JEE Main Questions
Using binomial theorem, write down the expansions of the following: (1+2x−3x2)5
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Find the following sum:
term is the first negative term in the expansion of (1+x)7/2,
then find the value of r˙
If the sum of the coefficient in the expansion of (α2x2−2αx+1)51
vanishes, then find the value ofα
divides the number 101100−1
then, find the greatest value of m˙
Show that the middle term in the expansion of (1+x)2nis n!184.108.40.206n−1˙˙2nxn2nxn, where n is a positive integer.
Using binomial theorem, evaluate : (96)3
Show that the coefficient of the middle term in the expansion of (1+x)2nis equal to the sum of the coefficients of two middle terms in the expansion of (1+x)2n−1.
Find the greatest coefficient in the expansion of (1+2x/3)15˙