general Maths Puzzle

The four digit number 2652 is such that any two consecutive digits from it make a multiple of 13. Another number N has this same property, is 100 digits long, and begins with 9. What is the last digit of N?

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general Other Question

In how many different ways can the letters of the word 'DETAIL' be arranged
in such a way that the vowels occupy only the odd positions ?

(a)32
(b)48
(c)36
(d)60
(e)120



When 1+3x+5x^2+7x^3+
+ ยทยทยท +99x^49 is divided by (x-1) the remainder is
(a) 2000 (b) 2500 (c) 3000 (d) 3500