The number of points in `[-oo,oo)` for which `x^(2)-xsin x - cos x=0` is

The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is 6 (b) 4 (c) 2 (d) 0

Find the number of integral vaues of 'a' for which the range of function f (x) = (x ^(2) -ax +1)/(x ^(2) -3x+2) is (-oo,oo),

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)

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. The minimum number of points where f'(x) is zero is: (a) 1 (b) 2 (c) 3 (d) 4

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)

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

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

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

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