Prove that the numbers of the sequence `121, 12321,1234321, ........... ` are each a perfect square of odd integer.

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is (i) an odd number (ii) a perfect square number

Find the smallest number by which 1100 must be multiplied so that the product becomes a perfect square. Also in each find the square root of the perfect square so obtained.

Find the least number which must be subtracted from 18265 to make it a perfect square. Also, find the square root of the resulting number.

A new sequence is obtained from the sequence of positive integers 1,2,…….., by deleting all the perfect squares. What is the 2015th term from the beginning of the new sequence ?

Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square.

Find the smallest number by which 9408 must be divided so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Find the least number that must be subtracted from 5607 so as to get a perfect square. Also find the square root of the perfect square.find the greatest 4 digit number which is a perfect square .

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.(i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412