Let the coefficients of x 1 and x 3 in the expansion of , be m and n respectively. If r is a positive integer such that , then the value of r is equal to __________. ...

Given, Binomial expansion General Term For term; m is the coefficient of term, For term; n is&nbs...

Let the coefficients of x1 and x3 in the expansion of 2x1 5 : (Mathematics)

Let the coefficients of x^{$-$ 1} and x^{$-$ 3} in the expansion of ${\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5}}}}}} \right)^{15}},x > 0$ , be m and n respectively. If r is a positive integer such that $m{n^2} = {}^{15}{C_r}\,.\,{2^r}$ , then the value of r is equal to __________.

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

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

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 (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 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

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 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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