1. 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[sup]5[/sup] times of the population at initial time.
3. Show that the set G of all positive rationals form a group under the composition *, defined by
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[sup]-3[/sup] = 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
7. Solve the following non-homogeneous system of linear equations by determinant method:
4x + 5y = 9; 8x + 10y = 18.
8. Show that the vectors
9. A force of magnitude 5 units acting parallel todisplaces the point of application from (1,2,3) to (5,3,7). Find the work done.
10. Show that
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.