Binomial Theorem for Positive Integral Index
Binomial Theorem for Positive Integral Index: Overview
This topic covers concepts, such as, General Term in Standard Binomial Expansion, Finding Last Digit, Numerically Greatest Coefficient in the Expansion of (a+b)^n & Finding Numerically Greatest Terms in the Expansion of (a+b)^n etc.
Important Questions on Binomial Theorem for Positive Integral Index
Find the term independent of in the expansion of

If and are respectively the coefficient of in and the coefficient of in then

If the term in the expansion of is , then

The coefficient of in is

If the digits at ten's and hundred's places in are and respectively, then the ordered pair is equal to

For if the coefficient of in the binomial expansion of and the coefficient of in the binomial expansion of are equal, then the value of is

Let denote the term in the binomial expansion of . If , then the sum of all the values of is

If the coefficient of and terms in the expansion of , are equal, then is equal to

In the expansion of , the coefficient of is

The greatest binomial coefficient in the expansion of is

Middle term in the expansion of is

If the fourth term in the binomial expansion of is equal to and then the value of is

The coefficient of in the expansion of is

In the expansion of the coefficient of will be

The middle term in the expansion of is

The coefficient of the term independent of in the expansion of is

The term in the expansion of (in decreasing powers of ) is

The coefficient of in the product is

If and are coefficients of in the expansion of and respectively, then the value of is

The coefficient of in the expansion of and are in the ratio
