GATE PI 2019 PYQ

If z is a complex variable with i = √-1, the length of the minor axis of an ellipse defined by |z - (1 + i) | + |z - (9 + i) | = 10 is ______

If the Laplace transform of e ωt is , the Laplace transform of t cosh t is

For a complex number z = 1 - 4i with i = √-1, the value of is

The solution of is

General solution of the Cauchy-Euler equation is

For any real, square and non-singular matrix B , the det B -1 is

The vector that is normal to the surface 2xz 2 - 3xy - 4x = 7 at the point (1, -1, 2) is

The numerical value of the definite integral using trapezoidal rule with function evaluations at points x = 0, 0.5 and 1 is ______ (round off to 3 decimal places)

If roots of the auxiliary equation of are real and equal, the general solution of the differential equation is

Two trains started at 7 AM from the same point. The first train travelled north at a speed of 80 km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km ap

Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. F

The fishermen, _______ the flood victims owed their lives, were rewarded by the government.

Some students were not involved in the strike. If the above statement is true, which of the following conclusions is/are logically necessary? 1. Some who were involved in the strike were students. 2.

The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is ______.

Until Iran came along, India had never been _________ in kabaddi.

Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below: 1. No two odd or even numbers are next to each other. 2. The second number from

The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and inst

In a country of 1400 million population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce por

“I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in

A cam is designed to achieve a simple harmonic motion of a flat-faced follower. Starting from the rest, the follower rises to the maximum height of 50 mm at 180° of cam rotation as shown in the fi

One kilogram of air is compressed at a constant temperature of 150°C until its volume is halved. Considering gas constant R = 0.287 kJ/kg-K for air, the magnitude of heat rejected (in kJ) in the c

During a storm, the wind speed is 90 km/hr. In a high-rise building, there is a window of size 1.2 m x 1.8 m facing the storm on an upper floor. Neglecting the ground effects on wind speed and conside

Three Carnot engines E 1 E 2 , E 3 ; operate as shown in the figure (T 1 > T 2 > T 3 ). The efficiency of the engine E 3 in terms of the efficiencies η 1 and η 2 of the engines E 1 and E 2 res

A uniform cantilever beam ABC of length L is subjected to a point load P at point B and a concentrated moment M at point C (as shown in figure). Let E be the Young’s modulus of the beam material

The link lengths of a planar four bar mechanism are AB = 100 mm, BC = 25 mm, CD = 75 mm and DA = 90 mm. For achieving the full rotation of both the input (crank) as well as the output (follower) links

A metallic rod of diameter d 0 is subjected to the tensile test. The engineering stress and the true stress at fracture are 800 MPa and 900 MPa, respectively. The ratio of the rod diameter at fracture

A heat pump is to supply heat at the rate of 10 kW to a building to be maintained at 22°C. The outside temperature is 2°C. The minimum power (in kW) required to run the heat pump is (round off

A thin walled cylindrical pressure vessel with an inside diameter of 300 mm and wall thickness of 3 mm is subjected to an internal gauge pressure of 1.5 MPa. The maximum shear stress (in MPa) at a poi

An open tank of 2 m x 2 m x 2 m is filled with layers of two fluids. Depth of each layer is one meter. The top layer is that of an oil of specific gravity 0.8. The bottom layer is of water. Consider t

Match the crystal structure in Column A with the corresponding packing fractions in Column B of the table Column A Column B 1. Simple cubic P. 0.74 2. Hexagonal close-packed Q. 068 3. Body-centered cu

An acceptance sampling plan is selected with sample size n = 80, acceptance number c = 2 for a lot size of 10,000 units. The probability of accepting the lot is based on Poisson distribution. Assuming

The capacity of a passenger airline is expressed in terms of

A firm, with a production target of 50,000 units/year, has the following data for the selection of a new location for its plant Location Fixed cost (Rs.) Variable costs per unit (Rs.) P 110,000 2 Q 95

A PERT project network consists of 5 activities A to E. The time estimates of these activities follow Beta-distribution. The predecessor—successor (P-S) relationships between the nodes and time

The average proportion non-conforming of 20 samples each of size 100 items is 0.12. The upper control limit for the relevant chart is ______ (round off to 2 decimal places)

A company has purchased an asset by investing Rs. 30,000. The useful life of the asset is 5 years and it has no salvage value at the end of its useful life. The depreciation cost (in Rs.) for the 2 nd

A company invests Rs. 50 thousand in assets. The initial investment is Rs. 30 thousand with two subsequent investments of Rs.10 thousand each at the end of 1 st year and 2 nd year. The useful life of

