Click to Chat
1800-2000-838
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
IIT JEE 2009 Mathematics Paper2 Code 1 Solutions 12. Let f:R --> R be a continuous function which satisfies f(x) = ∫0 x f(t) dt Then the value of f(ln5) is Sol. 0 f(x) = ∫0 x f(t) dt => f(0) = 0 also, f'(x) = f(x), x > 0 => f'(x) = kex, x > 0 f(0) = 0 and f(x) is continuous => f(x) = 0 for all x > 0 f(ln5) = 0. 13. The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and 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 Sol. 8 cosa = 2√2/3 sina = 1/3 tana = 2√2/R => R = 2√2/tanα = 8 units Alternate Solution: We have , from the figure (R + 1)2 = (R - 1)2 + (4√2)2 => R = 8. << Back || Next >>
12. Let f:R --> R be a continuous function which satisfies f(x) = ∫0 x f(t) dt Then the value of f(ln5) is
Sol. 0
f(x) = ∫0 x f(t) dt => f(0) = 0
also, f'(x) = f(x), x > 0
=> f'(x) = kex, x > 0
f(0) = 0 and f(x) is continuous => f(x) = 0 for all x > 0
f(ln5) = 0.
13. The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and 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
Sol. 8
cosa = 2√2/3
sina = 1/3
tana = 2√2/R
=> R = 2√2/tanα = 8 units
Alternate Solution:
We have , from the figure
(R + 1)2 = (R - 1)2 + (4√2)2
=> R = 8.
<< Back || Next >>
Signing up with Facebook allows you to connect with friends and classmates already using askIItians. It’s an easier way as well. “Relax, we won’t flood your facebook news feed!”
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
IIT JEE 2009 Mathematics Paper2 Code 1 Solutions...
