341Hint: x1 can at most be 4.
Casework should finish it off
number of positive integral solutions of x1x2x3x4x5=1050
give method tooo
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14 Answers
11sir im not able to proceed can you provide another hint ?
and isnt 1050x1x1x1x1
also a solution so how x1 cant be greater than 4
11just an extension to
http://targetiit.com/iit_jee_forum/posts/iit_2009_level_question_4250.html post #8
11050 = 2x3x52x7
no. of ways 2 gets distributed in 5 places = 1+5-1C5-1
no. of ways 3 gets distributed in 5 places = 1+5-1C5-1
no. of ways 5 gets distributed in 5 places = 2+5-1C5-1
no. of ways 7 gets distributed in 5 places = 1+5-1C5-1
hence total no. of +ve integral solutions = 5x5x5x15 = 1875.
correct me if i am wrong !
21Race : http://targetiit.com/iit_jee_forum/posts/iit_2009_level_question_4250.html post #8
11just for information this is part of a match type question
and answer given is 1875
1i've a doubt.
why should we consider 1 seperately? in the cases that i considered in my solution (#7), 1050x1x1x1 is also included. it's obvious that when no digit is allotted to any of the five places, it's given the value of 1. why should we consider it seperately then?
11When 1 is considered separately, we have to make sure that every place is filled.
Otherwise,as u said
" it's obvious that when no digit is allotted to any of the five places, it's given the value of 1 "
pls someone tell me if i'm wrong.
1@rkrish.
if that is the case, then what should be the power of 1 while writing 1050 = 1nx2x3x52x7 ?
it can any natural no. 1 → ∞.!
u must consider seperate cases for each now, when n=1, when n=2 and so on !!!
isn't that a cumbersome process ?
and btw, if u find any mistake in my solution, please point it out !
21AN EXTRACT FROM TMH
HOPE IT HELPS..............
@subhash : Use the abov techniQ u'll get Ans as 1875 [1]
1i'm sorry, i forgot including 7 in my solution. (edited it now)
even my method is correct. :)
Thanx evry1, specially rkrish atleast he responded to me !!! :)