Let for the term in the binomial expansion of , in the increasing powers of , to be the greatest for , the least value of is . If is the ratio of the coefficient of to the coefficient of , then is ...

is greatest of So, and (concept of numerically greatest term) Here, and and and So, in for i.e.,&...

Let for the 9 th term in the binomial expansion of 36 xn in : (Mathematics)

Let for the $9^{\text {th }}$ term in the binomial expansion of $(3+6 x)^{\mathrm{n}}$ , in the increasing powers of $6 x$ , to be the greatest for $x=\frac{3}{2}$ , the least value of $\mathrm{n}$ is $\mathrm{n}_{0}$ . If $\mathrm{k}$ is the ratio of the coefficient of $x^{6}$ to the coefficient of $x^{3}$ , then $\mathrm{k}+\mathrm{n}_{0}$ 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

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

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

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 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

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

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

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

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