Consider the following statements:
1. \( x^{4}(y - z) + y^{4}(z - x) + z^{4}(x - y) \) is positive if \( x > y > z \).
2. \( x^{4}(y - z) + y^{4}(z - x) + z^{4}(x - y) \) is negative if \( x < y < z \).
Which of the above statements is/are correct?
X and Y can do a piece of work in 45 days and 40 days respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to?
480 persons working 10 hours per day complete one-fourth of a work in 10 days. How many additional persons are to be employed in order to complete the remaining work in 20 days, working 8 hours per day?
There are two stations X and Y, 1320 km apart. A train starts from station X at 6 a.m. and moves at an average speed of 60 km/hr. At 2 p.m. another train starts from Y towards X and moves at an average speed of 80 km/hr. When do they meet?
Two glasses of equal volume are filled with a mixture of alcohol and water in the ratio 3 : 2 and 4 : 1, respectively. These glasses are emptied into a third glass. What is the ratio of alcohol and water in the third glass?
There are two natural numbers x and y, where \( x > y \). When x is divided by 6, it leaves the remainder 2 and; when y is divided by 6, it leaves the remainder 3. What is the remainder when (x - y) is divided by 6?
