11) 2 pages were torn
although m not the right person to give problem for practice but still m posting some ques for practice.....i jus started this cozz i thinkj the threads r still in the joy nd shock of jee results:P:D..
1)In a book with page numbers from 1 to 100 some pages are torn off. The sum of the numbers on the remaining pages is 4949. How many pages are torn off????
2)Find the sum of all 3-digit natural numbers which contain at least one odd digit and at least one even digit.
3)Find all pairs (a,b) of real numbers such that whenever \alpha is a root of x^2+ax+b=0,\alpha ^2-2is also a root of the equation.????
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8 Answers
1sum of first hundred pages=n(n+1)/2=100*101/2=5050
sum given in the problem after torn=4949
difference=101=50+51
so the 50 and 51 pages are torn...so i guessed 2 pages are torn
1061) sum of all pages (untorn book) = 5050
sum of torn pages = 5050 - 4949 = 101
This can lead to different answers unless we know how the pages are numbered. (eg. only one side numbered/ two sides numbered and numbering starts from the right side of an open book/two sides numbered and numbering starts from the left side of an open book)
1so bhaiiya u mean to say it can not have particular answer until we ve the order of numberin na......hmmm............kkk soo neone for other quess.
62To add to what asish has said, Most of these questions do assume that the pges are numbered consecutively...
So if there were more pages torn and not in a consecutive way, the pages could have been say
1,2, 3, 4, 45,46
This could be one option.
1look given whenever ∂2 is a root ∂2-2 is also a root
one possibility is these 2 r equal
then 2∂=a and ∂2=b and ∂2-2=∂
if u solve the equations u will get 2 pairs of a,b.
now comes the most important part
if ∂2≠∂
then observe as ∂2-2 is a root ,(∂2-2)2-2 is also a root
but a quadratic can not have 3 distinct roots
so (∂2-2)2-2 is either ∂ or (∂2-2)
from these u will get other 2 solutions.