Let . If , then is equal to _________. ...

Put aligned & lm(z^2+8 i z-15z^2-3 i z-2)=0 \\\\ & -(x^2-y^2-8 y-15)(2 x y-3 x)+ \\& (2 x y+8 x)(x^2-. .y^2+3 y-2)=0 \\\\ & (x^2-y^2)(2 x y+8 x-2 x y+3 x)+ \\& (8 y+15)(2 x y- 3 x)+(2 x y+8 x)(3 y-2)=0 \\\\ & 11 x^3-11 x y^2+16 x y^2-24 x y+30 x y- \\& 45 x+ 6 x y^2 -4 x y+24 x y-16 x=0 \...

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Let Sz Ci 2 i frac z28 i z15z23 i z2 R If alphafrac 1311 i S: null (Mathematics) | DivineJEE

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Let $\mathrm{S}=\left\{z \in \mathbb{C}-\{i, 2 i\}: \frac{z^{2}+8 i z-15}{z^{2}-3 i z-2} \in \mathbb{R}\right\}$ . If $\alpha-\frac{13}{11} i \in \mathrm{S}, \alpha \in \mathbb{R}-\{0\}$ , then $242 \alpha^{2}$ is equal to _________.

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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

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

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

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

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

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

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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