September 2023

Q. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is              (A) Linear                                 (B) […]

Q. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor F12 is (A) 0.0625 (B) 0.25 (C) 0.5 (D) 1.0 Ans: 1.0 Sol: By summation rule F1-1 + F1-2 = 1 ∵ F1-1 = 0 because no radiation leaving the surface 1

Q. A two-dimensional incompressible frictionless flow field is given by u = xˆi – yˆj . If r is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as Ans: – ρ (xi + yj)

Q. Endurance limit of a beam subjected to pure bending decreases with (A) decrease in the surface roughness and decrease in the size of the beam (B) increase in the surface roughness and decrease in the size of the beam (C) increase in the surface roughness and increase in the size of the beam (D)

Q. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is Ans: Option A

Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio ν = 0.3 are given. The principal strains in the plane of

Q. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of points P and R are VP and VR , in the x and y directions, respectively. The

Q. An analytic function f ( z ) of complex variable z = x + i y may be written asf ( z)= u ( x, y) + i v (x, y) . Then, u ( x, y) and v ( x, y) must satisfy Sol: Analytic function f(z) = u (x, y) + iv (x, y) If f(z) = u +

Q. The directional derivative of the function f (x, y) = x2 + y2 along a line directed from (0,0) to (1,1), evaluated at the point x = 1, y = 1 is     (A) √2 (B) 2   (C) 2√2   (D) 4√2 Ans: 2√2 Sol: