how will you explain liquefaction of gases in terms of the kinetic molecular theory of gases?

In many situations, we come across polynomials, which may not have common factors among its terms. In such cases, we group the terms of the expression in such a way that there are common factors among the terms of the groups so formed. Let us study such exampl..

Particular Terms for Fractional Index - Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (1+x) n . This can be done by expanding (1+x) n to certain terms and then locating the required term. Generall..

The General Term for Fractional Index is:..

For n Q and |x|<1, we have ...

Particular Terms for Positive Integral Index - Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a..

Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a tedious task, specially when the index n is large. In su..

The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or od..

Working rules for finding the greatest term: Step 1: In (a + b) n , the constants a and b must be positive. Step 2: Write T r+1 and T r and find the value of T r+1 /T r . Step 3: Simplify the inequality (T r+1 /T r ) greater than or equal to 1 and find the..

Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..

Greatest Terms for Positive Integral Index - In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r..