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Let us define a function f : N → Q as follows,
(n-1)/4 n is odd
f(n) = {
(n+1)/2 n is even
Which of the following are true?
f is not one to one.
f is not onto.
f is onto.
f is one to one.
In a Zoo, there are 6 Bengal white tigers and 7 Bengal royal tigers. Out of these tigers, 5 are males and 10 are either Bengal royal tigers or males. Find the number of female Bengal white tigers in the Zoo.
At the beginning of the school year, the mean score of a group of 24 students in an educational achievement test in reading was 45 with a standard deviation of 6. At the end of the school year, the mean score on an equivalent form of the same test was 50 with a standard deviation of 5. Has the class made significant progress in reading during the year? Use alpha equal to 0.05.
A lot of 1000 screws contain 1% with major defects and 5% with minor defects. If 50screws are picked at random and inspected, what are the expected numbers of major and minor defectives?
Three invoices prepared by Shanty , Jenny and Sherry . A sample of 500 invoices are selected . Two hundred were prepared by Shanty , 120 by Jenny and 180 by Sherry . The error rates of Shanty , Jenny and Sherry were found to be 2 % , 3 % and 4 % respectively . From the sample of 500 invoices , one was selected . a . Sketch a Tree Diagram based on the information given in the question b . Compute the probability that invoice contains error ?
Let f(x)=x3 +x2 +x+1 be an element of Z [x] . Write f(x) as a product of 2
irreducible polynomials over Z2.
Let f(x) = x3 + 6 be an element Z [x]. Write f(x) as a product of irreducible 7
polynomials over Z7.
Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inverse in Z4[x].
Let f(x)=5x4 +3x3 +1and g(x)=3x2 +2x+1 in Z9[x]. Determine the quotient and remainder upon dividing f(x) by g(x).
1. Write the multisets (bags) of prime factors of given numbers.
i. 160
ii. 120
iii. 250
2. Write the multiplicities of each element of multisets (bags) in Part 2-1(i,ii,iii) separately.
3. Determine the cardinalities of each multiset (bag) in Part 2-1(i,ii,iii).
