JEE Exam  >  JEE Notes  >  35 Years Chapter wise Previous Year Solved Papers for JEE  >  Integer Answer Type Questions: Circle | JEE Advanced

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE PDF Download

Q.1. The centres of two circles C1 and Ceach of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segement joining the centres of C1 and Cand C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is
      (2009)

Ans. (8)

Sol.   Let r be the radius of required circle.
Clearly, in ΔC1CC2 , C1C = C2C =r+ 1
and P is mid point of C1C
∴ CP ⊥ C1C2
Also PM ⊥ CC1
Now ΔPMC1 ~ΔCPC1 (by AA similarity)

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE r  + 1 = 9 ⇒ r =  8.

 

Q.2. The straight line 2x – 3y = 1 divides the circular region x2 + y2 ≤ 6 into two parts. 

If Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE then the number ofpoints (s) in S lying inside the smaller part is     (2011)

Ans.  (2)

 Sol. 
The smaller region of circle is the region given by x2 + y2 < 6 ...(1)
and 2x – 3y > 1 ...(2)

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

We observe that only two points Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE and  Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

satisfy both the inequations (1) and (2)

∴ 2 points in S lie inside the smaller part.

The document Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE is a part of the JEE Course 35 Years Chapter wise Previous Year Solved Papers for JEE.
All you need of JEE at this link: JEE
347 docs|185 tests

Top Courses for JEE

Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Summary

,

Viva Questions

,

study material

,

Previous Year Questions with Solutions

,

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

,

practice quizzes

,

Free

,

pdf

,

Objective type Questions

,

Sample Paper

,

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

,

past year papers

,

Integer Answer Type Questions: Circle | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE

,

Semester Notes

,

Extra Questions

,

Important questions

,

shortcuts and tricks

,

mock tests for examination

,

ppt

,

Exam

,

MCQs

,

video lectures

;