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

The number of solutions of the equation x^2+2x^2+6x+2cosx=0in[0,2pi] is one (b) two (c) three (d) zero

The number of solutions of 12cos^3x-7cos^2x+4cosx=9 is 0 (b) 2 (c) infinite (d) none of these

The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi] is 2 (b) 3 (c) 4 (d) 0

The number of solution of sinx+sin2x+sin3x=cosx+cos2x+cos3x ,0lt=xlt=2pi, is (a)7 (b)5 (c) 4 (d) 6

The number of solutions of 2cosx=|sinx|,0lt=xlt=4pi, is 0 (b) 2 (c) 4 (d) infinite

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 number of points of intersection of two curves y=2sinxa n dy=5x^2+2x+3i s a . 0 b. 1 c. 2 d. oo

Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the set of values of a for which f is onto is (a) (0,oo) (b) [2,1] (c) [1/4,oo] (d) none of these

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)

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