ga chapter 7

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So far, we have assumed that the elementary events are equally likely and we have used the corresponding definition of probability. However the same definition of conditional probability can also be used when the elementary events are not equally likely. This will be clear from the following examp..

Reaction takes place in acidic medium, so add H+ ions to the side deficient in H+ and balance H and O atoms..

Note that the 'NOT' operation is a unary operator, whereas 'AND' and 'OR' operators are binary operators. We have already discussed what a Boolean function is. Here is a formal definition for Boolean expression and Boolean functio..

A first - order first - degree differential equation is of the form If the function f turns out to be of the form f(x, y) = p(x) q(y) .(2) (i.e., the product of a function of x with a function of y, then the differential equation (1) is said to have the variable x, y separable.) In this case the..

You know that any polynomial of the form p(a) can also be written as If the remainder is zero, then p(a) = g(a) x h(a). That is, the polynomial p(a) is a product of two other polynomials g(a) and h(a). For example, 3a + 6a 2 = 3a x (1 + 2a). It may be possible to express a polyn..

Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Write and expr..

The electronic configuration of atom 'D' has seven electrons in the outermost shell. Each 'D' atom should share a pair of electrons with another 'D' atoms to form a substance containing only 'D' .i.e., Hence, the formula of the substance is D 2 . It is a covalent compoun..

has established fourteen different types of lattices called Bravais lattices according to the arrangement of the points in the different unit cells involved. These are listed below:..