An unbiased die with faces marked $$1,2,3,4,5$$ and $$6$$ is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than $$2$$ and the maximum face value is not greater than $$5,$$ is then:

$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and $$F$$ happen is $$1/12$$ and the probability that neither $$E$$ nor $$F$$ happens is $$1/2.$$ Then,

A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. NO other information is available about its motion at intermediate times ( 0 < t < 1 ). If $$\alpha $$ denotes the instantaneous acceleration of the particle, then:

A uniform rod of length L and density $$\rho $$ is being pulled along a smooth floor with a horizontal acceleration $$\alpha $$ (see Fig.). The magnitude of the stress at the transverse cross-secion through the mid-point of the rod is _________.