1. A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is (round off to 2 decimal places). 2. The Laplace transform of a function f(t)is L(f)=- 1 (A) f(t) = (1-cos ot) (C) f(t)= cos cot f(1)=000s (s+w) Then, f(t) is (B) f(t)=sin oot 1 (D) f (t) = (1-sin cot) 3. A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure. r = 100mm decimal places). B RUM The rotor is driven by a motor at uniform angular speed of 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is N (round off to 2 4. The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the -t plane is 1 MPa, the Mohr's circle representation of the state-of-stress is given by (A) a circle with radius equal to principal stress and its center at the origin of the -t plane (B) a circle with a radius of 10 units on the - plane (C) a point on the taxis is distance of 10 units from the origin (D) a point on the axis at a distance of 10 units from the origin 5. A single-degree-of-freedom oscillator is subjected to harmonic excitation F(t) = F cos (cot) the figure. Ea F(t) FOR C as shown in The non-zero value of co, for which the amplitude of the force transmitted to the ground will be Fo, is (A) m (B) 2m 2k (D) 2 m m