GATE Chemical Engineering Mock Test - 1 - GATE Chemical Engineering MCQ

The total number of students is 84, so:
3x + 4x = 84
Calculate the number of boys and girls:
Number of boys = 3x = 3 × 12 = 36  
Number of girls = 4x = 4 × 12 = 48  

"Exhausted" means extremely tired, which fits the context of needing rest after a long hike.

• A homophone refers to a word that is pronounced the same as another word but that has a different spelling and meaning.
• For example  - 
  • The words 'Peace' ( a stress-free state of security and calmness)  and 'piece' (one of the parts that something is made of)
  • The words 'cent' (small unit of money ) and  'scent' (a pleasant or distinctive smell produced by something)
• Based on the above given points,  the word 'tyre' fits in the first blank contextually. A tyre is a thick piece of rubber which is fitted onto the wheels of vehicles (रबड़ का एक मोटा टुकड़ा जो वाहनों के पहियों पर लगाया जाता है). ​
  • Ex: Tom was driving along the motorway when his tyre burst.
• Similarly, the word which is most suitable for the second blank is 'tire' which means 'to become weary' (थक जाना) as the sentence states how the smoke from a burning tire can weaken  a person.

Therefore, the correct answer is Option C.

Diameter of sphere = Side of cube
a = 2r
Volume of cube = (2r)³
= 8r³

According to given information let's check option;

A. False, because GSR is resilent under extreme weather.

B. True, GSR may be used in future because it is strong enough to survive in climate changes.

C. False, because GSR gives high yield.

D. False, reguler rice in extreme weather can't gives good yields.

Hence, the correct answer is "Option(B)".

Probability of getting only one number = 1/8
As they are independent spins probability of getting one number for each disc is
P = 1/8 x 1/8
Possible outcomes to the sum of 8 = (1, 7), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)
Required probability = 7/64

Adding both equation
2p + 2q < 16
p + q < 8

Since 12 men can complete the project in 15 days working 8 hours a day:
Total work = 12 × 15 × 8 = 1440 man-hours
Calculate the work completed in the first 5 days:
For the first 5 days, 12 men worked 8 hours each day:
Work done in 5 days = 12 × 5 × 8 = 480 man-hours
Calculate the remaining work:
Remaining work = 1440 - 480 = 960 man-hours
Determine the number of men remaining and the time left:
After 5 days, 4 men leave, so only 12 − 4 = 8 men are left.
There are 15 − 5 = 10 days left to complete the project.
Let x be the number of hours per day the remaining 8 men need to work to finish the project on time.
The total work required by these 8 men over the next 10 days is: 8 x 10 * x = 960
x = 960/8 x 10 = 960/80 = 12
Therefore, the remaining 8 men must work 12 hours per day to complete the project on time.

A strain gauge converts mechanical displacement (strain) into an electrical signal, while thermocouples measure temperature, capacitors store charge, and optical sensors detect light.

In P&ID diagrams, valves are often represented by circles or similar shapes with specific annotations indicating valve type.

For,    |A| = 0
Row 2 element is 2 times of Row 1
=> y = 2x
So, option (b) satisfies this equation.

Clauses inequality

Its states that in a cyclic operation, the sum of the dQ/T terms around a complete cycle is less than or equal to zero depending on whether the process is irreversible or reversible.

According to Archimedes' Principle, the buoyant force is equal to the weight of the fluid displaced by the submerged object. The buoyant force can be calculated by the difference in the object's weight in air and its weight when submerged in water.
Weight in air = 100 N
Weight in water = 80 N
Thus, the buoyant force is:
Buoyant Force = Weight in air − Weight in water = 100 N − 80 N = 20 N

Q = mC_p​ ΔT + mλ_V​
Q = 0.01(4.2 × 100 + 2260 × 100)
ΔT = 373K − 273K
(373K − Boiling point of water; 273 K – Initial Temperature)
= 26800 J = 

We know mass transfer rate, W = Flux × Area

For spherical pure water droplets of d₁, rate of diffusion of CO₂ is W₁ mol/s

For droplet of diameter 2d₁, rate of diffusion of CO₂ is W₂ mol/s

So,

Initial moisture content (x_i) = 0.2
Critical moisture content (x_c) = 0.1
Time taking in constant rate period,

Given: t_c = 4 hr


So,

In case II^nd: Falling rate period is linear and rate of drying in falling period is half of rate of drying in constant rate period.

[Given: f = 1 hr]

Assume at point '2' temperature is T.

In process 1 to 2 volume is constant so

du = dQ - dw

du₁ = dQ₁

du₁ = C_V (T - T₁)

In process 2-3 pressure is constant so

du₂ = dQ₂ - dw

Here,

dw = P₂ (V₂ - V₁)

du₂ = C_V (T₂ - T)

So, heat gained by process

dQ₁ + dQ₂ = du₁ + du₂ + dw

= P₂ (V₂ - V₁) + C_V (T₂ - T) + C_V (T₂ - T₁)

= P₂ (V₂ - V₁) + C_V (T₂ - T) + C_V (T₂ - T₁)

Correct option is (a).

