Directions: Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate boxes — one for the numerator and one for the denominator.
1. Which is the smallest number that is a perfect square and is a multiple of 7936?
2. Which is the smallest number that should be added to 192 to make it a perfect square?
3. Let f and g be two real functions defined by f(x) = √ X - 3 and g(x) = √ 9 - x2. What is the positive value of (g/f)(-39)?
4. Working 7 hours a day, 24 men can complete a piece of work in 27 days. If 14 men have to complete the work in 36 days how many hours will they have to put in every day?
hours
5. Sam completes a work in 26 hours and earns Rs. 20000 for it. If the ratio of the amount earned by Sam in one hour to the amount earned by Pam in one hour is 17:13, then how many hours does Pam take to earn Rs.20000?
hours
6. A machine can do a work in 24 hours and a man can do it in 36 hours. If a man can finish 8 tasks in two hours, then how many tasks can the machine do in three hours?
7. Penny cycles at 12 km/hr and covers a distance of 18 km. At what speed in km/hr should she cycle for the next 1.5 hours so that her average speed for the whole cycling session is 18km/hr?
km/hr
8. Working 7 hours a day, 24 men earn Rs.36000. If 14 men have to earn the same amount in the same time, how many hours will they have to work for each day?
hours
9. Find the value of a for which the point (a,0) lies on the parabola y2=4x-16.
10. Find the value of b for which the point (5, b) is the center of the circle x2+10x+y2+6y + 30=0