Let X ={(,y) in ZZ timesZZ : (x^2)/8 +(y...

Let `X ={(,y) in ZZ timesZZ : (x^2)/8 +(y^2)/(20) < 1 and y^2 < 5x}`. Three distinct points P, Q and R are randomly chosen from X . Then the probability that P, Q and R form a triangle whose area is a positive integer, is

`(71)/(200)`

`(73)/(220)`

`(79)/(220)`

`(83)/(220)`

Text Solution

AI Generated Solution

Topper's Solved these Questions

JEE ADVANCED 2022
JEE ADVANCED PREVIOUS YEAR|Exercise MATHEMATICS (SECTION -3)|4 Videos
MOCK TEST 2022
JEE ADVANCED PREVIOUS YEAR|Exercise Question|18 Videos

Similar Questions

Explore conceptually related problems

Let ZZ be the set of all integers, A={(x,y) in ZZ xx ZZ : (x-2)^(2)+y^(2)le 4} , B={(x,y) in ZZ xx ZZ : x^(2)+y^(2) le 4} and C={(x,y) in ZZ xx ZZ : (x-2)^(2) +(y-2)^(2) le 4} If the total number of relations from A cap B to A cap C is 2^(p) , then the value of pis :

Let S={(x,y):(x^(2))/(9)+(y^(2))/(4)<=1} and T={(x,y):|x|<=3;|y|<=2}

Let S={(x,y):(x^(2))/(9)+(y^(2))/(4)<=1} and T={(x,y):|x|<=3 and |y|<=2}

Let A={(x, y): x, y in z , x^(2)+y^(2) <= 16 }. Then the number of reflexive relations on set A is

Let A={2,3,4,5,6,7,8,9} Let R be the relation on A defined by {(x,y):x epsilonA,yepsilonA & x^(2)=y or x=y^(2) }. Find domain and range of R .

Let the equation of circle is x^(2) + y^(2) - 6x - 4y + 9 = 0 . Then the line 4x + 3y - 8 = 0 is a

Let x, y be real variable satisfying x^(2) + y^(2) + 8x - 10y - 59 = 0 Let a = max {(x-3)^(2) + (y-4)^(2) and b = min {(x-3)^(2) + (y-4)^(2)) , then a + b + 2010 is ______ .

Let the foci of the ellipse (x^(2))/(9)+y^(2)=1 subtend a right angle at a point P. Then,the locus of P is (A) x^(2)+y^(2)=1(B)x^(2)+y^(2)=2 (C) x^(2)+y^(2)=4(D)x^(2)+y^(2)=8

Let (x,y) satisfying x^(2)+y^(2)-4x+4y-12=0 Now if A=Max(x^(2)+y^(2)-6x+8y+25)&B=Max(x^(2)+y^(2)+24x-10y+169) Calculate 2A+3B

JEE ADVANCED PREVIOUS YEAR-JEE ADVANCED 2023-Question

Let T1 and T2 be two distinct common tangents to the ellipse E: (x^2)...
Text Solution
|
Let Q be the cube with the set of vertices {(x1,x2,x3) in RR^3:x1x2,x^...
Text Solution
|
Let X ={(,y) in ZZ timesZZ : (x^2)/8 +(y^2)/(20) < 1 and y^2 < 5x}. Th...
Text Solution
|
Let P be a point on the parabola y^2 =4ax , where a>0 . The normal to ...
Text Solution
|
Let tan^-1(x)in(-pi/2,pi/2) , for x in RR. Then the number of real sol...
Text Solution
|
Let nge2 be a natural number and f:[0,1]rarrRR be the function defined...
Text Solution
|
Let obrace(75* * *57)^(" r") denote the (r+2) digit number where the f...
Text Solution
|
Let A={(1967+ 1686i sin theta)/(7-3icostheta): theta in RR} . If A con...
Text Solution
|
Let a and b be two nonzero real numbers. If the coefficient of 5 x in...
Text Solution
|
Let alpha,beta and gamma be real numbers. Consider the following syst...
Text Solution
|
Consider the given data with frequency distribution {(xi,3,8,11,10,5...
Text Solution
|
Let l1 and l2 be the lines vec r1= gamma (hati+ hatj +hat k ) and vecr...
Text Solution
|
Let z be a complex number satisfying |z|^3 +2z^2 +4barz -8 =0 , where ...
Text Solution
|
Let f:[1,oo) to RR be a differentiable function such that f(1)=1/3 and...
Text Solution
|
Consider an experiment of tossing a coin repeatedly until the outcomes...
Text Solution
|
For any y in RR , let cot^-1(y) in (0,pi) and tan^-1(y) in (-pi/2,pi/2...
Text Solution
|
Let the position vectors of the points P ,Q, R and S be veca=hati +2ha...
Text Solution
|
Let M = (a(ij)) , i , j in {1,2,3}, be the 3 xx 3 matrix such that a(i...
Text Solution
|
Let f:(0,1) to RR be the function defined as f(x)=[4x](x-1/4)^2(x-1/2)...
Text Solution
|
Let S be the set of all twice differentiable functions f from RR to RR...
Text Solution
|