Let `x_1 < alpha < beta < gamma < x_4, x_1 < x_2 < x_3`. If f(x) is a cubic polynomial with real coefficients such that `(f(alpha))^2 + (f(beta))^2 + (f(gamma))^2 = 0, f(x_1)f(x_2) < 0, f(x_2) f(x_3) < 0, F(x_1) f(x_3) >0` then which of the following are correct

Let f:R-(0,oo) be a real valued function satisfying int_(0)^(1)tf(x-t)dt=e^(2x)-1 then which of the following is/are correct?

Let f(x) be a non negative continuous and bounded function for all xge0 .If (cos x)f(x) lt (sin x- cosx)f(x) forall x ge 0 , then which of the following is/are correct?

Let f:R->[-1, 1] be defined as f(x) = cos(sin x), then which of the following is(are) correct ?

Let f:R rarr[-1,1] be defined as f(x)=cos(sin x), then which of the following is(are) correct?

Consider the points O(0,0),A(0,1), and B(1,1) in the x-y plane. Suppose that points C(x,1)andD(1,y) are chosen such that 0 < x < 1. And such that O,C,andD are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?.

Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fractional part of x. Then, which of the following is/are correct?

Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fractional part of x. Then, which of the following is/are correct?