wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let g(x)=x0f(t) dt where 12f(t)1,tϵ[0,1] and 0f(t)12 for tϵ(1,2), then [IIT Screening 2000]


A
32g(2)<12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
0g(2)<2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
32<g(2)52
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2<g(2)<4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 0g(2)<2

g(2)=20f(t)dt=10f(t)dt+21f(t)dt
As 12f(t)1 for 0t1,
1012dt10f(t)dt10t dt or 1210f(t) dt1(i)
As 0f(t)12 for 1<t2,210 dt21f(t) dt2112 dt
021f(t) dt12(ii)
Adding (i) and (ii), 12g(2)32
g(2) satisfies the inequality 0g(2)<2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Property 4
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon