Question 11. The direction of vector A is radially outward from the origin, with |A| = k rn where r2 = x2 + y2 + z2 and k is a constant. The value of n for which ∇ . A = 0 is

Question 12. The maximum value of f(x) = x3 - 9x2 + 24x + 5 in the interval [1, 6] is

Question 13. The open loop transfer function of a unity negative feedback control system is given by G(s) = 150/[s(s + 9)(s + 25)]. The gain margin of the system is

Question 14. Water (density: 1000 kgm“3) stored in a cylindrical drum of diameter 1 m is emptied through a
horizontal pipe of diameter 0.05 m. A pitot-static tube is placed inside the pipe facing the flow.
At the time when the difference between the stagnation and static pressures measured by the pitotstatic
tube is 10 kPa, the rate of reduction in water level in the drum is,

Question 15. A U-tube manometer of tube diameter D is filled with a liquid of zero viscosity. If the volume of
the liquid filled is V, the natural frequency of oscillations in the liquid level about its mean position,
due to small perturbations, is

Question 16. The open loop transfer function of a unity gain negative feedback control system is given by G(s) = (s2 + 4s + 8)/[s(s + 2)(s + 8)]. The angle θ , at which the root locus approaches the zeros of the system,
satisfies

Question 17. A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is

Question 18. What is the chance that a leap year, selected at random, will contain 53 Saturdays?

Question 19. The set of values of p for which the roots of the equation 3x2+2x+p(p“1) = 0 are of opposite sign is

Question 20. Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement?