A circle with centre (2, 3) and radius 4 intersects the line at the points P and Q. If the tangents at P and Q intersect at the point , then is equal to ___________. ...

The line x + y = 3 ..... (i) is polar of S( , ) w.r.t. circle (x - 2)^2 + (y - 3)^2 = 16 x^2 + y^2 - 4x - 6y - 3 = 0 Equation of polar is x + y - 2(x + ) - 3(4 + ) - 3 = 0 ( - 2)x + ( - 3)y - (2 + 3 + 3) = 0 ..... (ii) (i) and (ii) represent the ...

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A circle with centre (2, 3) and radius 4 intersects the line $x+y=3$ at the points P and Q. If the tangents at P and Q intersect at the point $S(\alpha,\beta)$ , then $4\alpha-7\beta$ is equal to ___________.

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

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

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

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

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} =)

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

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