Numbers Questions

If 49 is subtracted from the square of a number, then the result obtained is 576. What is the number?

Which of the numbers given below is NOT rational?

A number is greater than 58 times its reciprocal by 3/4. What is the number?

Find a two digit number which is exactly three times the product of its digits?

Convert binary 10110 to decimal.

What is the sum of the first 11 terms of an arithmetic progression if the first term is -31 and last term is 29?

Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime:

1) Both p and q may be prime numbers.

2) Both p and q may be composite numbers

3) one of p and q may be prime and the other composite.

Which of the above statements are correct?

The sum of a non-zero number and twenty times its reciprocal is 9. What is the number?