Mechanical Engineering - (ME) 2018 GATE Paper (Practice Test - 2) - GATE MCQ

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

The value of the expression 

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

A wire would enclose an area of 1936 m², if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

An unbiased coin is tossed six times in a row and four different such trials are conducted.
One trial implies six tosses of the coin.

If H stands for head and T stands for tail, the following are the observations from the four trials:

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?  

The Fourier cosine series for an even function f (x) is given by

The value of the coefficient a 2 for the function f ( x) = cos ² ( x) in [0, π] is

The divergence of the vector field

Consider a function u which depends on position x and time t.

The partial differential equation
 
is known as the

If y is the solution of the differential equation , y(0) = 1 , the value of y(-1)is

The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is

A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is

In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?

Pre-tensioning of a bolted joint is used to

The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the temperature (in K) of the black body is

For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (Δs) from state 1 to 2?

Select the correct statement for 50% reaction stage in a steam turbine.

Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by 

During solidification of a pure molten metal, the grains in the casting near the mould wall are 

Match the following products with the suitable manufacturing process

Feed rate in slab milling operation is equal to

Metal removal in electric discharge machining takes place through

The preferred option for holding an odd-shaped workpiece in a centre lathe is

A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is

If  then det(A^-1) is __________ (correct to two decimal places).

A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ________ (correct to two decimal places).