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Question Bank : Age Group 16-17 : V
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 35 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
intersect and find their point of intersection.
7. Solve the following non-homogeneous 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.