Home
Class 12
MATHS
If x lt 4 " and " x, y in {1, 2, 3, .., ...

If `x lt 4 " and " x, y in {1, 2, 3, .., 10}`, then find the number of ordered pairs (x,y).

Text Solution

Verified by Experts

We have `x lt 4 lt y`, where `x, y in {1,2,3,..,10}`
`therefore ` x can be 1,2 or 3 and y can be 5,6,7,8,9, 10.
Thus, for x we have 3 options and for y we have 6 options.
So, using multiplication rule of counting, Number of ordered paris `=3xx6=18`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

If x, y in [0,2pi] then find the total number of order pair (x,y) satisfying the equation sinx .cos y = 1

If x in[0,6 pi],y in[0,6 pi] then the number of ordered pair (x,y) which satisfy the equation sin^(-1)sin x+cos^(-1)cos y=(3 pi)/(2) are

Consider the system in ordered pairs (x,y) of real numbers sin x+sin y=sin(x+y) , |x|+|y|=1 . The number of ordered pairs (x,y) satisfying the system is

If (x^(4)+2x i)-(3x^(2)+yi)=(3-5i)+(1+2yi) then the number of ordered pairs (x, y) is/are equal to {AA x,y in R and i^(2)=-1}

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

If x and y are positive integer satisfying tan^(-1)((1)/(x))+tan^(-1)((1)/(y))=(1)/(7) , then the number of ordered pairs of (x,y) is

If x,y in (0,30) such that [x/3]+[(3pi)/2]+[y/2]+[(3pi)/4]=11/6x+5/4 y (where {x} denotes greatest integer <=x ) number of ordered pairs (x, y) is (A) 0 (B) 2 (C) 4 (D) none of these

For the smallest positive values of x \and\ y , the equation 2(sinx+sin y)-2cos(x-y)=3 has a solution, then which of the following is/are true? (a) sin(x+y)/2=1 (b) cos((x-y)/2)=1/2 (c)number of ordered pairs (x , y) is 2 (d)number of ordered pairs (x , y)i s3

If (log)_(10)(x^3+y^3)-(log)_(10)(x^2+y^2-x y)lt=2, and x ,y are positive real number, then find the maximum value of x ydot