Mathematics Mechanical previous year questions with answer

Ques 21 Gate 2022 Set-1

---

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

See Answer Video Solution

Ques 22 Gate 2022 Set-1

---

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

See Answer Video Solution

Ques 23 GATE 2022 SET-1

---

The limit has a finite value for a real α. The value of α and the corresponding limit p are?

A

α = −3π, p = π

B

α = −2π, p = 2π

C

α = π, p = π

D

α = 2π, p = 3π

See Answer Video Solution

Ques 24 GATE 2022 SET-1

---

Given a function 𝜑 = 1/2(x² + y² + z²) in three-dimensional Cartesian space, the value of the surface integral

where 𝑆 is the surface of a sphere of unit radius and 𝐧' is the outward unit normal vector on 𝑆, is

A

4π

B

3π

C

4π/3

D

0

See Answer Video Solution

Ques 25 GATE 2022 SET-1

---

If is a symmetric matrix, the value of k is?

A

8

B

5

C

−0.4

D

(1 + √1561)/12

See Answer Video Solution

Ques 26 GATE 2022 SET-1

---

The value of the integral

evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, is?

A

(-1 + i)π

B

(1 + i)π

C

2(1 - i)π

D

(2 + i)π

See Answer Video Solution

Ques 27 GATE 2022 SET-1

---

The system of linear equations in real (x, y) given by

involves a real parameter 𝛼 and has infinitely many non-trivial solutions for special value(s) of 𝛼. Which one or more among the following options is/are non-trivial solution(s) of (𝑥,𝑦) for such special value(s) of 𝛼?

A

x = 2, y = -2

B

x = -1, y = 4

C

x = 1, y = 1

D

x = 4, y = -2

See Answer Video Solution

Ques 28 GATE 2022 SET-1

---

Let a random variable X follow Poisson distribution such that

The value of Prob(X = 3) is __________ (round off to 2 decimal places).

See Answer Video Solution

Ques 29 GATE 2022 SET-1

---

Consider two vectors
A⃗ = 5i + 7j + 2k
B⃗ = 3i - j + 6k.
Magnitude of the component of 𝑎⃗ orthogonal to 𝑏⃗ in the plane containing the vectors 𝑎⃗ and 𝑏⃗ is __________ (round off to 2 decimal places).

See Answer Video Solution

Ques 30 Gate 2020 Set-2

---

The sum of two normally distributed random variables X and Y is

A

always normally distributed

B

normally distributed, only if X and Y have the same standard deviation

C

normally distributed, only if X and Y have the same mean

D

normally distributed, only if X and Y are independent

See Answer Video Solution