Previous Year Questions
1 paper · 65 questions — organised by subject with solutions and explanations.
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Given, , where and . All the variables are real. The total differential is
Given matrices and is skew-symmetric matrix of . is
The power series expansion of a function is given as for . The values of constants and , respectively, are
For the matrix , eigenvalue corresponding to the eigenvector is _____(in integer).
The following equation is solved using Newton-Raphson method with initial value . The value of first approximation is _____(round off to 2 decimal places).
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squa
"You are delaying the completion of the task. Send contributions at the earliest."
The Euler's method is used to solve , The step size is 0.1. The approximate value of is ________ (round off to 2 decimal places).
In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads
The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy fr
Two cards are drawn one after the other from a regular deck of 52 playing cards without replacement. The probability that the drawn cards are of different suits is
The non-linear differential equation from the following options is
References: : ____________ : Guidelines : Implement (By word meaning)
Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings
Three unbiased coins are tossed. Provided that at least two outcomes are tails, the probability of having all three outcomes as tails is
To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2. If the total cost of sand and cement to construct the wall is 1000 rupe
Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copie
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.)
The coefficient of in the polynomial is equal to ________.
Match the engineering materials at room temperature with the given crystal structures. Engineering material Crystal structure P Si 1 FCC Q Fe 2 HCP R Al 3 Diamond Cubic S Zn 4 BCC
A solid circular disk of 0.025 m thickness is used as flywheel. The density of the disk material is 7800 and the mass moment of inertia of the disk about its center is 4.36 . The radius, in m, of the
A massless beam is fixed at one end and supported on a roller at other end. A point force P is applied at the midpoint of the beam as shown in figure. The reaction at the roller support is
In an ideal air-standard Brayton cycle, air enters the compressor at 100 kPa and 300 K. Thermal efficiency of the cycle is 50 %. The heat added to air is 1000 kJ/kg. Air has constant specific heat kJ/
A pair of spur gears is designed to transmit 20 kW power at a pitch line velocity of 10 m/s. Diameter of the driving gear is 0.5 m. The tangential force, in N, between the driver and the driven gear i
The qualitative method of forecasting amongst the given options is
A symbol for surface texture parameters is shown in figure. The difference between maximum and minimum values of surface roughness ( ) is
A straight turning operation is carried out at the feed rate of 100 mm/min using a single point cutting tool with signature 8 - 8 - 5 - 5 - 7 - 25 - 0 (ASA).The spindle speed is 1600 rpm. The roughnes
As per the Fe-C phase diagram, the microstructure of plain carbon steel with 0.4 wt.% carbon at room temperature contains
A metal rod of diameter 14 mm is subjected to a tensile test. After the test, its cross-sectional diameter at the fractured end is 12 mm. The ductility, in %, is ________ (round off to 2 decimal place
Creep of mild steel at elevated temperature involves
Water flows through a pipe of diameter 0.02 m. The Reynolds number of the flow is 1000. The pipe is heated from outside with a uniform heat flux. The flow and heat transfer in the pipe are steady and
Under steady state conditions, superheated steam enters the turbine with enthalpy, and wet steam leaves the turbine at pressure . The heat loss is and work output is . Kinetic and potential energies f
A wooden cubical block of side 0.1 m has specific gravity (SG) of 0.75. It is held submerged in a pool of oil and water by a massless rigid wire as shown in figure. The density of water is 1000 and ac
A key of width and height of 6 mm each is used to fix a gear on a shaft of 20 mm diameter. The shaft is used to transmit 10 kW power at 600 rpm to the gear. Permissible shear stress in the key is 80 N
A thin cylinder has length L, diameter d, and thickness t. It is made of a material with modulus of elasticity E and Poisson's ratio . When the cylinder is subjected to an internal pressure P, the cha
Two plane parallel surfaces exchange heat by thermal radiation. A radiation shield is placed in between at equal distance from the two surfaces to reduce heat transfer. All surfaces are black with inf
The work sampling study, with 100 observations, revealed 25 % idle time of a worker. The number of observations required for % accuracy and 95.45 % confidence level is _____(in integer).
