Mechanical Engineering - ME 2014 GATE Paper (Practice Test) - GATE MCQ

The next term in the series 81, 54, 36, 24 … is ________

(Important - Enter only the numerical value in the answer) 

In which of the following options will the expression P < M be definitely true?

Q. No. 6 – 10 Carry Two Marks Each

Q. Find the next term in the sequence: 7G, 11K, 13M, ___

The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are:

(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest

A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour.

(Important - Enter only the numerical value in the answer) 

A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw material expenses increased by 30% and all other expenses increased by 20%. If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air purifier sold?

(Important - Enter only the numerical value in the answer) 

A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________

(Important - Enter only the numerical value in the answer) 

Q. No. 11 – 35 Carry One Mark Each
1. Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a = 0 , b = 0 with respective eigen vectors  . If a = b then x₁y₁ + x₂y₂ + x₂y₂ equals

If a function is continuous at a point,

Divergence of the vector field at (1, -1, 1) is

A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______

(Important - Enter only the numerical value in the answer)

The definite integral  is evaluated using Trapezoidal rule with a step size of 1. The correct answer is ________

(Important - Enter only the numerical value in the answer) 

A rotating steel shaft is supported at the ends. It is subjected to a point load at the centre. The maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance strength of the shaft material is 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of safety for the shaft is _______

(Important - Enter only the numerical value in the answer) 

Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear stresses developed in the two shafts are τ₁ and τ₂ . If R1 / R2=2, then τ₂ / τ₁ is _______

(Important - Enter only the numerical value in the answer) 

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m₂ of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

Which one of following is NOT correct?

Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is

Consider a long cylindrical tube of inner and outer radii, r_i and r_o , respectively, length, L and thermal conductivity, k. Its inner and outer surfaces are maintained at T_i and T₀, respectively ( T_i > T_O ). Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

Which one of the following pairs of equations describes an irreversible heat engine?

Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of statements.
I. The fluid is well-mixed
II. The fluid is unmixed
III. Re_D < 2300
IV. Re_D > 2300

For a gas turbine power plant, identify the correct pair of statements. 

P. Smaller in size compared to steam power plant for same power output

Q. Starts quickly compared to steam power plant

R. Works on the principle of Rankine cycle

S. Good compatibility with solid fuel

A source at a temperature of 500 K provides 1000 kJ of heat. The temperature of environment is 27^OC. The maximum useful work (in kJ) that can be obtained from the heat source is_______

(Important - Enter only the numerical value in the answer) 

A sample of moist air at a total pressure of 85 KPa has a dry bulb temperature of 30°C (saturation vapour pressure of water = 4.24 KPa). If the air sample has a relative humidity of 65%, the absolute humidity (in gram) of water vapour per kg of dry air is _______

(Important - Enter only the numerical value in the answer) 

The process utilizing mainly thermal energy for removing material is

The actual sales of a product in different months of a particular year are given below:

The forecast of the sales, using the 4-month moving average method, for the month of February is _______

(Important - Enter only the numerical value in the answer) 

A straight turning operation is carried out using a single point cutting tool on an AISI 1020 steel rod. The feed is 0.2 mm/rev and the depth of cut is 0.5 mm. The tool has a side cutting edge angle of 60°. The uncut chip thickness (in mm) is _______

(Important - Enter only the numerical value in the answer)