If `(x-a) (x-b) lt 0`, then `x lt a, and x gt b`.

Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs intersect at the three points (0,4),(2,2) and (4,0) with f(x) gt g(x) for 0 lt x lt 2 and f(x) lt g(x) for 2 lt x lt 4 . If int_0^4[f(x)-g(x)]dx=10 and int_2^4[g(x)-f(x)]dx=5 the area between two curves for 0 lt x lt 2 ,is (A) 5 (B) 10 (C) 15 (D) 20

If -1lt x lt 0 then tan^(-1) x equals

Let f(x)={1+(2x)/a ,0lt=x<1 and ax ,1lt=x<2 If lim_(x->1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

If -1 lt x lt 0 , then cos^(-1) x is equal to

Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis(a) R = {(x, y) : 0 le x le a, 0 le y le b} (b) R = {(x,y) : 0 le x lt a, 0 le y le b} (c) R = {(x,y): 0 le x le a, 0 lt y lt b} (d) R = {(x,y): 0 lt x lt a, 0 lt y lt b}

If a lt 0 and b lt 0 , then (a +b)^(2) gt 0 .

If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4

If z =x +iy lies in the third quadrant then (barz)/(z) also lies in third quadrant if (i) x gt y gt 0 (ii) x lt y lt 0 (iii) y lt x lt 0 (iv) y gt x gt 0

If A = {x in R : 0 lt x lt 4} and B = {x in R : 1 le x le 7} then find A Delta B .