A warehouse has a loading dock and 3 persons for loading operations. The arrival rate of trucks follows a Poisson distribution with a mean of 4 trucks/hour. The average loading time (by three persons

In a work study experiment, normal time was recorded as 140 sec with a rating of 100%. Considering 2% allowance, the standard time (in s) is ______ (round off to 1 decimal place)

The man-hours required (T n ) to manufacture the n th unit in a plant is given by T n = T 1 n b , where b = -0.322 at the 80% learning rate. If the manufacturing time for the first unit (T 1 ) is 80 m

The layout for an AGV system is shown in figure. The loading time is 0.5 minutes and the unloading time is also 0.5 minutes. All distances are in meters. Considering a vehicle velocity of 50 m/min, av

REL chart is used in

A monitoring system has seven components. The reliability of each component is shown in the figure. The system reliability is ______ (round off to 2 decimal places)

The mean time to repair (MTTR) for a repairable system is 30 minutes. When maintenance time changes from 20 minutes to 40 minutes, the net increase in maintainability is closest to

The sales data of a product for 5 years are Year 2014 2015 2016 2017 2018 Sales (units) 280 268 259 270 287 Assume the forecast for the year 2014 as 260 units. Using an exponential smoothing method wi

For a classical (Wilson) model of determining economic order quantity (EOQ), the carrying and ordering costs are C r and C o , respectively. For an annual demand D, the minimum yearly total inventory

The SQC chart based on Binomial distribution is

An LPP is defined as Minimize z = 15x 1 + 12x 2 subject to, x 1 + 2x 2 ≤ 3 2x 1 - 4x 2 ≤ 5 x 1 , x 2 ≥ 0 The objective function of the dual of this LPP is

For a process which is in a state of statistical control (within ± 3σ), the estimated process standard deviation (σ) is 3 mm. The specification limits for the corresponding product

A process which is in a state of statistical control (within ± 3σ) has an estimate of standard deviation (σ) 2 mm. The specification limits for the corresponding product are 120 &pl

The end product obtained using spinning process is shown in the figure. The initial blank thickness is 2.5 mm. The blank diameter (in mm) is

Considering included angle θ of the thread to be 60° using the Best-Wire method, the difference between the effective diameter (E) and the dimension under the wire (T) for M 10 x 1.0 mm is c

During a turning operation of a specific work material having a shear strength of 220 MPa under orthogonal cutting condition, the process parameters are Feed 0.2 mm/rev Depth of cut 1 mm Rake angle -5

For the abrasive jet machining process, the ratio of abrasive volume to carrier gas volume is 0.25. Further, the ratio of abrasive density to carrier gas density is 25. The mass ratio of abrasive to t

A 20 mm HSS drill with a point angle of 118° is used for drilling a through hole on a metallic plate of thickness 100 mm with a cutting speed of 333.33 mm/s and feed of 0.22 mm/rev. Assuming that

The correct statement pertaining to the friction welding process is

The process used for producing continuous insulation coating on an electrical wire is

True centrifugal casting process in horizontal configuration is to be used for casting a metallic cylinder with outside diameter 0.275 m and inside diameter 0.250 m. If G-factor (ratio of centrifugal

A sand casting process has a mold constant of 2 s/mm 2 and solidification exponent of 2. If the solidification time is to be doubled for a given unit volume of material, the corresponding reduction in

In an NC milling operation, the tool path is generated using absolute programming for the trajectory shown in the figure The corresponding block of the NC program is

The heat transfer efficiency in arc welding of a plate using a current of 250 A at 20 V is 90%. The heat required to melt the material is 10 J/mm 3 . If the cross-sectional area of the weld joint is 3

A CO 2 laser in continuous mode is used for drilling a plate. The process parameters and their values are Laser power intensity 1 × 10 8 W/mm 2 Vaporization energy 5 × 10 6 J/mm 3 Efficien

A 100 mm long cylindrical workpiece of diameter 50 mm is reduced to 25 mm diameter using extrusion process. The flow curve for the metal has strength coefficient as K = 750 MPa and the strain hardenin

Ina sine bar, let h denote height of slip gauge and l be the distance between the rollers. The relationship between error in angular measurement (dθ) and errors in the slip gauge combination (dh

In a typical turning tool life test, the following data are generated for tools A and B: Tool name Cutting speed (m/min) Tool life (min) A 200 20 B 150 58 Assuming the same tool life exponent for the