The coefficient of in the expansion of is equal to _________. ...

aligned & (1-x)(1-x)^2007(1+x+x^2)^2007 \\ & (1-x)(1-x^3)^2007 \\ & (1-x)( ^2007 C_0- ^2007 C_1(x^3)+ .) aligned General term aligned & (1-x)((-1)^r ^2007 C_r x^3 r) \\ & (-1)^r 2007 C_r x^3 r-(-1)^r 2007 C_r x^3 r+1 \\ & 3 r=2012 \\ & r 20123 \\ & 3 r+1=2012 \\ & 3 r=2011 \\ & r 20...

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The coefficient of x2012 in the expansion of 1x20081xx22007 : null (Mathematics) | DivineJEE

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Mathematics

The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}\left(1+x+x^2\right)^{2007}$ is equal to _________.

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The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated, is

Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

The integral int_0^1 \frac{1}{7^{\left[\frac{1}{x}\right]}} {dx}, where [.] denotes the greatest integer function is equal to

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The area of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :

Let Z be the set of integers. If A = { x in Z:2^{(x + 2) ( x^{2} - 5x + 6 )} = 1 } and = { x in Z : - 3 < 2x - 1 < 9}, then the . number of subsets of the set A X B is

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