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 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

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

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

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

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

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

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

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

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

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