If he expression `[m x-1+(1//x)]` is non-negative for all positive real `x ,` then the minimum value of `m` must be `-1//2` b. `0` c. `1//4` d. `1//2`

For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2)) is

The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

The real number x when added to its inverse given the minimum value of the sum at x equal to 1 (b) -1 (c) -2 (d) 2

If f(x)={(sin(2x^2)/a+cos((3x)/b))^a b//x^2,x!=0e^3, x=0 is continuous at x=0AAb in R then minimum value of a is -1//8 b. -1//4 c. -1//2 d. 0

All the values of ' a ' for which the quadratic expression a x^2+(a-2)x-2 is negative for exactly two integral values of x may lie in [1,3/2] (b) [3/2,2) [1,2) (d) [-1,2)

If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-48=0, then the minimum value of (1//l)+(2//m)+(3//n) equals (a) 1 (b) 2 (c) 3//2 (d) 5//2

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

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]

The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime)(x^2) for all real xdot Given that f(1)=1 and f^(1)=8 , then the value of f^(prime)(1)+f^(1) is 2 b. 4 c. 6 d. 8

If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuous at x=0 then the value of m+n is a. 2 b. 3 c. -3 d. 7