Let C r denote the binomial coefficient of x r in the expansion of . If for , R, ....... upto 10 terms then the value of + is equal to ___________. ...

Given, ...... upto 10 terms ( + ..... upto 10 terms) Now, L.H.S. :- ...... upto 10 terms ..... upto 10 terms [We know, and ] Put ...

Let Cr denote the binomial coefficient of xr in the expansio: null (Mathematics)

Let C_r denote the binomial coefficient of x^r in the expansion of ${(1 + x)^{10}}$ . If for $\alpha$ , $\beta$ $\in$ R, ${C_1} + 3.2{C_2} + 5.3{C_3} +$ ....... upto 10 terms $= {{\alpha \times {2^{11}}} \over {{2^\beta } - 1}}\left( {{C_0} + {{{C_1}} \over 2} + {{{C_2}} \over 3} + \,\,.....\,\,upto\,10\,terms} \right)$ then the value of $\alpha$ + $\beta$ is equal to ___________.

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

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

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

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

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

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

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

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

Area of the region (x,y):x^2+(y-2)^2≤4,x^2≥2y is

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

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