List of practice Questions

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

The frequency of pulsing in a die-sinking electric discharge machine (EDM) is 10 kHz. The pulse off-time is set at 40 micro-seconds. The duty factor at this setting is

Pearlite microstructure in an eutectoid steel consists of alternating layers of two phases, namely \( \alpha \) ferrite and

Which one of the following defects is NOT associated with welding processes?

In a turning operation, doubling the cutting speed \(V\) reduces the tool life \(T\) to \( \frac{1}{8} \) of the original tool life. The exponent \(n\) in the Taylor’s tool life equation, \( V T^n = C \), is

Which one among the following mechanisms is NOT used for transforming rotation to translation in machine tools?

When acceptance number of a single sampling plan under attribute category is zero with sample size less than or equal to 10, the Operating Characteristic (OC) curve is

Which one of the following is an improvement type heuristic algorithm for computerized layout design technique?

Which one of the following is NOT a measure of forecast error?