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Column 1: real valued function, Column-2: domain of the function, Column 3: range of the function. Match the following Column(s) (where [.] denotes the greatest integer function and {.} denotes fractional part function) Which of the following combination is correct?A. (I)(iv)(P)B. (I)(iv)`(R)`C. (II)(ii)`(R)`D. (III)(i)(S) |
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Answer» Correct Answer - B::C (I) `((3-1)^(3))/3le |x-1|^(3)+|x-3|^(3)ltoo` (II) `u=sin(In((sqrt(4-x^(2)))/(1-x)))+cos(In((sqrt(4-x^(2)))/(1-x)))` `:.0le (sqrt(4-x^(2)))/(1-x) lt oo` `-oo lt In ((sqrt(4-x^(2)))/(1-x))lt oo` So, `-sqrt(2) le u le sqrt(2)` (III) Let `|x+5|=t,g(t) in (0, 1/2]-{1/4}` `g(t)=((t-2))/((t-2)(t+2))` (IV) `thetalecos^(-1)xlepi` `-oo lt In (cos^(-1)x)le In pi lt 2` |
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