In a barn there are 30 rats. `5` more rats enter the barn.`6` of the total rats were eaten by cats.If `8` rats are born during the time period under consideration and `7` rats left the barn,find out the resultant population at time `(t+1)`.

A biologist studied of population of rats in a barn. He found that average natality was 250, average mortality 240 immigration 20 and emigration 30. the net increase in population is

A total amount of Rs 7000 is deposited in three different savings bank accounts with annual interest rats 5%. 8% and 8 (1/2)% respectively. The total annual interest from these three accounts is Rs.550.Equal amount have been deposited in the 5% and 8% savings account. Find the amount deposited in each of the three accounts, with the help of matrices.

A proton enters a magnetic field of 4 T intensity with a velocity of 2.5 xx 10^6 ms^-1 at an angle of 30^@ with the field. Find the magnitude of the force on the proton. Charge of the proton = 1.602 xx 10^-19 coulomb.

In part (ii), For a loaded die,the probabilities of outcomes are given as under :P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6.the die is thrown two times.Let A and B be the events, same number each times, and a total score is 10 or more, respectively.Determine if the dice were fair, whether or not the events A and B would be independent.