has a choice of ...

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  16. There are 5 routes from place A to place B and 3 routes from place B t...

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  17. If there are 20 steamers plying between places A and B, in how many wa...

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  18. If there are 20 steamers plying between places A and B, in how many wa...

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  19. In how many ways can 5 persons draw water from 5 taps, assuming no tap...

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  20. In how many ways can 3 people be seated in a row containing 7 seats ?

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