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Construct a K-map for F(x, y, z) = xz + yz + xyz. Use this K-map to find the implicants, prime
implicants, and essential prime implicants of F(x, y, z).
Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3
The average hospitality girls working in a certain area is 19 years old. A civic oriented group made a recent survey on the age of the hospitality girls working in the same locality. A random sample of 20 respondents showed an average of 15.4 years old with a standard deviation of 2.14 years old. Using a 0.05 level of significance, has the hospitality girls gone lower?
The following contingency table represents the voters’ opinion concerning a new tax
reform bill and their level of income.
Levels of Income
Opinion Low Medium High
For 213 203 182
Against 138 110 154
Apply chi-square (χ2
) test to examine whether the opinion of people on new tax bill is
independent from their income level. [Table value of chi- square (χ2
) at 5% level of
significance and for 2 degrees of freedom is 5.99
Suppose p=0.9 and n=4 ,C={0000,1010,1100}.Compute pC,v where
v=1100
Proof that an undirected graph has an even number of vertices of odd degree.
Define Semigroup and Monoid. Show that the set of positive Integer is a monoid for the operation
defined by aOb = max{ a,b}.
[C] Solve the following differential equation:
x^ 2 y^ " - 2xy'-4y=x^ 2 +2 log x
Two ideal dice are thrown . Let X1 be the score on the first die and X2 be the score on the second die. Let Y = max(X1, X2) then
(i) Evaluate Corr(Y, X1).
(ii) Evaluate Corr(Y, X2).
Show whether the following functions are uniformly continuous on the given domain.
1. F(x)=x^3 on [-1,1]
2. F(x)= 2x/2x-1 on [1, infinity]
3. F(x)= sinx/x on (0,1)
4. F(x)= 1/x on (0,1)
