Let the line meet the plane at the point . If the angle between the line and the plane is , then is equal to ___________. ...

Vector parallel to line : Normal vector to plane Angle between plane and line is Then, 314=1+4+3 ^2+5 14 =23 L_1 x-03=y-16=z-32= Any point on line : It lies on P aligned & 3 +12 +2+6 +9=4 \\\\ & =...

Let the line l xfrac 1y2frac z3lambda lambda R meet the plan: null (Mathematics)

Let the line $l: x=\frac{1-y}{-2}=\frac{z-3}{\lambda}, \lambda \in \mathbb{R}$ meet the plane $P: x+2 y+3 z=4$ at the point $(\alpha, \beta, \gamma)$ . If the angle between the line $l$ and the plane $P$ is $\cos ^{-1}\left(\sqrt{\frac{5}{14}}\right)$ , then $\alpha+2 \beta+6 \gamma$ 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

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

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

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

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

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