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

The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0

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 complete set of values of x for which (x^(3)(x-1)^(2)(x+4))/((x+1)(x-3)) ge 0 is

The set of values of a for which a x^2+(a-2)x-2 is negative for exactly two integral x , is a. (0,2) b. [1,2) c. (1,2] d. (0,2]

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

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

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)

The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the greatest integer less than or equal to x , is (a) R (b) [0,+oo) (c) (-oo,0) (d) none of these

Consider the ellipse (x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1. If f(x) is a positive decreasing function, then (a)the set of values of k for which the major axis is the x-axis is (-3,2)dot (b)the set of values of k for which the major axis is the y-axis is (-oo,2)dot (c)the set of values of k for which the major axis is the y-axis is (-oo,-3)uu(2,oo) (d)the set of values of k for which the major axis is the y-axis is (-3,-oo,)

For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is (-oo,-7]uu[1,oo) b. (-3,oo) c. (-oo,-7) d. [1,oo)