Consider the following in respect of the numbers \( \sqrt{2}, \sqrt[3]{3}, \sqrt[6]{6} \):
1. \( \sqrt[6]{6} \) is the greatest number.
2. \( \sqrt{2} \) is the smallest number.
Which of the above statements is/are correct?
A water pipe is cut into two pieces. The longer piece is 70% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?
If the roots of the equation \( (a^{2} - bc)x^{2} + 2(b^{2} - ac)x + (c^{2} - ab) = 0 \) are equal, where \( b \neq 0 \), then which one of the following is correct?
A, B and C can do a piece of work individually in 8, 12 and 15 days respectively. A and B start working, but A quits after working for 2 days. After this, C joins B till the completion of work. In how many days will the work be completed?
