Math Answers

Suppose we model the spread of a virus in a certain population as follows. On day 1, one person is infected. On each subsequent day, each infected person gives the cold to two others.

(a) Write down a recurrence relation for this model.

(b) What are some of the limitations of this model? How does it fail to be realistic?

Which of the following statement are True.(1) if a matrix has n^2 entries , where n belongs to N , then it is a square matrix.

Which of the following statement are True.(1) Any system of three linear equations in two variables has no solution.

Which of the following statement are True.(1) x>0 is necessary for x+2>1?

2 kg of water is heated from 0°C to 100°C and converted into steam at the same temperature. Calculate the increase in entropy, given that specific heat of water is 4.18 × 10^3 J/kg/K and Latent heat of vaporisation is 2.27 × 10^7 J/kg .

If y=e^(arc tanx) ,show that ( 1+x^2)yn+1 +(2nx-m)yn + n(n-1)yn-1 = 0

Show that the function u(x,t)=e^(-6t)cos2x is a solution of the one dimensional heat equation

Use the fact that nCk equals n!/k!(n-k)! to express in factorials
1) The coefficient "u" of x^n in the expansion of (1+x)^2n
2) the coefficient "v" of x^n in the expansion of (1+x)^2n-1, Hence show that u=2v

Find the coefficient of x^6 in the expansion of (1-3x)(1+2x)^9 using the general term: t= nCr a^n-r b^r

The hieght of 100 students of a study centre of IGNOU is approximately normally distributed with mean (u) 65 inches and standard deviation 2.5 inches. Find the no of students whose weight is
(i) less than 65 inches,
(ii) between 60 inches and 70 inches