Travel details of two persons P and Q travelling from city X to city Y are given as Person Mode of travel Monetary worth of functions (travel time and comfort), in Rupees Ticket cost, in Rupees P Airc
There are four locations (P, Q, R, S) and four factors to be considered for setting up a facility. The scores (on a scale of 0 to 10, with 10 being the maximum) for the given locations and the weight
The standard time for completing a job on a machine is 10 minutes. Number of machines available is 5, each machine is available for 300 hours/month, and average machine utilization is 80 %. The maximu
Match the recording techniques used in method study with the most appropriate application areas. Recording technique Application area P Outline process chart 1 Factory layout – movement of workers Q S
Two products, P and Q, are sold in the ratio of 10:1. The fixed cost is Rs. 1,40,000. The selling price of P is Rs. 10/unit and Q is Rs. 40/unit. The variable costs of P and Q are Rs. 5/unit and Rs. 2
A CNC water jet cutting machine is used to cut a straight slot between the points (2, 1) and (10, 10) on the XY plane (dimensions are in mm). If the feed rate is 1.5 mm/s, the time, in s, required to
Number of minimum control points required to generate a quadratic B-Spline curve is
Match the machine elements with their functions. Machine element Function P Collet 1 Indexing Q Dividing head 2 Thread cutting R Lead screw 3 Holding the tool in place
The solidification of a cubical casting of side 100 mm takes place with volumetric solidification shrinkage and solid contraction of 10 % each. The shape of the casting is retained on cooling to room
A cylindrical casting has 10 cm diameter and a mass of 12.56 kg. The material density is kg/cm . The value of exponent 'n' is 2 and solidification time is 12 min. The Chvorinov's constant, in min/cm ,
The most appropriate process for manufacturing of plastic chair is
Match the products to be manufactured with the given metal working processes. Product Process P Beverage can 1 Forging Q Seamless pipe 2 Skew Rolling R Connecting rod 3 Extrusion S Steel balls for bea
A copper rod of 200 mm diameter and 400 mm length is extruded to the final diameter of 100 mm. The extrusion ratio is
In NC machine, the function of interpolator is to
The combination of Directrix and Generatrix in a machining operation is shown in figure. The surface produced is
An arc welding operation is performed at 25 V and 200 A at welding speed of 2 mm/s. The heat used for melting is 80 % of the total heat generated. The unit melting energy of the metal to be joined is
Two metal sheets are joined using resistance spot welding. A welding current of 4500 A is applied for 0.2 s. The effective contact resistance at the sheet interface is . The thermal efficiency of the
Transformation matrix to translate a point P from (10, 15) to (15, 25) is
As per the ANSI marking system, a grinding wheel with alumina as abrasive is designated as 51 A 36 K 5 V 23 Here, K indicates that
Vacuum in the machining zone is an essential requirement for
In an orthogonal cutting with a tool of rake angle , the value of the cutting force is two times of the thrust force. The coefficient of friction is _____(round off to 1 decimal place).
The dual of a LPP is [equation] subject to, [equation] and for The objective function of the primal is
Six jobs (1, 2, 3, 4, 5, 6) undergo drilling, followed by reaming operation. The time required for each operation is given as Job Drilling(min) Reaming(min) 1 30 45 2 30 15 3 60 40 4 20 25 5 35 28 6 4
Details of activities of a project are given as Activity A B C D E F G H I J Time (days) 8 10 8 7 16 15 18 14 9 4 Predecessors - - - A A B, D C C F, G E, I, H The time required, in days, to complete t
The information of two products P and Q is given as Product Annualdemand(units) Ordering costper order(Rupees) Holding costper unit per year(Rupees) P 2500 60 30 Q 3600 80 40 The value of is _____(rou
A system shown in figure has seven components with reliabilities , , , , , , and .The reliability of the system is _____(round off to 2 decimal places).
A system has 10 essential components. Each component has an exponential time-to-failure distribution with constant failure rate of 0.04 per 4000 hours.The mean-time-to-failure, in hours, of the system
The total number of nonconformities is 420 from 30 samples. The size of each sample is 100. The lower control limit for the control chart for number of nonconformities is ________ (round off to 2 deci