Consider a polynomial `f(x)=(a-1)x^2 + ax + a +1`. On the basis of above information, answer the following questions: If `f(x)gt 0AA xin R`, then set of values of 'a'is-

Let f : R -> R is a function satisfying f(2-x) = f(2 + x) and f(20-x)=f(x),AA x in R . On the basis of above information, answer the following questions If f(0)=5 , then minimum possible number of values of x satisfying f(x) = 5 , for x in [0, 170] is

Let f : R -> R is a function satisfying f(2-x) = f(2 + x) and f(20-x)=f(x),AA x in R . On the basis of above information, answer the following questions If f(0)=5 , then minimum possible number of values of x satisfying f(x) = 5 , for x in [10, 170] is

Let f : R -> R is a function satisfying f(2-x) = f(2 + x) and f(20-x)=f(x),AA x in R . On the basis of above information, answer the following questions If f(0)=5 , then minimum possible number of values of x satisfying f(x) = 5 , for x in [10, 170] is

If f(x)=|x-3|+2|x-1| and g(x)=-2x^(2)+3x-1 On the basis of above information answer the following questions: Minimum value of f(x) is

Let f(x)={x;x =0 and g(x)+{x^(2);x<-1 and 2x+3;-1<=x<=1 and x ; On the basis of above information,answer the following questions Range of f(x) is

Given int_(0)^(g(x))f(t)dt=h(x)+C, where g(x) is a polynomial and C is arbitrary constant, then On the basis of above information, answer the following questions: If g(x)=x, f(t)=((t-|t|)^(2))/(1+t^(2)), then h(x) will be equal to

Let f:R rarr[0,oo) be a derivable function which satisfies f(x^(2)+y^(2))=f(2xy)+f(x^(2)-y^(2))AA x,y in R Also f(1)=2 On the basis of above information,answer the following questions: f(3)+f(4) is equal to -

If f(x) is a monic polynomial of degree '3' such that lim_(x to 0) (1+f(x))^(1/(x^(2)))=e^(-3), g(x)=(f(x))/(x^(3))dx and g(1)=1 then On the basis of above information, answer the following question: Value of g(e) is

Let f,g, h be 3 functions such that f(x)gt0 and g(x)gt0, AA x in R where int f(x)*g(x)dx=(x^(4))/(4)+C and int(f(x))/(g(x))dx=int(g(x))/(h(x))dx=ln|x|+C . On the basis of above information answer the following questions: int f(x)*g(x)*h(x)dx is equal to

Let there are two functions defined of f(x)="min"{|x|,|x-1|,|x+1+] and g(x)="min"{e^(x),e^(-x)} on the basis of above information answer the following question: Number of solutions of f(x)=g(x) in the interval [0,1] is