Let the image of the point frac 53 frac 53 frac 83 in the pl: null (Mathematics) Question | DivineJEE | DivineJEE

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Let the image of the point $\left(\frac{5}{3}, \frac{5}{3}, \frac{8}{3}\right)$ in the plane $x-2 y+z-2=0$ be P. If the distance of the point $Q(6,-2, \alpha), \alpha > 0$ , from $\mathrm{P}$ is 13 , then $\alpha$ 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

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

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

Consider the following relations: R = |(x,y)|x,y are real numbers and x = wy for some rational mumber w/; S = { ( frac{m}{n},frac{p}{q} )| m,n,p and q are integers such that n,q X 0 and qm = pm}. Then

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

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

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

Let P(S) denote the power set of S = { 1,2,3,...,10}. Define the relations R_{1} and R_{2} on P(S) as AR_{1}B if ( A cap B^{C} ) cup ( B cap A^{C} ) = phi and AR_{2}B if cup B^{C} = B cup A^{C},forall A,B in P(S). Then

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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