Number System MCQs

How many pairs of natural numbers is there the difference of whose squares are 45.

The remainder when 1010 + 10100 + 101000 + . . . . . . + 101000000000 is divided by 7 is

There are 154 beads in a rosary and all are coloured, either RED or BLUE or GREEN. The number of blue ones is three less than red and five more than green. The number of Red beads are:

Recently, a small village, in Tamilnadu where only male shepherd reside with four sheep each, was devastated by Tsunami waves. Therefore 8 persons and 47 sheep were found to be dead and the person who luckily survived, left the village with one sheep each since 21 sheep were too injured to move so have left on their on luck, in the village. The number of sheep which were earlier in the village was :

A boy appeared in CAT for four consecutive year years, but coincidentally each time his net score was 75. He told me that there was $$\frac{1}{3}$$rd negative marking for every wrong answer and 1 mark was allotted for every correct answer. He has attempted all the questions every year, but certainly some answers have been wrong due conceptual problem. Which is not the total number of questions asked for CAT in any year, in that period?

The highest power of 17 which can divide exactly the following: (182 - 1) (184 - 1) (186 - 1) (188 - 1) . . . . (1816 - 1) (1818 - 1) is :

The total number of 3 digit numbers which have two or more consecutive digits identical is:

A magazine publisher publishes a monthly magazine of 84 pages. One I found that in a magazine 4 pages was missing. One out of them was page number 29 it is known that the page number of the last page of the magazine is 84, (including the cover pages). The numbers printed on the missing pages were :

The remainder when 6666..∞ is divided by 10 is :