List of top Questions asked in GATE PI

A single point cutting tool with \( 15^\circ \) orthogonal rake angle is used to machine a mild steel plate under orthogonal machining condition. The depth of cut (uncut thickness) is set at 0.9 mm. If the chip thickness is 1.8 mm, then the shear angle in degree is _________.
\text{[round off to one decimal place]}

The top layer of a flat 750 mm \( \times \) 300 mm rectangular mild steel plate is to be machined with a single depth of cut using a shaping machine. The plate has been fixed by keeping 750 mm side along the tool travel direction. If the approach and the over-travel are 25 mm each, average cutting speed is 10 m/min, feed rate is 0.4 mm/stroke, and the ratio of return time to cutting time of the tool is 1:2, the time (in minutes) required to complete the machining operation is _________.

A 3 mm thick steel sheet, kept at room temperature of 30ºC, is cut by a fiber laser beam. The laser spot diameter on the top surface of the sheet is 0.2 mm. The laser absorptivity of the sheet is 50%. The properties of steel are density = 8000 kg/m\(^3\), specific heat = 500 J/kg.°C, melting temperature = 1530ºC, and latent heat of fusion = \( 3 \times 10^5 \) J/kg. Assume that melting efficiency is 100% and that the kerf width is equal to the laser spot diameter. The maximum speed (in m/s) at which the sheet can be fully cut at 2 kW laser power is _________.

A time study is carried out for a spot welding operation which is being performed by an operator. The time taken (in seconds) for five observations are recorded as 40, 35, 45, 37 and 43, respectively. If the standard time and the allowance for this operation are 45 seconds and 9 seconds, respectively, then the performance rating (in percentage) of the operator is _________.

The initial cost of a machine is INR 10,00,000 and its salvage value after 10 years of use is INR 50,000. Using the straight line depreciation method, the book value in INR of the machine at the end of 7th year is _________.

A wire of 5 mm diameter is drawn into a wire of 4 mm diameter through a conical die at a constant pulling speed of 5 m/s. Neglecting the coefficient of friction and redundant work, the drawing stress \( \sigma_d \) in MPa for the above process is given by \( \sigma_d = \sigma \ln \left( \frac{1}{1 - r} \right) \), where \( \sigma \) is the mean flow strength of wire material in MPa, and \( r \) is the ratio of decrease in area of cross-section to initial area of cross-section of the wire. If the mean flow strength of wire material is 600 MPa, then the power required in kW in the above wire drawing process is _________.
\text{[round off to 2 decimal places]}

In an arc welding process, the DC power source characteristic is linear with an open circuit voltage of 60 V and short circuit current of 600 A. The heat required for melting a metal during the welding is 10 J/mm³, and the heat transfer and melting efficiencies are 80% and 25%, respectively. If the weld cross-sectional area of 20 mm² is made using the maximum arc power, then the required welding speed in mm/s is _________.
\text{[round off to one decimal place]}

A circular tank of 4 m diameter is filled up to a height of 3 m. Assuming almost steady flow and neglecting losses, the time taken in seconds to empty the tank through a 5 cm diameter hole located at the center of the tank bottom (take acceleration due to gravity \( g = 9.81 \, \text{m/s}^2 \)) is [round off to the nearest integer].

The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is _________.
\text{[round off to 3 decimal places]}

A tool of an NC machine has to move along a circular arc from (20,20) to (10,10), while performing an operation. The center of the arc is at (20,10). Which one of the following NC tool commands performs the above mentioned operation?

In a shaft-hole assembly, the hole is specified as \( 30.040^{0.000} \) mm. The mating shaft has a clearance fit with minimum clearance of 0.01 mm. The tolerance on the shaft is 0.03 mm. The maximum clearance in mm between the hole and the shaft is

‘GO’ and ‘NO GO’ snap gauges are to be designed for a shaft \( 36.000^{+0.070} \, +0.010 \) mm. Gauge tolerance can be taken as 5% of the hole tolerance. Following the ISO system of gauge design, the respective sizes of ‘GO’ and ‘NO GO’ gauges are

In the classical economic order quantity (EOQ) model, let \( Q \) and \( C \) denote the optimal order quantity and the corresponding minimum total annual cost (the sum of the inventory holding and ordering costs). If the order quantity is estimated incorrectly as \( Q' = 2Q \), then the corresponding total annual cost \( C' \) is

For a given process control chart, there are four rules for determining out-of-control state of the process which are being used simultaneously. The probability of Type-I error for the four rules are 0.005, 0.02, 0.03, and 0.05. Assuming independence of the rules, the probability of overall Type-I error when all the four rules are used simultaneously is

An in-control process has an estimated standard deviation of 2 mm. The specification limits of the component being processed are 120 ± 8 mm. When the process mean shifts to 118 mm, the values of the process capability indices, \( C_p \) and \( C_{pk} \), respectively, are

There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).

Heat is being removed from a refrigerator at a rate of 300 kJ/min to maintain its inside temperature at \( 2^\circ \text{C} \). If the input power to the refrigerator is 2 kW, the coefficient of performance of the refrigerator is _________.
\text{[round off to one decimal place]}

In an ideal Otto cycle, 800 kJ/kg is transferred to air during the constant volume heat addition process and 381 kJ/kg is removed during the constant volume heat rejection process. The thermal efficiency in % of the cycle is _________.

The minimum value of the function \( f(x, y, z) = x^2 + 5y^2 + 5z^2 - 4x + 40y - 40z + 300 \) is _________ (in integer).

A given steel has identical yield strength of 700 MPa in uni-axial tension and uni-axial compression. If the steel is subjected to pure shear stress such that the three principal stresses are \( \sigma_1 = \sigma, \sigma_2 = 0, \sigma_3 = -\sigma \) with \( \sigma_1 \geq \sigma_2 \geq \sigma_3 \), then the stress \( \sigma \) in MPa for the initiation of plastic yielding in the steel as per von Mises yield criterion is _________.
\text{[round off to 2 decimal places]}

A cylindrical mild steel tensile test specimen of gauge length 50 mm and diameter 10 mm is extended in two stages at a deformation speed of 4 mm/min. The specimen is extended from 50 mm to 55 mm in the first stage, and from 55 mm to 60 mm in the second stage. Neglecting elastic deformation, the total longitudinal true strain is _________.
\text{[round off to 2 decimal places]}

A M30 bolt needs to be subjected to pretension \( F_1 = 350 \, \text{kN} \). If the torque coefficient \( K \) of the bolt is 0.2, then the torque in Nm needed to achieve this pretension is _________.
\text{[in integer]}

A 150 mm wide polyamide flat belt is transmitting 15 kW power through a belt-pulley system. The driving pulley of 150 mm pitch diameter is rotating at 200 RPM. If \( F_1 \) is the belt tension on high tension side, and \( F_2 \) is the belt tension on low tension side, then the difference in belt tensions \( \Delta F = F_1 - F_2 \) in N is _________.
\text{[round off to one decimal place]}

The dimensionless number defined by the ratio of inertial force to viscous force is called

A small capillary tube of 3 mm inner diameter is inserted into a fluid having density 900 kg/m\(^3\), surface tension 0.1 N/m, and contact angle 30°. The rise in the height of fluid in the capillary tube due to surface tension is