Simplify the following trigonometric expression:

Find the smallest number greater than 300 which leaves a remainder 1 when divided by 4, 5 and 6.

Sum of digits of a two-digit number is 9. When 27 is subtracted from the number, its digits get interchanged. Find the original number.

Find the range of the given data:

14, 28, 35, 21, 42, 56, 49

A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?

How many 4-digit numbers greater than 3000 can be formed using the digits 1, 2, 3, 4, 5 without repetition?

The sum of two distinct positive natural numbers is 246, and their difference is 34. Calculate 10% of the product of these two numbers.

Three numbers are in the ratio 6:9:13. The difference of the sums (first + third) and (first + second) is 52. Find the largest number.

The value of a machine depreciates every year by 12%. What will be its value after 2 year if its value is Rs 19,650?