A line passes through and . The point , where are non-negative integers, on the line lies at a distance of 21 units, from the point . The distance between the points and is equal to __________. ...

A line passes through A462 and B1624 The point Pa b c where : (Mathematics)

A line passes through $A(4,-6,-2)$ and $B(16,-2,4)$ . The point $P(a, b, c)$ , where $a, b, c$ are non-negative integers, on the line $A B$ lies at a distance of 21 units, from the point $A$ . The distance between the points $P(a, b, c)$ and $Q(4,-12,3)$ 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

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

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

The area enclosed by the curves xy+4y=16 and x+y=6 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 of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to

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

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

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