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theta is said to be well behaved if it l...

`theta` is said to be well behaved if it lies in interval `[0,(pi)/(2)].` They are intelligent if they make domain of `f +g and g` equal. The vlaue of `theta` for which `h (theta)` is defined are handosome. Let
`f (x)= sqrt(thetax ^(2) -2 (theta^(2) -3) x-12theta,) g (x)=ln (x^(2) -49),`
`h (theta) ln [int_(0)^(theta) 4 cos ^(2)t dt - theta ^(2)],` where `theta` is in radians.
Complete set of vlaues of `theta` which are well behaved as well as intellignent is:

A

`(0, (pi)/(2)]`

B

`[(6)/(7), (pi)/(2)]`

C

`[(3)/(4), (pi)/(2)]`

D

`[(3)/(5), (pi)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
B
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theta is said to be well behaved if it lies in interval [0,(pi)/(2)]. They are intelligent if they make domain of f +g and g equal. The vlaue of theta for which h (theta) is defined are handosome. Let f (x)= sqrt(thetax ^(2) -2 (theta^(2) -3) x-12theta,) g (x)=ln (x^(2) -49), h (theta) ln [int_(0)^(theta) 4 cos ^(2)t dt - theta ^(2)], where theta is in radians. Complete set of alues of theta which are intelligent is :

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