Let the mirror image of the point a b c with respect to the : null (Mathematics) Question | DivineJEE | DivineJEE

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Let the mirror image of the point (a, b, c) with respect to the plane 3x $-$ 4y + 12z + 19 = 0 be (a $-$ 6, $\beta$ , $\gamma$ ). If a + b + c = 5, then 7 $\beta$ $-$ 9 $\gamma$ is equal to ______________.

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

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

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

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

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

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

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 :

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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