Applying momentum balance, we get

In a counter-flow heat exchanger, the LMTD is generally higher than in a parallel flow heat exchanger for the same inlet and outlet temperatures, making counter-flow more efficient for heat transfer.

In Michaelis-Menten kinetics, at high substrate concentrations, the enzyme active sites become saturated, and the reaction rate reaches a maximum, constant rate (Vmax​).

Given,
Area = 70 m²
Latent heat of vaporization (λ_v) = 500 Kcal/kg
Steam economy = 0.8
Feed flow rate = 10000 kg/h at T = 40°C
Steam rate = 7500 kg/h at T = 150°C
Boiling point of solution, T = 80°C,
Applying energy balance,
FC_p(T- T_F) + Vλ_V= Sλ_S = U₀A₀ (Ts- T)
V/S = 0.8
0.8 x 7500 = 6000 kg/n
10000 X 0.8 (80 - 40) + 6000 X 500 = X 70 X (150 - 80)
U₀= 677.55 Kcal/m².h.k

Equimolar binary mixture, x 05
Feed flowrate = 50 kmol/min
x_{D =} 0.9, x_w= 0.01
Stripping line equation:
1.5x - 0.005
and Saturated feed (q) = 1

Fx_F = Dx_D + Wx_W
50 x 0.5 = D x 0.9 + w x 0.01
25 = D x 0.9 + (50 - D) x 0.01
25 - 0.5 = D(0.9 - 0.01)
D = 27.52, w = 22.47


For saturated feed

For enriching section
V= L + D
44.94 - 27.52 = L = 17.42 kmol/min
So,

After step unit, we have


16s + 16 = s²(A + B + C) + s{6A + 4 B + 2 C) + 8 A
Solving,
A = 2
B = 4 
C = -6
y{f) = 2 + 4er^-2t - 6e^-4t

e^-2t + 4t = 3
e^2t = 3

Rounding 0.549 to two decimal places gives 0.55 minutes.

Final Answer:
The time at which the output response reaches its peak value is 0.55 minutes.

Sphericity is a measure that describes how closely the shape of an object approaches that of a perfect sphere. It is calculated using the formula:

Sphericity (φ) = (π^(1/3) × (6V)^(2/3)) / A

Where:

• V is the volume of the object.
• A is the surface area of the object.

Step-by-Step Calculation

1. Calculate Volume and Surface Area for Both Cubes

• Original Cube (Side = a)

  • Volume (V1) = a³
  • Surface Area (A1) = 6a²

• Scaled Cube (Side = 2a)

  • Volume (V2) = (2a)³ = 8a³
  • Surface Area (A2) = 6(2a)² = 24a²

2. Calculate Sphericity for Both Cubes

• Sphericity of Original Cube (φ1):
  φ1 = (π^(1/3) × (6V1)^(2/3)) / A1
  = (π^(1/3) × (6a³)^(2/3)) / 6a²

  Simplifying (6a³)^(2/3):
  = 6^(2/3) × a²

  Substituting back:
  φ1 = (π^(1/3) × 6^(2/3) × a²) / (6a²)

  Cancelling a²:
  φ1 = (π/6)^(1/3)

• Sphericity of Scaled Cube (φ2):
  φ2 = (π^(1/3) × (6V2)^(2/3)) / A2
  = (π^(1/3) × (6 × 8a³)^(2/3)) / 24a²

  Simplifying (48a³)^(2/3):
  = 48^(2/3) × a²

  Substituting back:
  φ2 = (π^(1/3) × 48^(2/3) × a²) / (24a²)

  Cancelling a²:
  φ2 = (π/6)^(1/3)

3. Determine the Ratio of Sphericities

From the calculations above:

φ1 = φ2 = (π/6)^(1/3)

Thus, the ratio of φ1 to φ2 is:

φ1 / φ2 = 1

 Mass mean diameter = 
= 308.04 μm

Annual cost of capital recovery option 2 = 
Total annual cost = 5131.12 + 500 = Rs. 5631.12

At the condition of perfectly mixed streams (when the liquid and vapor phases are perfectly mixed and in equilibrium on each tray or stage), the Murphree efficiency and the point efficiency are equal. This happens because when the system is perfectly mixed:
The vapor and liquid are in perfect equilibrium at every stage, and there is no concentration gradient to cause deviations from the ideal behavior.
The mass transfer is happening ideally, so there is no difference between the actual change in composition and the theoretical change.
Thus, the ratio of the point efficiency to the Murphree efficiency will be E_p/E_M = 1: 

dy/dx = xy² + 2y + x - 4.5

Given:

y(0) = 1

h = 0.5

→ x₁ = x₀ + h = 0 + 0.5 = 0.5

by Implicit Euler formula

y₁ = y₀ + h f(x₁, y₁)

dy = (x y² + 2y + x - 4.5) dx



By trapezoidal rule,

Data given: C_d = 0.98

Pipe diameter, D₀ = 50 mm, d₀ = 20 mm (throat diameter)

ΔP = 50 kPa

ρ_w = 1000 kg/m³

For venturimeter, the flow rate is given by