For relation `2logy-logx-"log"(y-1)` a. Domain `=[4,+oo)`,range-`(1,+oo)` b. Domain `=[4,+oo),` range- `(2,+oo)` c. Domain `=(2,+oo)` ,range-`(2,+oo)` d. None of these

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

The least natural number a for which x+a x^(-2)>2AAx in (0,oo) is 1 (b) 2 (c) 5 (d) none of these

The domain of f(x)="log"|logx|i s (a) (0,oo) (b) (1,oo) (c) (0,1)uu(1,oo) (d) (-oo,1)

Let the functions defined in Column I (1+2x) , tan xhave domain (-pi/2, pi/2) and range (-oo, oo)

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1)= -8, then the range of f(x) is

IF the domain of the function f(x) =x^2 -6x +7 is (-oo , oo) then range of the function is

For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is (-oo,-7]uu[1,oo) b. (-3,oo) c. (-oo,-7) d. [1,oo)

The values of a for which the integral int_0^2|x-a|dxgeq1 is satisfied are (a) (2,oo) (b) (-oo,0) (c) (0,2) (d) none of these

Let f(x) be a function such that f(x)=(log)_(1/2)[(log)_3(sinx+a]dot If f(x) is decreasing for all real values of x , then a in (1,4) (b) a in (4,oo) a in (2,3) (d) a in (2,oo)

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(x)=0 has four real roots, then the range of values of leading coefficient of polynomial is