Prove that in a sequence of numbers 49,4489,444889,44448889 in which every number is made by inserting 48-48 in the middle of previous as indicated, each number is the square of an integer.

There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to 1000 and the first term is equal to 1 . The second term of this sequence is equal to

Give one example each to the following statements. i. A number which is rational but not an integer

Four different movies are running in a town. Ten students go to watch these four movies. The number of ways in which every movie is watched by atleast one student, is (Assume each way differs only by number of students watching a movie)

Find the middle term of sequence formed by all three digit numbers which leave a remainder 3 when divided by 4. Also find sum of all numbers on both sides of the middle term.

Find the number of positive integers, which can be formed by using any number of digits from 0, 1, 2, 3, 4, 5 but using each digit not more than once in each number. How many of these integers are greater than 3000? What happened when repetition is allowed?

There are 'n' different books and 'p' copies of each. The number of ways in which a selection can be made from them is

Column I, Column II The number of five-digit numbers having the product of digit 20 is, p. > 70 A closest has five pairs of shoes. The number of ways in which four shoes can be drawn from it such that there will be no complete pair is, q. <60 Three ladies have each brought their one child for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. The number of ways in which interview can be arranged is, r. in (50 ,110) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is, s. in (40 ,70)

Give one example each to the following statements. iv. A number which is natural number, whole number, integer and rational number.