GATE PH case studies
GATE PH · Put your knowledge to work in context.
GATE - the Graduate Aptitude Test in Engineering - is a computer-based examination conducted jointly by the Indian Institute of Science (IISc), Bangalore, and the Indian Institutes of Technology (IITs) on behalf of the Ministry of Education (MoE), Government of India. It tests a candidate's comprehensive understanding of undergraduate subjects in Engineering/Technology/Architecture and of post-graduate level subjects in Science. The GATE PH case studies are 5 cases and about 2,496 words.
1Keyhole Contour and the Missing Factor of Two
A student is asked to evaluate I = ∫ 0^∞ (ln x)/(x^2+4) dx. They use f(z) = (log z)^2/(z^2+4), with the branch cut on the positive real axis and 0 < arg z < 2π, and a keyhole contour.
575 words, about 3 min2Bead on a Rotating Hoop: Wrong Sign, Wrong Equilibrium
A bead of mass m slides without friction on a circular hoop of radius R = 0.50 m. The hoop rotates about its vertical diameter at constant angular speed ω.
495 words, about 2 min3Coaxial Cable Loss Budget: Dielectric Alone Is Not Enough
A 10 m length of coaxial cable has inner conductor radius a = 1.0 mm and outer conductor inner radius b = 4.0 mm. The dielectric has ε r = 2.25 and tanδ = 1.0×10^-3 at 1.0 GHz.
451 words, about 2 min4Degenerate Perturbation Theory: Zero Diagonal Does Not Mean No Splitting
A particle of mass m moves in a two-dimensional isotropic harmonic oscillator H0 = p²/(2m) + (1/2)mω²(x²+y²). The first excited level (n x+n y=1) is two-fold degenerate, spanned by 1,0 and 0,1 .
488 words, about 2 min5Schottky Anomaly and the Limits of Equipartition
A solid contains N = 1.0×10^22 independent two-level systems with energy gap Δ = 0.050 eV. A calorimetry student measures the heat capacity between 10 K and 600 K.
487 words, about 2 min