Previous Year Questions
1 paper · 65 questions — organised by subject with solutions and explanations.
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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 mu
The eigenvalues of matrix A = are 5 and 10. For matrix B = A + αI, where α is a constant and I is 2 × 2 identity matrix, its eigenvalues are
If (3i + 1)x + (4i + 4)y + 5 = 0 with x, y being real and i = , then x = ________. [ correct up to one decimal place ]
Values of function y(x) at discrete values of x for 0 ≤ x ≤ 10 are given in table. Using trapezoidal rule, y(x)dx = _______. [ round off to one decimal place ] x 0 1 2 3 4 5 6 7 8 9 10 y(x) 5 3
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
A retail chain company has identified four sites A, B, C and D to open a new retail store. The company has selected four factors as the basis for evaluation of these sites. The factors, their weights,
The minimum value of function f defined by f(x, y, z) = x 2 + 5y 2 + 5z 2 - 4x + 40y - 40z + 300 is _____ [ in integer ]
The probability mass function P(x) of a discrete random variable X is given by P(x) = , where x = 1, 2, ⋯ , ∞. The expected value of X is _______. [ in integer ]
p and q are positive integers and then,
Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to
The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
Given below are two statements and two conclusions. Statement 1: All purple are green. Statement 2: All black are green. Conclusion I: Some black are purple. Conclusion II: No black is purple. Based o
Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular convex hexagon to the area of the original equilater
Nostalgia is to anticipation as _______ is to ________. Which one of the following options maintains a similar logical relation in the above sentence?
The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above. The number of days in the given week in which one of the students spent a m
Consider the following sentences: (i) I woke up from sleep. (ii) I woked up from sleep. (iii) I was woken up from sleep. (iv) I was wokened up from sleep. Which of the above sentences are grammaticall
The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________.
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 tensi
A fluid with dynamic viscosity μ = 1 Pa.s is flowing through a circular pipe with diameter 1 cm. If the flow rate (discharge) in the pipe is 0.2 liter/s, the maximum velocity in m/s of the fluid in
A circular rod of length l = 2 m is subjected to a compressive load P , as shown in the figure. The bending (flexural) rigidity of the rod is 2000 Nm 2 . If both ends are pinned, then the critical loa
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 th
A M30 bolt needs to be subjected to pretension F i = 350 kN. If the torque coefficient K of the bolt is 0.2, then the torque in Nm needed to achieve this pretension 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 σ
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
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
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 efficie
Which one among the following mechanisms is NOT used for transforming rotation to translation in machine tools?
Pearlite microstructure in an eutectoid steel consists of alternating layers of two phases, namely α ferrite and
The dimensionless number defined by the ratio of inertial force to viscous force is called
A cantilever beam of length 0.3 m is subjected to a uniformly distributed load C = 10 kN/m, as shown in the figure. The bending (flexural) rigidity of the beam is 5000 Nm 2 . Neglecting the self-weigh
Heat is being removed from a refrigerator at a rate of 300 kJ/min to maintain its inside temperature at 2° C. If the input power to the refrigerator is 2 kW, the coefficient of performance of the
Two cylindrical parts of equal length l, as shown in the figure, made of steel having Young’s modulus E = 200 GPa and Poisson’s ratio v = 0.33 are press fitted upon one another. If radial
Temperature field inside a sphere of radius R = 1 m with origin at its center is T(x, y, z) = 100 – 70x + 51y – 80z – 10x 2 – 20y 2 – 20z 2 . If thermal conductivity of t
Consider the truss shown in the figure. The members AB, BC, and CA are all rigid and form an equilateral triangle. The contact between roller and ground at C is frictionless. If the self-weight of mem
A 30 kg smooth, solid sphere rests on two frictionless inclines as shown in the figure. The magnitude of contact force in N acting at the point A is (take acceleration due to gravity g = 9.81 m/s 2 an
Which one of the following is NOT a measure of forecast error?
In a typical product development process under concurrent engineering approach, all elements of product life cycle from conception to disposal are considered at
Which one of the following is an improvement type heuristic algorithm for computerized layout design technique?
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
A machine shop has received four jobs A, B, C and D for processing on a single CNC machine. All jobs are available for processing on the first day of the production schedule calendar, and processing t
A project consists of eight activities. The time required for each activity and its immediate predecessor(s) are given in the table below. Activity Activity time (in days) Immediate predecessor(s) A 2
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
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.
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
A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the req
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 o
A product has an exponential time-to-failure distribution with a constant failure rate of 0.00006 per hour. The reliability of the product after 4000 hours of operation is
The top layer of a flat 750 mm × 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 t
In a turning operation, doubling the cutting speed ( V ) reduces the tool life ( T ) to 1/8 th of the original tool life. The exponent n in the Taylor’s tool life equation, VT n = C is
‘GO’ and ‘NO-GO’ snap gauges are to be designed for a hole mm. Gauge tolerance can be taken as 5% of the hole tolerance. Following the ISO system of gauge design, the respectiv
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
A 3 mm thick steel sheet, kept at room temperature of 30° C, 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
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 weldin
In a shaft-hole assembly, the hole is specified as 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 betwee
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 perfo
In a point-to-point open-loop NC drive, a stepper motor with 1.8° step angle is coupled to a leadscrew through a gear reduction of 4 : 1 (4 rotations of the motor enables 1 rotation of leadscrew).
A 3.5 mm thick sheet is rolled using a two high rolling mill to reduce the thickness under plane strain condition. Both rolls have a diameter of 500 mm and are rotating at 200 RPM. The coefficient of
A company is producing a disc-shaped product of 50 mm thickness and 1.0 m diameter using sand casting process. The solidification time of the above casting process is estimated by Chvorinov’s eq
Which one of the following defects is NOT associated with welding processes?
Match the component with the corresponding manufacturing process in the table below. Component Manufacturing process P Aluminum alloy piston for IC engine 1 Blow molding Q Low carbon steel oil pan 2 P
Match the measuring feature with the corresponding measuring instrument in the table below. Measuring feature Measuring instrument P Flatness error of a surface plate 1 Autocollimator Q Profile of a c
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
A single point cutting tool with 15° 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 c