Electronics and Communication Gate 2024 Questions with Answer

Ques 40 GATE 2024

Two identical sheets A and B, of dimensions 24 cm 16 cm, can be folded into half using two distinct operations, FO1 or FO2.
In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge.
If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is

14:11

11:14

18:11

11:18

(A) is the correct answer.

Ques 41 GATE 2024

The general form of the complementary function of a differential equation is given by $y(t)=(At+B)e^{-2t}$, where A and B are real constants determined by the initial condition.
The corresponding differential equation is

$\frac{d^{2}y}{dt^{2}}+4\frac{dy}{dt}+4y=f(t)$

$\frac{d^{2}y}{dt^{2}}+4y=f(t)$

$\frac{d^{2}y}{dt^{2}}+3\frac{dy}{dt}+2y=f(t)$

$\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=f(t)$

(A) is the correct answer.

Ques 42 GATE 2024

Let $ρ(x,y,z,t)$ and $u(x,y,z,t)$ represent density and velocity, respectively, at a point $(x,y,z)$ and time t.
Assume $\frac{∂ρ}{∂t}$ is continuous. Let V be an arbitrary volume in space enclosed by the closed surface S and $n̂$ be the outward unit normal of S.
Which of the following equations is/are equivalent to $\frac{∂ρ}{∂t}+∇⋅(ρu)=0$?

$\int_{V}\frac{∂ρ}{∂t}dv=-\iint_{S}ρu⋅n̂ ds$

$\int_{V}\frac{∂ρ}{∂t}dv=[\oint_{S}ρu⋅n̂ ds$

$\int_{v}\frac{∂ρ}{∂t}dv=-\int_{V}∇⋅(ρu)dv$

$\int_{V}\frac{∂ρ}{∂t}dv=\int_{V}∇⋅(ρu)dv$

(A;C) is the correct answer.

Ques 43 GATE 2024

In a number system of base r, the equation $x^2-12x+37=0$ has x=8 as one of its solutions.
The value of r is

(10) is the correct answer.

Ques 44 GATE 2024

Let R and ℝ³ denote the set of real numbers and the three dimensional vector space over it, respectively.
The value of α for which the set of vectors
{[2 -3 α], [3 -1 3], [1 2 7]}
does not form a basis of ℝ³ is __________.

(4) is the correct answer.

Ques 45 GATE 2024

Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval.
The probability that X≥Y is

(0.5) is the correct answer.

Ques 46 GATE 2024

Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the 60°N latitude circle, that contains the north pole in its interior is

$(2-√3)πR^2$

$\frac{(√2-1)πR^2}{2}$

$\frac{2πR^2}{3}$

$\frac{(2+√3)πR^2}{8√2}$

(A) is the correct answer.

Ques 47 GATE 2024

Let z be a complex variable.
If $f(z) = \frac{sin(πz)}{z^2 (z-2)}$
and C is the circle in the complex plane with |z| = 3 then ∫∫Cf(z) dz is

$π^2 j$

$jπ(\frac{1}{2} - π)$

$jπ(\frac{1}{2} + π)$

$-π^2 j$

(D) is the correct answer.

Ques 48 GATE 2024

Let $F_1$, $F_2$ and $F_3$ be functions of (x, y, z).
Suppose that for every given pair of points A and B in space, the line integral $∫_C (F_1 dx + F_2 dy + F_3 dz)$ evaluates to the same value along any path C that starts at A and ends at B.
Then which of the following is/are true?

For every closed path $Γ$, we have $∫_Γ (F_1 dx + F_2 dy + F_3 dz) = 0$.

There exists a differentiable scalar function $f(x, y, z)$ such that $F_1 = \frac{∂f}{∂x}$, $F_2 = \frac{∂f}{∂y}$, $F_3 = \frac{∂f}{∂z}$

$\frac{∂F_1}{∂x} + \frac{∂F_2}{∂y} + \frac{∂F_3}{∂z} = 0$.

$\frac{∂F_3}{∂y} = \frac{∂F_2}{∂z}$, $\frac{∂F_1}{∂z} = \frac{∂F_3}{∂x}$, $\frac{∂F_2}{∂x} = \frac{∂F_1}{∂y}$

(A;B;D) is the correct answer.

Ques 49 GATE 2024

Consider the matrix

where k is a positive real number.
Which of the following vectors is/are eigenvector(s) of this matrix?

(B;D) is the correct answer.

Ques 50 GATE 2024

If ' → ' denotes increasing order of intensity, then the meaning of the words [charm → enamor → bewitch] is analogous to [bored → ________ →weary].
Which one of the given options is appropriate to fill the blank?

jaded

baffled

dead

worsted

(A) is the correct answer.

Ques 51 GATE 2024

P, Q, R, S, and T have launched a new startup.
Two of them are siblings. The office of the startup has just three rooms.
All of them agree that the siblings should not share the same room.
If S and Q are single children, and the room allocations shown below are acceptable to all.

then, which one of the given options is the siblings?

P and T

P and S

T and Q

(A) is the correct answer.

Ques 52 GATE 2024

Five years ago, the ratio of Aman's age to his father's age was 1:4, and five years from now, the ratio will be 2:5.
What was his father's age when Aman was born?

28 years

30 years

35 years

32 years

(B) is the correct answer.

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