Math Answers

Suppose the gene ‘A’ stands for tall and gene ‘a’ stands for short, and ‘A’ is dominant over
‘a’. Suppose the parents are of genotype aa and Aa.
i) In a family like this what is the probability of having a short child?
ii) In a family like this if there are four children, what is the probability that two children
are tall and two children are short?
iii) If you survey a large number of such families having four children, what is the average
number of tall children to be expected in a family?
iv) If you survey 256 families of this type, each having four children, how many families
are expected to have all tall children?

Find the centre of gravity of a mass in the shape of a semicircular disc of radius 4,
if the density at (x, y) is (2y)/(x^2+y^2)

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria
present in the culture originally, how many bacteria will be present at the end of
18th hour?

Compute 5 (98) using Binomial theorem

Find the volume of the solid bounded by the planes z=0, x=1, x=2, y=-1, y=1 and the surface z=x^2 + y^2

There is a tower the angle of elevation from the point 'A' which is situated South of the tower is 30°. And angle of elevation of the tower from point 'B' which is to the West of point 'A' is 18°.
If AB = a
Find the height of tower using 'a'.
(sin 18°= (√5-1)/4 )

For what value of x will the angle between the lines with direction ratios (x, 2, 4) and
(1, 0, 1) be o 45 ?

In a railway yard, goods trains arrive at the rate of 60 trans per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 72 minutes, calculate the following:

i) The average number of trains in the queue.
ii) The probability that the queue size is greater than or equal to 10.

If u = x cosy, v= ye^x , w = sinxz , find the Jacobian ∂(u,v,w)/∂(x,y,z), and evaluate it at (2,0,π/3).