Electronics and Communication GATE 2025 Questions with Answer

Ques 53 General Aptitude

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is:
Note: The figures shown are representative.

(5/3)^n/2

(5/3)ⁿ

(5/3)²

(5/3)^n(2n-1)

Ques 54 General Aptitude

Which one of the following plots represents f(x)=-|x|/x, where x is a non-zero real number?
Note: The figures shown are representative.

Ques 55 General Aptitude

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
P. Over time, such adaptations lead to significant evolutionary changes with the potential to shape the development of new species.
Q. In natural world, organisms constantly adapt to their environments in response to challenges and opportunities.
R. This process of adaptation is driven by the principle of natural selection, where favorable traits increase an organism's chances of survival and reproduction.
S. As environments change, organisms that can adapt their behavior, structure and physiology to such changes are more likely to survive.

P→Q→R→S

Q→S→R→P

R→S→Q→P

S→P→R→Q

Ques 56 General Aptitude

A stick of length one meter is broken at two locations at distances of b₁ and b₂ from the origin (0), as shown in the figure. Note that 012<1. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?
Note: All lengths are in meter. The figure shown is representative.

b₁<0.5

b₂>0.5

b₂1+0.5

b₁+b₂<1

Ques 57 General Aptitude

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1^st round, 4^th student behind P leaves the game. After 2^nd round, 5^th student behind Q leaves the game. After 3^rd round, 3^rd student behind V leaves the game. After 4^th round, 4^th student behind U leaves the game. Who all are left in the game after the 4^th round?
Note: The figure shown is representative.

P; T; Q; S

V; P; T; Q

W; R; Q;

Q; T; V; W

Ques 58 General Aptitude

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?

Nation	Gold	Silver	Bronze
USA	40	44	41
Canada	39	24	27
Japan	20	12	13
Australia	19	17	16
France	16	26	22

France will occupy the third place if the list were made on the basis of the total number of medals won.

The order of the top two nations will not change even if the list is made on the basis of the total number of medals won.

USA and Canada together have less than 50% of the medals awarded to the nations in the above table.

Canada has won twice as many total medals as Japan.

Ques 59 General Aptitude

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to 5,00,000. For higher fees, the overhead is 1,00,000 plus 10% of the amount by which the fee exceeds 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than 10,00,000, what is the maximum consulting fee that the employee can charge?

7,01,438

7,24,961

7,51,232

7,75,784

Ques 60 Signals and Systems

Consider the discrete-time system below with input x[n] and output y[n]. In the figure, h₁[n] and h₂[n] denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, δ[n] is the unit impulse, and b>0.
Assuming h₂[n]≠δ[n], the overall system (denoted by the dashed box) is

linear and time invariant

linear and time variant

nonlinear and time invariant

nonlinear and time variant

Ques 61 Signals and Systems

Consider a continuous-time, real-valued signal f(t) whose Fourier transform F(ω)=∫_-∞^∞f(t)exp(-jωt) dt exists.
Which one of the following statements is always TRUE?

|F(ω)| ≤ ∫_-∞^∞|f(t)|dt

|F(ω)| > ∫_-∞^∞|f(t)|dt

|F(ω)| ≤ ∫_-∞^∞f(t)dt

|F(ω)| ≥ ∫_-∞^∞f(t)dt

Ques 62 Signals and Systems

Let x[n] be a discrete-time signal whose Z-transform is X(z).
Which of the following statements is/are TRUE?

The discrete-time Fourier transform (DTFT) of x[n] always exists

The region of convergence (ROC) of X(z) contains neither poles nor zeros

The discrete-time Fourier transform (DTFT) exists if the region of convergence (ROC) contains the unit circle

If x[n]=αδ[n], where δ[n] is the unit impulse and α is a scalar, then the region of convergence (RoC) is the entire Z-plane

Ques 63 Signals and Systems

Consider a continuous-time finite-energy signal f(t) whose Fourier transform vanishes outside the frequency interval [-ω_c,ω_c], where ω_c is in rad/sec.
The signal f(t) is uniformly sampled to obtain y(t)=f(t)p(t). Here, p(t)=Σ_n=-∞^∞δ(t-τ-nT_s), with δ(t) being the Dirac impulse, T_s>0, and τ>0. The sampled signal y(t) is passed through an ideal lowpass filter h(t)=ω_cT_ssin(ω_ct)/(πω_ct) with cutoff frequency ω_c and passband gain T_s.
The output of the filter is given by

f(t) if T_s<π/ω_c

f(t-τ) if T_s<π/ω_c

f(t-τ) if T_s<2π/ω_c

T_sf(t) if T_s<2π/ω_c

Ques 64 Signals and Systems

Consider a real-valued random process
f(t)=Σ_n=1^Na_np(t-nT),
where T>0 and N is a positive integer. Here, p(t)=1 for t∈[0,0.5T] and 0 otherwise. The coefficients a_n are pairwise independent, zero-mean unit-variance random variables.
Read the following statements about the random process and choose the correct option.
(i) The mean of the process f(t) is independent of time t.
(ii) The autocorrelation function E[f(t)f(t+τ)] is independent of time t for all t.
(Here, E[⋅] is the expectation operation.)

(i) is TRUE and (ii) is FALSE

Both (i) and (ii) are TRUE

Both (i) and (ii) are FALSE

(i) is FALSE and (ii) is TRUE

Ques 65 Signals and Systems

Let f(t) be a periodic signal with fundamental period T₀>0. Consider the signal y(t)=f(αt), where α>1. The Fourier series expansions of f(t) and y(t) are given by

Which of the following statements is/are TRUE?

c_k=d_k for all k

y(t) is periodic with a fundamental period αT₀

c_k=d_k/α for all k

y(t) is periodic with a fundamental period T₀/α

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Electronics and Communication GATE 2025 Questions with Answer