(a) Consider the relation scheme $$R(A, B, C)$$ with the following functional dependencies:
$$\eqalign{ & A,B \to C \cr & \,\,\,\,\,\,C \to A \cr} $$
Show that the scheme $$R$$ is the Third Normal Form $$(3NF)$$ but not in Boyce-Code Normal Form $$(BCNF).$$

(b) Determine the minimal keys of relation $$R.$$

$$\mathop {Lim}\limits_{x \to \infty } {{{x^3} - \cos x} \over {{x^2} + {{\left( {\sin x} \right)}^2}}} = \_\_\_\_\_\_.$$

A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is

Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then