Let l 1 be the line in xy-plane with x and y intercepts and respectively, and l 2 be the line in zx-plane with x and z intercepts and respectively. If d is the shortest distance...

Equation of L1 Equation of L2 $aligned d &= | (c - a) (b d)|b d| | \\[12pt] &= ( 14i ) ( 42i + 4j + 36k )(42)^2 + 4^2 + (36)^2 \\[12pt] &= 232 + 16 + 54 \\[10pt] &= 151 aligned \\\\$...

Let l1 be the line in xyplane with x and y intercepts 1 8 an: null (Mathematics)

Let l₁ be the line in xy-plane with x and y intercepts ${1 \over 8}$ and ${1 \over {4\sqrt 2 }}$ respectively, and l₂ be the line in zx-plane with x and z intercepts $- {1 \over 8}$ and $- {1 \over {6\sqrt 3 }}$ respectively. If d is the shortest distance between the line l₁ and l₂, then d^{$-$ 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

The area enclosed by the curves xy+4y=16 and x+y=6 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

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

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

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

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

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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