1.

Match the following lists : A. `{:(a,b,c,d),(s,r,q,p):}`B. `{:(a,b,c,d),(q,s,r,p):}`C. `{:(a,b,c,d),(s,r,p,q):}`D. `{:(a,b,c,d),(r,p,s,q):}`

Answer» Correct Answer - B
(a) `sin^(-1) (3x -4x^(3)) in [-(pi)/(2), (pi)/(2)]`
`rArr pi - 3 sin^(-1) x in [-(pi)/(2), (pi)/(2)]`
`rArr 3 sin^(-1) x in [(pi)/(2), (3pi)/(2)]`
`rArr sin^(-1) x in [(pi)/(6), (pi)/(2)]`
`rArr x in [(1)/(2), 1]`
(b) `sin^(-1).(2x)/(1 + x^(2)) in [-(pi)/(2), (pi)/(2)]`
`rArr pi - 2 tan^(-1) x in [-(pi)/(2), (pi)/(2)]`
`rArr 2 tan^(-1) xin [(pi)/(2), pi)`
`rArr tan^(-1) x in [(pi)/(4), (pi)/(2))`
`rArr x in [1, oo)`
(c) `tan^(-1).(2x)/(1 -x^(2)) in (-(pi)/(2), (pi)/(2))`
`rArr 2 tan^(-1)x - pi in (-(pi)/(2), (pi)/(2))`
`rArr 2 tan^(-1) x in ((pi)/(2), pi)`
`rArr tan^(-1) x in ((pi)/(4), (pi)/(2))`
`rArr x in (1, oo)`
(d) `sin^(-1) (2x sqrt(1 -x^(2))) in [-(pi)/(2), (pi)/(2)]`
`rArr pi - 2 sin^(-1) x in [-(pi)/(2), (pi)/(2)]`
`rArr 2sin^(-1) x in [(pi)/(2), pi]`
`rArr x in [(1)/(sqrt2) ,1]`


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