1. The average of the two digit numbers, which remain the same when the digits interchange their positions is :
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By: anil on 05 May 2019 01.41 am
Two digit numbers which remain same after interchanging the digits = 11,22,33,....,99 The above expression is an A.P with first term, $$a = 11$$ and common difference, $$d = 11$$ Number of terms = 9 Sum of A.P. = $$frac{n}{2} (a + a_n)$$ = $$frac{9}{2} (11 + 99) = frac{9}{2} imes 110$$ = $$9 imes 55$$ $$ herefore$$ Required average = $$frac{9 imes 55}{9} = 55$$
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