Mechanical Engineering - (ME) 2018 GATE Paper (Practice Test - 1) - GATE MCQ

 A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters? 

 A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?  

F or integers a, b and c, what would be the minimum and maximum values respectively of
a + b + c if log |a| + log |b| + log |c| = 0?

 Given that a and b are integers and a +a² b³ is odd, which one of the following statements is correct?  

 From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?  

 Which of the following functions describe the graph shown in the below figure? 

 Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly. 
 
Which of the following statements can be logically inferred from the above statements? 

 Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is  

The rank of the matrix   

According to the Mean Value Theorem, for a continuous function f(x)in the interval [a,b], ab there exists a value in this interval such that

Fz is a function of the complex variable z = x + iy given by  F(z) = i z + k Re(z) + i Im(z).   For what value of k will F(z) satisfy the Cauchy-Riemann equations? 

 A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.    

  The tensions in the strings are

If σ₁ and σ₃ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

The equation of motion for a spring-mass system excited by a harmonic force is

where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to

For an Oldham coupling used between two shafts, which among the following statements are correct?
I. Torsional load is transferred along shaft axis.
II. A velocity ratio of 1:2 between shafts is obtained without using gears.
III. Bending load is transferred transverse to shaft axis.
IV. Rotation is transferred along shaft axis. 

For a two-dimensional incompressible flow field given by  which one of the following statements is FALSE?

Which one of the following statements is correct for a superheated vapour?

In a linearly hardening plastic material, the true stress beyond initial yielding

The type of weld represented by the shaded region in the figure is

Using the Taylor’s tool life equation with exponent n = 0.5, if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

A grinding ratio of 200 implies that the

Interpolator in a CNC machine

The time series forecasting method that gives equal weightage to each of the m most recent observations is

The number of atoms per unit cell and the number of slip systems, respectively, for a facecentered cubic (FCC) crystal are

A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is

A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is ____ (correct to two decimal places).

A four  bar mechanism  is made  up of  links of length  100, 200, 300 and 350 mm. If  the 350 mm link is fixed, the number of links that can rotate fully is __________.