List of top Mathematics Questions asked in GATE NM

Consider a truss as shown in the following figure. The length of each member is 2 m. The area of cross section of each member is 100 \(mm^2\) and Young's modulus is \(2 x 10^5 N/mm^2\). The vertical deflection at C is .................... mm (round off to one decimal place) 

An air-standard diesel cycle, as shown in the following figure with a compression ratio of 16, has an initial pressure 0.9 bar and temperature 300 K. Assume \(\gamma = 1.4\) and \(C_p = 1.004\) kJ/kg-K. If the heat added during the constant pressure process is 900 kJ/kg, then the peak temperature during the cycle is .................... K (round off to the nearest integer) 

 

A simple vapor compression refrigeration cycle with ammonia as the working fluid operates between 30°C and -10 °C as shown in the following figure. The saturated liquid and vapor enthalpies at 30 °C and -10 °C are provided in the table below. If the COP of the cycle is 5.6, the specific enthalpy at the inlet to the condenser is .................... kJ/kg (round off to the nearest integer) 

A vessel of 100 m length has a constant triangular cross-section with a depth of 12 m and breadth of 15 m as shown in following figure. The vessel has a vertical center of gravity (KG) = 6.675 m. The minimum draft (d), at which the vessel will become stable is .................... m (round off to one decimal place) 

 

A 'T' section is welded to the flat bottom shell plate of a ship as shown in the following figure (bottom shell longitudinal). The neutral axis of the ship's midship section is 14 m above the bottom shell plate. The distance (X) of neutral axis of the 'T' section from the ship's neutral axis is .................... m (round off to two decimal places) 

 

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)