Question 1. Consider the differential equation x2 d2y/dx2 + x dy/dx - 4y = 0 with the boundary conditions of
y(0) = 0 and y(1) = 1. The complete solution of the differential equation is

Question 2. x + 2y + z = 42x + y + 2z = 5x - y + z = 1The system of algebraic equations given above has

Question 3. Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal
interviews to collect and collate economic data. Requirements: High School-pass, must be
available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed. Which one of the following is the best inference from the above advertisement?

Question 4. A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x “ 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is

Question 5. An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable.
Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y
is

Question 6. Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged

Question 7. Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counter flow heat exchanger with a mass flow rate of 0.5 kg/s. Air (Cp = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is

Question 8. A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by ∆T. If the thermal coefficient of the material is α, Young's modulus is E and the Poisson's ratio is υ , the thermal stress developed in the cube due to heating is

Question 9. A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear
stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design
diameter in mm is

Question 10. A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one
after another, without replacement. The probability that the selected set contains one red ball and
two black balls is