List of top Questions asked in GATE XE

Glass-fiber composite: 40% glass fibers ($E_f = 69$ GPa), 60% polyester resin ($E_m=3.4$ GPa). Find modulus of elasticity of composite in longitudinal direction.
Choose the correct group of fat-soluble vitamins.
The synthesis of thyroxine T4 in the human body requires .............
Among the options given, which agents are used to vulcanize or cure rubbers?
Lipase is a natural enzyme, which cleaves carboxylic ester bonds. Among the options given, identify the polymer(s) degraded by lipase.
Among the options given, identify the correct pair(s) of catalyst and co-catalyst that form a Ziegler–Natta catalyst.
Stress versus elongation profiles for different polymeric materials are shown in the figure. Choose the combination that best describes these profiles.
Among the options given, which method(s) is/are used for the synthesis of atactic polystyrene?
Polymer wetting is improved by the addition of fillers with functional groups. In a typical case-study, natural-clay was modified with hydroxyl groups and compounded with Nylon 6 along with an antioxidant. The resulting composite exhibited poor mechanical properties. Which one among the options given explains this observation?
Among the options given, identify the correct match between the polymers and their glass transition temperatures ($T_g$).
Choose the correct option that best correlates the graphs with the polymerization methods.
In an air-conditioning system, air enters at 20$^\circ$C and 30% relative humidity at a steady rate of 30 m$^3$/min in a humidifier and it is conditioned to 25$^\circ$C and 60% relative humidity. Assuming entire process takes place at pressure of 100 kPa, the mass flow rate of steam added to air in the humidifier is $____________$ kg/min (rounded off to three decimal places).
An office uses a heat pump to receive 500 kJ/day heat in winter to maintain its temperature at 300 K. The ambient temperature is 280 K. If the COP of the heat pump is 60% of its theoretical maximum value, the ratio of actual work input to the minimum theoretical work input to the heat pump is $____________$ (rounded off to one decimal place).
In a liquid-vapour phase change process, $\left(\dfrac{dP}{dT}\right)_{sat}$ at 100$^\circ$C for saturated water is 3750 Pa/K. If the resulting change in specific volume ($v_g - v_f$) is 1.672 m$^3$/kg, the enthalpy of vaporization ($h_{fg}$) will be $____________$ kJ/kg (in integer).
Which one of the monomers given is used in the synthesis of cellulose?
A copper wire upon loading instantaneously increases in length to $l$, and then continues to elongate gradually. Upon unloading, the wire retracts to length $l$. According to the Maxwell model, which one of the options given correctly relates the total strain $E$, the applied stress $S$, the modulus $G$, the material’s resistance to flow $\eta$, and the elapsed time $t$ between loading and unloading?
Consider the structure of a crosslinked polymer shown in the figure. From the options given, identify the monomers that are used in the synthesis of the polymer.
Among the options given, choose the most suitable compatibilizer for blending Polyvinylidene fluoride (PVDF) and Acrylonitrile butadiene styrene (ABS).
A high molecular weight polymer passes through different zones from the hopper to the die in an extruder. Among the options given, identify the correct match between the zones and their key functions.
A $5 \, kg$ metal block ($c_p = 0.5 \, kJ/kgK$) at $373 \, K$ is placed in $10 \, kg$ of water ($c_p = 4.2 \, kJ/kgK$) at $293 \, K$ inside an insulated rigid container. Find entropy change of universe.
Match the following thermodynamic functions/equations with their expressions:
A piston–cylinder device initially contains $1 \, m^3$ of air at $200 \, kPa$ and $25^\circ C$. Air expands at constant pressure while a heater of $250 \, W$ is switched on for 10 minutes. There is a heat loss of $4 \, kJ$. Assuming air as an ideal gas, the final temperature of air is $____________________$ $^\circ C$ (rounded off to one decimal place). Given: $R = 0.287 \, kJ/kgK$, $c_p = 1.005 \, kJ/kgK$.
Steam at 2 MPa and 300$^\circ$C steadily enters a nozzle of inlet diameter 20 cm. Steam leaves with a velocity of 300 m/s. The mass flow rate of steam through the nozzle is 10 kg/s. Assume no work interaction and no change in potential energy. If the heat loss from the nozzle per kg of steam is 3 kJ, the exit enthalpy per kg of steam is $__________$ kJ (rounded off to nearest integer). Given: At 2 MPa and 300$^\circ$C, $v = 0.12551 \, m^3/kg, \, h = 3024.2 \, kJ/kg$
A rigid tank of 2 $m^3$ internal volume contains 5 kg of water as a saturated liquid–vapor mixture at 400 kPa. Half of the mass of the saturated liquid in the tank is drained-off while maintaining constant pressure of 400 kPa. The final quality of the mixture remaining in the tank is $____________$ (rounded off to two decimal places). Given: At 400 kPa: $v_f = 0.001084 \, m^3/kg$, $v_{fg} = 0.46138 \, m^3/kg$, $v_g = 0.46246 \, m^3/kg$.
Consider a spark ignition engine which operates on an ideal air-standard Otto cycle. It uses a fuel which produces 44 MJ/kg of heat in the engine. If the engine requires 40 mg of fuel to produce 1 kJ of work output, then the compression ratio of the Otto cycle is $____________$ (rounded off to two decimal places). For the entire cycle, use $\dfrac{c_p}{c_v} = 1.4$.