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

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 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

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2sin^2x/2 does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

The equation cos^8x+bcos^4x+1=0 will have a solution if b belongs to (A) (-oo,2] (B) [2,oo] (C) [-oo,-2] (D) none of these

The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^2+(a-1)x+2 possesses a negative point of inflection is (-oo,-2)uu(0,oo) (b) {-4/5} (-2,0) (d) empty set

Set of all real value of a such that f(x)=((2a-1)+x^2+2(a+1)x+(2a-1))/(x^2-2x+40) is always negative is a. -oo,0 b. 0,oo c. -oo,1//2 d. none

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

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

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 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)