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 set of value(s) of a for which the function f(x)=(ax^(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

f(x) = x^2 increases on: (a) ( 0,oo) (b) (-oo,0) (c) (-7,-3) (d) (-oo,-3)

If the function f(x)=2x^(2)-kx+5 is increasing on [1,2], then k lies in the interval (a) (-oo,4)(b)(4,oo)(c)(-oo,8)(d)(8,oo)

if the complete set of values (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 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 range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

f(x)=(x-2)|x-3| is monotonically increasing in (a)(-oo,(5)/(2))uu(3,oo)(b)((5)/(2),oo)(c)(2,oo)(d)(-oo,3)

Range of the function f(x)=(ln x)/(sqrt(x)) is (a) (-oo,\ e) (b) (-oo,\ e^2) (c) (-oo,2/e) (d) (-oo,1/e)

The function f(x)=cot^(-1)x+x increases in the interval (a)(1,oo)(b)(-1,oo)(c)(-oo,oo)(d)(0,oo)

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),