Solution set of the inequality `1/(2^x-1)>1/(1-2^(x-1))` is `1,oo)` (b) `0,(log)_2(4/3)` (c) `(-1,oo)` `(0,(log)_2(4/3)uu(1,oo)`

The solution set of the inequality (log)_(10)(x^2-16)lt=(log)_(10)(4x-11) is 4,oo) (b) (4,5) (c) ((11)/4,oo) (d) ((11)/4,5)

The domain of the function f(x)=(sin^(-1)(3-x))/(I n(|x|-2))i s [2,4] (b) (2,3)uu(3,4] (c) (0,1)uu(1,oo) (d) (-oo,-3)uu(2,oo)

The domain of the function f(x)=1/(sqrt(|x|-x)) is: (1) (-oo,oo) (2) (0,oo (3) (-oo,""0) (4) (-oo,oo)"-"{0}

The true solution set of inequality (log)_((x+1))(x^2-4)>1 is equal to 2,oo) (b) (2,(1+sqrt(21))/2) ((1-sqrt(21))/2,(1+sqrt(21))/2) (d) ((1+sqrt(21))/2,oo)

The solution of the inequality (log)_(1/2sin^(-1)x >(log)_(1//2)cos^(-1)x is x in [(0,1)/(sqrt(2))] (b) x in [1/(sqrt(2)),1] x in ((0,1)/(sqrt(2))) (d) none of these

If a in R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] denotes the greatest integer le x ) has no integral solution, then all possible values of a lie in the interval: (1) (-2,-1) (2) (oo,-2) uu (2,oo) (3) (-1,0) uu (0,1) (4) (1,2)

The domain of the following function is f(x)=(log)_2(-(log)_(1/2)(1+1/((x^(1/4)))-1) (a) (0,1) (b) (1,0) (1,oo) (d) (1,oo)

The solution set of the equation sin^(-1)sqrt(1-x^2)+cos^(-1)x=cot^(-1)(sqrt(1-x^2))/x-sin^(-1)x is (a) [-1,1]-{0} (b) (0,1)uu{-1} (c) [-1,0)uu{1} (d) [-1,1]

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

Number of integers satisfying the inequality (log)_(1/2)|x-3|>-1 is.....