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Question Bank : Age Group 1617 : V1. The number of bacteria in a yeast culture grows at a rate which is proportional to the number present. If the bacteria triple in 1 hour, show that the number of bacteria at the end of five hours is 3^{5} times of the population at initial time. when x = log 2, y = 0 and when x = 0, y = 0. 3. Show that the set G of all positive rationals form a group under the composition *, defined by for all . 4. The number of accidents in a year involving taxi drivers in a city follows a Poisson distribution with mean equal to 3. Out of 1000 taxi drivers, find approximately the number of drivers with (i) no accident in a year (ii) more than 3 accidents in a year (e^{3} = 0.0498). 5. Find the equation of the hyperbola if its asymptotes are parallel to x + 2y  12 = 0 and x  2y + 8 = 0 respectively, (2,4) is the center of the hyperbola and the hyperbola passes through (2,0). 6. Show that the lines and intersect and find their point of intersection. 7. Solve the following nonhomogeneous system of linear equations by determinant method: 4x + 5y = 9; 8x + 10y = 18. 8. Show that the vectors form a right angled triangle. 9. A force of magnitude 5 units acting parallel to displaces the point of application from (1,2,3) to (5,3,7). Find the work done. 10. Show that . Character is who you are when no one is looking. 