The number of integral vaues of which `f : R to R ,f (x) = (x ^(2))/(3) + (m -1) x ^(2) + (m +5) x+n` is bijective is :

The number of integral values of m for which f : R to R ,f (x) = (x ^(2))/(3) + (m -1) x ^(2) + (m +5) x+n is bijective is :

The number of integral values of a for which f(x)=x^(3)+(a+2)x^(2)+3ax+5 is monotonic in AA x in R

The number of integral values which can be taken by the expression, f (x) = (x ^(3)-1)/((x-1) (x ^(2) -x+1)) for x in R, is:

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),

The number of integral values of m for which the quadratic expression (1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R , is always positive is

Let f : R to R be defined by f(x) = x^(3) + x^(2) + 5x + 2 sin x , Then

Let a_(m)(m=1,2, p) be the possible integral values of a for which the graphs of f(x)=ax^(2)+2bx+b and g(x)=5x^(2)-3bx- ameets at some poin for which the graphs o t for all real values of b Let t_(r)=prod_(m=1)^(m=1)(r-a_(m)) and S_(n)=sum_(r=1)^(n)t_(r).n in N The minimum possible value of a

Let f: R to R be defined by f(x) = 5^(2x)/(5^(2x) + 5) , then f(x) + f(1-x) is equal to

f:R rarr R,f(x)=(2x^(2)-5x+3)/(8x^(2)+9x+11), then f is

Which of the followingthe followings is not f:R rarr R,f(x)=x^(3)+x^(2)+3x+sin x is bijective