GATE Mechanical (ME) Practice Test: Engineering (ME)- 3 Free Online Test

Answer D Listlessness

Option D is correct.

Since is a subordinating conjunction that expresses reason; it properly introduces a clause giving the cause for the result stated in the main clause.

Despite and other concessive connectors express contrast and cannot directly introduce a finite clause without additional words (for example, despite the fact that), so option A is ungrammatical here.

Option B is incorrect because of subject-verb agreement and form errors: the noun should be plural and the verb form does not agree.

Option C uses besides, which normally adds information rather than states a cause; it is stylistically unsuitable to indicate the causal relationship required here.

Therefore, a conjunction indicating reason is required and Option D is the grammatically correct choice.

For steel and pinion gears tooth form factor (K) is 0.111 and modulus of elasticity for pinion and gear is 207 x 103 N/mm2.

Substituting these values in formula for deformation factor

C = K.e [(Ep x Eg ) / (Ep + Eg )]

C = 11500e

Therefore substituting value of e = 32 x 10-3, we get

C = 368 N/mm

Correct option: A ( 133.33 min ).

Number of cutting strokes per minute = 10 (one cutting stroke in each double stroke).

Feed per minute = 0.3 mm/stroke × 10 strokes/min = 3 mm/min.

Stroke length (width converted to mm) = 40 cm = 400 mm.

Time for single pass = stroke length ÷ feed per minute = 400 mm ÷ 3 mm/min = 133.33 min.

Therefore the planing time for a single pass is 133.33 min.

In a gas turbine operating on the Brayton cycle with intercooling, the effects of intercooling are as follows:

1. Efficiency of the cycle increases: True. Intercooling reduces the temperature of the compressed air between stages, which decreases the amount of work required by the compressor and results in improved overall cycle efficiency. The compression work is reduced, allowing more energy for the expansion process, which boosts efficiency.

2. Work ratio increases: True. With intercooling, the compressor work decreases, and as a result, the ratio of work output from the turbine to the work input to the compressor (the work ratio) increases.

3. Compressor work decreases: True. Intercooling reduces the temperature and, consequently, the volume of the compressed air, which reduces the compressor work required for the same pressure ratio.

So, all three statements are true.

To calculate the DC component of the periodic signal x(t)x(t), we find the average value over one period T₀:

Step 1: Formula for DC Component
The DC component (average value) is given by:
DC = (1/T₀) * ∫ x(t) dt over one period.

Step 2: Signal Analysis
The signal x(t)x(t):

• x(t)=1x(t) = 1 for |t| < T₁.
• x(t)=0x(t) = 0 for T₁ < |t| < T₀/2.

Integral Calculation

Since x(t)=1x(t) = 1 only between −T1-T₁ and T1T₁, integrate only over this range:
DC = (1/T₀) * ∫ (from -T₁ to T₁) 1 dt.

The integral of 1 over −T1-T₁ to T1T₁ is:
(T₁ - (-T₁)) = 2T₁.

Step 3: Final Result
DC = 2T₁ / T₀.

Correct Answer: (c) 2T₁ / T₀.

• For a non-ideal gas, use the Van der Waals equation:

  (P + a(n/V)²)(V - nb) = nRT

• Given:
  
  
  • n = 1 kmol
  
  
  • V = 0.15 m³ kg^-1 x 32 kg/kmol = 4.8 m³
  
  
  • T = 350 K
  
  
  • a = 139.35 x 10³ m⁶ Pa mol^-2
  
  
  • b = 0.0314 m³ kmol^-1 
  
   
• Calculate pressure (P):
  
  
  • (P + (139.35 x 10³ / 4.8²))(4.8 - 0.0314) = 1 x 8.314 x 350
  
  
  • Solve for P: P ≈ 6.04 bar 
  
   
• Correct answer: B (6.04 bar)

Option C is correct: the system is critically damped.

Compare with the standard form x'' + 2ζω_n x' + ω_n² x = 0.

Equating coefficients gives ω_n² = 1, so ω_n = 1.

Also 2ζω_n = 2, therefore ζ = 1.

Since ζ = 1, the damping is critical, so the system is critically damped. Hence option C is correct.

Option D is correct.

For a rigid rod the component of the velocity of one end along the rod equals the component of the velocity of the other end along the rod because the distance between the ends does not change.

Let v_A and v_B be the speeds of the two ends, with v_A = v.

The component of v_A along the rod is v_A cos μ.

The component of v_B along the rod is v_B cos b.

Equating these components gives v_B cos b = v_A cos μ.

Substituting v_A = v and solving for v_B gives v_B = v (cos μ / cos b).

Thus the required speed is v cos μ / cos b, which matches option D.