Let be the equation of a plane passing through the point and perpendicular to the line joining the points and . Then the value of is equal to _____________. ...

Plane : a(x-3)+b(y+2)+c(z-5)=0 Dr's of plane : aligned & \\\\ & P: 3(x-3)-1(y+2)-2(z-5)=0 \\\\ & 3 x-9-y-2-2 z+10=0 \\\\ & 3 x-y-2 z=1 \\\\ & =3, =-1, =-2 \\\\ & =6 aligned...

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Let alpha x beta y gamma z1 be the equation of a plane passi: null (Mathematics) | DivineJEE

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Mathematics

Let $\alpha x+\beta y+\gamma z=1$ be the equation of a plane passing through the point $(3,-2,5)$ and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$ . Then the value of $\alpha \beta y$ is equal to _____________.

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

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

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

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

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 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

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