• 072920 77839
  • info@smartachievers.in
Menu
Back
  • JEE ADVANCE
  • JEE MAIN
  • NEET
  • BITSAT
  • CBSE BOARD
  • UP BOARD
  • CUET
JEE ADVANCE
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
JEE MAIN
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
NEET
  • CLASS XI - XII
  • CRASH COURSE
BITSAT
  • CLASS XI - XII
CBSE BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
  • CLASS VI
  • CLASS VII
  • CLASS VIII
UP BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
CUET
  • CRASH COURSE
Courses


Solution


Q.

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2, 5) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval (α,β), then 3β–2α is equal to:          [2025]
1 12  
2 14  
3 10  
4 15  

Ans.

(4)

Circle with radius r touches the circle C, when r + 2 = distance between their centres

i.e., r+2=42+32=5

Also, if circle C touches the circle with radius r internally, then

r=2+42+32=2+5=7

Since, circle with radius r intersects the circle C at exactly 2 points.

∴  r+2>5 and r<7 i.e., 3<r<7

∴  α=3, β=7

⇒ 3β–2α=(3)(7)–(2)(3)=21–6=15.