Gate 2011 Mechanical Engineering (ME) Question Paper

A streamline and an equipotential line in a flow field

If a mass of moist air in an airtight vessel is heated to a higher temperature, then

In a condenser of a power plant, the steam condenses at a temperature of 0 . The cooling water enters at 0 and leaves at 0 . The logarithmic mean temperature difference (LMTD) of the condenser is

A simply supported beam PQ is loaded by a moment of 1kN-m at the mid-span of the beam as shown in the figure. The reaction forces and at supports P and Q respectively are

A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is

The maximum possible draft in cold rolling of sheet increases with the

The operation in which oil is permeated into the pores of a powder metallurgy product is known as

A hole is dimension mm. The corresponding shaft is of dimension mm. The resulting assembly has

Heat and work are

A column has a rectangular cross-section of 10mm x 20mm and a length of 1m. The slenderness ratio of the column is close to

A series expansion for the function sinq is

Green sand mould indicates that

What is equal to?

Eigen values of a real symmetric matrix are always

A pipe of 25mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 5W / K . It is proposed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of 0.05W / mK. Which one of the following statements is TRUE?

The contents of a well-insulated tank are heated by a resistor of 23 in which 10A current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer to the system are positive. The rates of heat (Q), work (W) and change in internal energy (U) during the process in kW are

Match the following criteria of material failure, under biaxial stresses and and yield stress , with their corresponding graphic representations :

The product of two complex numbers 1 + i and 2-5i is

Cars arrive at a service station according to Poisson’s distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10minutes. At steady state, the average waiting time in the queue is

The word kanban is most appropriately associated with

If f(x) is an even function and a is a positive real number, then f(x) dx equals

The coefficient of restitution of a perfectly plastic impact is

A thin cylinder of inner radius 500mm and thickness 10mm is subjected to an internal pressure of 5MPa. The average circumferential (hoop) stress in MPa is

Which one among the following welding processes uses non-consumable electrode?

The crystal structure of austenite is

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist at the free end is

Figure shows the schematic for the measurement of velocity of air (density = 1.2kg / ) through a constant–area duct using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg / ) in the two columns of the manometer is 10mm. Take acceleration due to gravity as 9.8m / . The velocity of air in m/s is

The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 2800kJ/kg and 1800kJ/kg respectively. Neglecting pump work, the specific steam consumption in kg/kW-hour is

The integral dx, when evaluated by using Simpson’s 1/3 rule on two equal subintervals each of length 1, equals

Two identical ball bearings P and Q are operating at loads 30kN and 45kN respectively. The ratio of the life of bearing P to the life of bearing Q is

For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. the length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is

A stone with mass of 0.1kg is catapulted as shown in the figure. The total force (in N) exerted by the rubber band as a function of distance x (in m) is given by . If the stone is displaced by 0.1m from the un-stretched position (x=0) of the rubber band, the energy stored in the rubber band is

Consider the differential equation x. The general solution with constant c is

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

A mass of 1kg is attached to two identical springs each with stiffness k = 20kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to

The shear strength of a sheet metal is 300MPa. The blanking force required to produce a blank of 100mm diameter from a 1.5 mm thick sheet is close to

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids P and Q on a flat plate are and 2 respectively. The Reynolds number based on the plate length for both the flows is . The Prandtl and Nusselt numbers for P are and 35 respectively. The Prandtl and Nusselt numbers for Q are respectively

The crank radius of a single–cylinder I. C. engine is 60mm and the diameter of the cylinder is 80mm. The swept volume of the cylinder in is

A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the density of the liquid as 990 kg / . The isentropic specific work done by the pump in kJ/kg is

A spherical steel ball of 12mm diameter is initially at 1000K. It is slowly cooled in a surrounding of 300K. The heat transfer coefficient between the steel ball and the surrounding is 5W / . The thermal conductivity of steel is 20W /mK . The temperature difference between the centre and the surface of the steel ball is

An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300K and 1500K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures in Kelvin at the end of the compression and expansion processes are respectively

A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

A 1 kg block is resting on a surface with coefficient of friction = 0.1. A force of 0.8N is applied to the block as shown in figure. The friction force is

Consider the following system of equations





This system has

A single–point cutting tool with rake angle is used to machine a steel work– piece. The depth of cut, i.e. uncut thickness is 0.81mm. The chip thickness under orthogonal machining condition is 1.8mm. The shear angle is approximately

Match the following non-traditional machining processes with the corresponding material removal mechanisms :

Machining process	Mechanism of material removal
P. Chemical machining	1. Erosion
Q. Electro-chemical machining	2. Corrosive reaction
R. Electro – discharge machining	3. Ion displacement
S. Ultrasonic machining	4. Fusion and vaporization

A cubic casting of 50mm side undergoes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No. riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is

Directions for next two questions: In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150kPa and 350K. The temperature at station Q is 300K.

The following are the properties and relations pertaining to air:

Specific heat at constant pressure, = 1.005kJ /kgK;

Specific heat at constant volume, = 0.718kJ /kgK;

Characteristic gas constant, R = 0.287kJ /kgK

Enthalpy, h = T

Internal energy, u = T

If the air has to flow from station P to station Q, the maximum possible value of pressure in kPa at station Q is close to

If the pressure at station Q is 50kPa, the change in entropy in kJ/kgK is

Directions for next two questions: One unit of product requires 3 kg of resource and 1kg of resource . One unit of product requires 2kg of resource and 2kg of resource . The profits per unit by selling product and are Rs.2000 and Rs.3000 respectively. The manufacturer has 90kg of resource and 100kg of resource .

The unit worth of resource i.e., dual price of resource in Rs. Per kg is

The manufacturer can make a maximum profit of Rs.

Directions for next two questions: A triangular–shaped cantilever beam of uniform–thickness is shown in the figure. The Young’s modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is

The maximum deflection of the beam is

Directions for next two questions: The temperature and pressure of air in a large reservoir are 400K and 3 bar respectively. A converging–diverging nozzle of exit area 0.005 is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287kJ/kgK and 1.4 respectively.

The density of air in kg/ at the nozzle exit is

The mass flow rate of air through the nozzle in kg/s is

Choose the word from the options given below that is most nearly opposite in meaning to the given word:

Amalgamate

Which of the following options is the closest in the meaning to the word below:

Inexplicable

If Log (P) = (1/2)Log (Q) = (1/3) Log®, then which of the following options is TRUE?

Choose the most appropriate word(s) from the options given below to complete the following sentence.

I contemplated________Singapore for my vacation but decided against it.

Choose the most appropriate word from the options given below to complete the following sentence.

If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or_____.

A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting.

Based on the above passage which topic would not be included in a unit on bereavement?

P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?