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 (a) `(-oo,-2)uu(0,oo)` (b) `{-4/5}` (c) `(-2,0)` (d) empty set

The exhaustive set of value of 'a' for which the function f(x)=a/3(x^3+(a+2)x^2+(a-1)x+2 possess a negative point of minima is (q,oo) . The value of q is

If the complete set of value(s) of a for which the function f (x) =(ax^(3))/(3)+(a+2) x^(2) +(a-1) x+2 possess a negative point of inflection is (-oo, alpha)uu(beta,oo)" then " |alpha|+|beta| is ___________ .

The set of all values of a for which the function f(x)=(a^2-3a+2)(cos^2\ x/4-sin^2\ x/4)+(a-1)x+sin1 does not possess critical points is (A) [1,oo) (B) (0,1) uu (1,4) (C) (-2,4) (D) (1,3) uu (3,5)

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

The set of all values of ' a ' for which the quadratic equation 3x^2+2(a^2-3a+2)=0 possess roots of opposite sign, is a. (-oo,1) b. (-oo,0) c. (1,2) d. (3//2,2)

The set of all values of m for which both the roots of the equation x^2-(m+1)x+m+4=0 are real and negative is (a) (-oo,-3]uu[5,oo) (b) [-3,5] (c) (-4,-3] (d) (-3,-1]

the interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing, is (a) ( -(oo) , (oo) ) (b) ( -(oo) , 0 ) (c) ( 2 , (oo) ) (d) ( 0 , 2 )

the interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing, is (a) ( -(oo) , (oo) ) (b) ( -(oo) , 0 ) (c) ( 2 , (oo) ) (d) ( 0 , 2 )

If (log)_3(x^2-6x+11)lt=1, then the exhaustive range of values of x is: (a) (-oo,2)uu(4,oo) (b) (2,4) (c) (-oo,1)uu(1,3)uu(4,oo) (d) none of these

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