Mechanical Engineering - ME 2013 GATE Paper (Practice Test) - GATE MCQ

Choose the grammatically INCORRECT sentence:

What will be the maximum sum of 44, 42, 40, ... ?

Q. No. 6 – 10 Carry Two Marks Each

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is

Find the sum of the expression

The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history.

Which one of the following assertions is best supported by the above information?

Q. No. 11 – 35 Carry One Mark Each

The partial differential equation  is a

The eigen values of symmetric matrix are all

Match the CORRECT pairs:

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E₁ to E₂ along the length of the rod, the normal stress developed at the section-SS is

The threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is

A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1m, the magnitude of the absolute acceleration of the block at location A in m/s² is

For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop Δp over a length L and the wall shear stress τ_w are related by

The pressure, dry bulb temperature, and relative humidity of air in a room are 1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is 4.25kPa, the specific humidity of the room air in kg water vapour/kg dry air is

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The  conductivity of the wall is given by k = k₀ + bT ; where k₀ and b are positive constants and T is temperature.

As x increases, the temperature gradient (dT / dx) will

In a rolling process, the state of stress of the material undergoing deformation is

Match the CORRECT pairs.

A metric thread of pitch 2mm and thread angle 60º is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is

Customers arrive at a ticket counter at a rate of 50 per hour and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in minutes is:

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm³/s is 

A cube shaped casting solidifies in 5 minutes. The solidification time in minutes for a cube of the same material, which is 8 times heavier than the original casting will be

For a ductile material, toughness is a measure of

In order to have maximum power from a Pelton turbine, the bucket speed must be

Consider one-dimensional steady state heat conduction along x-axis (0 < x < L) , through a plane wall with the boundary surfaces (x = 0 and x = L) maintained at temperatures 0ºC and 100ºC. Heat is generated uniformly throughout the wall. 

Choose the CORRECT statement.

A cylinder contains 5m³ of ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is