MEDIUM
JEE Main
IMPORTANT
Earn 100

The coefficient of x256 in the expansion of 1-x101x2+x+1100 is:

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Important Questions on Binomial Theorem

MEDIUM
JEE Main
IMPORTANT
The number of rational terms in the binomial expansion of 414+516120is_______.
HARD
JEE Main
IMPORTANT
For the natural numbers m, n, if (1-y)m(1+y)n=1+a1y+a2y2+.+am+nym+n and a1=a2=10, then the value of m, n, is equal to:
HARD
JEE Main
IMPORTANT
If the constant term, in binomial expansion of 2xr+1x210 is 180, then r is equal to ____________.
HARD
JEE Main
IMPORTANT
The number of elements in the set {n{1,2,3,,100}(11)n>(10)n+(9)n is ___________.
HARD
JEE Main
IMPORTANT
If b is very small as compared to the value of a, so that the cube and other higher powers of ba can be neglected in the identity

1a-b+1a-2b+1a-3b+.+1a-nb=αn+βn2+γn3

then the value of γ is :

EASY
JEE Main
IMPORTANT

The ratio of the coefficient of the middle term in the expansion of (1+x)20 and the sum of the coefficients of two middle terms in expansion of (1+x)19 is           .

EASY
JEE Main
IMPORTANT
The term independent of x in the expansion of x+1x2/3-x1/3+1-x-1x-x1/210, where x0,1 is equal to
MEDIUM
JEE Main
IMPORTANT
The sum of all those terms which are rational numbers in the expansion of 213+31412 is: