The set of all real numbers `x` for which `x^2-|x+2|+x >0` is `(-oo,-2)` b. `(-oo,-sqrt(2))uu(sqrt(2),oo)` c. `(-oo,-1)uu(1,oo)` d.`(sqrt(2),oo)`

If two chords drawn from the point A(4,4) to the parabola x^2=4y are bisected by the line y=m x , the interval in which m lies is (-2sqrt(2),2sqrt(2)) (-oo,-sqrt(2))uu(sqrt(2),oo) (-oo,-2sqrt(2)-2)uu(2sqrt(2)-2,oo) none of these

If the ellipse (x^2)/(a^2-7)+(y^2)/(13-5a)=1 is inscribed in a square of side length sqrt(2)a , then a is equal to (a) 6/5 (b) (-oo,-sqrt(7))uu(sqrt(7),(13)/5) (c) (-oo,-sqrt(7))uu((13)/5,sqrt(7),) (d)no such a exists

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

Evaluate: lim_(x to oo) (sqrt(x+2)-sqrt(2))/(x) .

The range of a for which the equation x^2+ax-4=0 has its smaller root in the interval (-1,2)i s a. (-oo,-3) b. (0,3) c. (0,oo) d. (-oo,-3)uu(0,oo)

lim_(xto oo)(sqrt(4x^(2)+2x+1)-sqrt(4x^(2)+1)) is

Th range of k for which the inequaliity kcos^2x-kcosx+1>=0 AA x in(-oo,oo) is

The domain of the function f(x)=sqrt(log_((|x|-1))(x^2+4x+4)) is (a) (-3,-1)uu(1,2) (b) (-2,-1)uu(2,oo) (c) (-oo,-3)uu(-2,-1)uu(2,oo) (d)none of these

The domain of the function f(x)=sqrt(10-sqrt(x^4-21 x^2)) is [5,oo) b. [-sqrt(21),sqrt(21)] c. [-5,-sqrt(21)]uu[sqrt(21),5]uu{0] d. (-oo,-5)

The exhaustive set of values of a for which inequation (a -1)x^2- (a+1)x+ a -1>=0 is true AA x >2 (a) (-oo,1) (b)[7/3,oo) (c) [3/7,oo) (d) none of these