Let the complex numbers alpha and frac 1bar alpha lie on the: null (Mathematics) Question | DivineJEE | DivineJEE

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Let the complex numbers $\alpha$ and $\frac{1}{\bar{\alpha}}$ lie on the circles $\left|z-z_0\right|^2=4$ and $\left|z-z_0\right|^2=16$ respectively, where $z_0=1+i$ . Then, the value of $100|\alpha|^2$ is __________.

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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

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

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

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

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

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

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