The integral , where [.] denotes the greatest integer function is equal to...

aligned & _0^1 17^[1x] dx=-_1^0 17^[1x] dx \\ = & (-1)[_1^1 / 2 17 dx+_1 / 2^1 / 3 17^2 dx+_1 / 3^1 / 4 17^3 dx+ ] \\ = & (17+12.7^2+13.7^3+ )-(17.2+17^2 .3+17^2 .4 ) \\ = & - (1-17)-7(17^2 .2+17^3 .3+17^4 .4+ . ) \\ & [ as (1+x)=x-x^22+x^33-x^44 . ] \\ & [ as (1-x)=-(x+x^22+x^33+x^44 . )] \\ = & - ...

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

The integral

\int_0^1 \frac{1}{7^{\left[\frac{1}{x}\right]}} \mathrm{dx}

, where [.] denotes the greatest integer function is equal to

1+6 \log _{\mathrm{e}}(6 / 7)

1-6 \log _{\mathrm{e}}(6 / 7)

1+6 \log _e(7 / 6)

1-6 \log (6 / 7)

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 :

Let R be the set of real numbers. end{enumerate} Statement-1: A = {(x,y) in R X R:y - x is an integer } is an equivalence . relation on R. Statement-2: B = {(x,y) in R X R:x = alpha y for some rational number } is . an equivalence relation on R.

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

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

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

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

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

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