Question 51. After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before
committing suicide, he came across a spider attempting tirelessly to have its net. Time and again,
the spider failed but that did not deter it to refrain from making attempts. Such attempts by the
spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to
have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of
the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won
many a battle, and the rest is history. Which of the following assertions is best supported by the above information?

Question 52. Find the sum of the expression
1/(√1 + √2) + 1/(√2 + √3) + 1/(√3 + √4) + .... + 1/(√80 + √81)

Question 53. During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current
of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If
Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of
2000 A with 90% current efficiency, the expected material removal rate in gm/s will be

Question 54. A simply supported beam of length L is subjected to a varying distributed load sin(3 π x/L) Nm-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

Question 55. A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm2 of the bar for a factor of safety of 2 is

Question 56. A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10-4 seconds. The amplitude in mm of the resulting free vibration is

Question 57. Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67 * 10-8W/m2K4, the net radiation heat exchange rate in kW/m2 between the two plates is

Question 58. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is

Question 59. The solution to the differential equation d2u/dx2 - k du/dx = 0 where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

Question 60. The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s,
respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK
and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the
surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is