Binomial Theorem for Positive Integral Index

IMPORTANT

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

MEDIUM
IMPORTANT

Find the term independent of x in the expansion of x3+32x210

HARD
IMPORTANT

If L and M are respectively the coefficient of x-7 in ax+bx211 and the coefficient of x7 in bx2+ax11 then L+M=

EASY
IMPORTANT

If the 4th term in the expansion of x2-2y36 is -20, then xy=

MEDIUM
IMPORTANT

The coefficient of x9 in x2-13x9 is

MEDIUM
IMPORTANT

If the digits at ten's and hundred's places in 112016 are x and y respectively, then the ordered pair x,y is equal to

EASY
IMPORTANT

For β0, if the coefficient of x3 in the binomial expansion of (1+βx)6 and the coefficient of x4 in the binomial expansion of (1-βx)8 are equal, then the value of β is

MEDIUM
IMPORTANT

Let Tr denote the rth term in the binomial expansion of a+150. If T25+T27=12552T26, then the sum of all the values of a is

EASY
IMPORTANT

If the coefficient of 7th and 13th terms in the expansion of 1+xn, nN are equal, then n is equal to

MEDIUM
IMPORTANT

In the expansion of 1+x15+ 1+x16+ 1+x17+...+ 1+x30, the coefficient of x10 is

EASY
IMPORTANT

The greatest binomial coefficient in the expansion of 1+x2n+2 nN is

MEDIUM
IMPORTANT

Middle term in the expansion of x2+1x2+2n is (nN)

HARD
IMPORTANT

If the fourth term in the binomial expansion of x11+log10x+x1126 is equal to 200, and x>1, then the value of x is

MEDIUM
IMPORTANT

The coefficient of x4 in the expansion of x2-3x210 is

MEDIUM
IMPORTANT

In the expansion of ax+bx12, the coefficient of x-10 will be

EASY
IMPORTANT

The middle term in the expansion of x+12x2n is

MEDIUM
IMPORTANT

The coefficient of the term independent of x in the expansion of x3+3x210 is

EASY
IMPORTANT

The 10th term in the expansion of (x-1)11 (in decreasing powers of x) is

HARD
IMPORTANT

The coefficient of x18 in the product 1+x1-x101+x+x29  is

EASY
IMPORTANT

If A and B are coefficients of x11 in the expansion of 1+x22 and 1+x21 respectively, then the value of AB is

HARD
IMPORTANT

The coefficient of xn in the expansion of 1+x2n and 1+x2n-1 are in the ratio