Mechanical Gate 2022 Set-I Questions

After playing _________ hours of tennis, I am feeling _________ tired to walk back.

a) too/too
b) too/two
c) two/two
d) two/too

A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18kmph.
What percentage of the total distance is travelled at a uniform speedof 10 kmph?

a) 28.25
b) 37.25
c) 43.75
d) 50.00

Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning Dutch and Japanese.
Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch is easier than Japanese, and Spanish is easier than French.
Based on the above information, which girl is learning the most difficult pair of languages?

a) P
b) Q
c) R
d) S

Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear “lost”, it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets that had a key and money are more likely to be returned than wallets with the same amount of money alone. This suggests that the primary reason for this behavior is compassion and empathy.
Which one of the following is the CORRECT logical inference based on the information in the above passage?

a) Wallets with a key are more likely to be returned because people do not care about money.
b) Wallets with a key are more likely to be returned because people relate to suffering of others.
c) Wallets used in experiments are more likely to be returned than wallets that are really lost.
d) Money is always more important than keys.

A rhombus is formed by joining the midpoints of the sides of a unit square.What is the diameter of the largest circle that can be inscribed within the rhombus?

a) 1/√2
b) 1/2√2
c) √2
d) 2√2

An equilateral triangle, a square and a circle have equal areas.What is the ratio of the perimeters of the equilateral triangle to square to circle?

a) 3√3 ∶ 2 ∶ √𝜋
b) √(3√3):2:√𝜋
c) √(3√3):4:2√𝜋
d) √(3√3):2:2√𝜋

Given below are three conclusions drawn based on the following three
statements
Statement 1: All teachers are professors.
Statement 2: No professor is a male.
Statement 3: Some males are engineers.

Conclusion I: No engineer is a professor.
Conclusion II: Some engineers are professors.
Conclusion III: No male is a teacher.
Which one of the following options can be logically inferred?

a) Only conclusion III is correct
b) Only conclusion I and conclusion II are correct
c) Only conclusion II and conclusion III are correct
d) Only conclusion I and conclusion III are correct

In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?

a) 11
b) 12
c) 144
d) 2

The average of the monthly salaries of M, N and S is ₹ 4000. The average of the monthly salaries of N, S and P is ₹ 5000. The monthly salary of P is ₹ 6000.What is the monthly salary of M as a percentage of the monthly salary of P?

a) 50
b) 75%
c) 100%
d) 125%

Solution of ∇²𝑇 = 0 in a square domain (0 < 𝑥 < 1 and 0 < 𝑦 < 1) with boundary conditions:

𝑇(𝑥, 0) = 𝑥; 𝑇(0, 𝑦) = 𝑦; 𝑇(𝑥, 1) = 1 + 𝑥; 𝑇(1, 𝑦) = 1 + 𝑦

is

a) T(x, y) = x − xy+ y
b) T(x,y)=x+y
c) T(x,y)=-x+y
d) T(x,y)=x+xy+y

The Fourier series expansion of x³ in the interval −1 ≤ 𝑥 < 1 with periodic continuation has

a) only sine terms
b) only cosine terms
c) both sine and cosine terms
d) only sine terms and a non-zero constant