Mechanical Engineering Gate 2013 Set-1 Questions with Answer

Ques 14 GATE 2013 SET-1

Choose the grammatically INCORRECT sentence:

Ques 15 GATE 2013 SET-1

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

Ques 16 GATE 2013 SET-1

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?

Ques 17 GATE 2013 SET-1

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

Ques 18 GATE 2013 SET-1

Find the sum of the expression
1/(√1+√2) + 1/(√2+√3) + 1/(√3+√4) + ... + 1/(√80+√81)

Ques 19 GATE 2013 SET-1

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

Ques 20 GATE 2013 SET-1

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

Ques 21 GATE 2013 SET-1

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure. 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

Ques 22 GATE 2013 SET-1

Two 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 bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is

Ques 23 GATE 2013 SET-1

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 = 1 m, the magnitude of the absolute acceleration of the block at location A in m/s² is

Ques 24 GATE 2013 SET-1

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

Ques 25 GATE 2013 SET-1

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

Ques 26 GATE 2013 SET-1

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.