What is the value of
\( \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \ldots + \frac{1}{\sqrt{99} + \sqrt{100}} \)?
The simple interest on a certain sum is one-fourth of the sum. If the number of years and the rate of annual interest are numerically equal, then the number of years is
A 60-page book has n lines per page. If the number of lines were reduced by 3 in each page, the number of pages would have to be increased by 10 to give the same writing space. What is the value of n?
If x men working x hours per day can do x units of work in x days, then y men working y hours per day in y days would be able to do k units of work. What is the value of k?
Let d(n) denote the number of positive divisors of a positive integer n. Which of the following are correct?
1. d(5) = d(11)
2. d(5).d(11) = d(55)
3. d(5) + d(11) = d(16)
Select the correct answer using the code given below:
If \( A_{n} = P_{n} + 1 \), where \( P_{n} \) is the product of the first n prime numbers, then consider the following statements:
1. \( A_{n} \) is always a composite number.
2. \( A_{n} + 2 \) is always an odd number.
3. \( A_{n} + 1 \) is always an even number.
Which of the above statements is/are correct?
