1
GATE ECE 2025
MCQ (More than One Correct Answer)
+2
-0

Let $f(t)$ be a periodic signal with fundamental period $T_0>0$. Consider the signal $y(t)=f(\alpha t)$, where $\alpha>1$.

The Fourier series expansions of $f(t)$ and $y(t)$ are given by

$$ f(t)=\sum\limits_{k = - \infty }^\infty c_k e^{j \frac{2 \pi}{T_0} k T} \text { and } y(t)=\sum\limits_{k = - \infty }^\infty d_k e^{j \frac{2 \pi}{T_0} \alpha k T} . $$

Which of the following statements is/are TRUE?

A
$c_k=d_k$ for all $k$
B
$y(t)$ is periodic with a fundamental period $\alpha T_0$
C
$c_k=d_k / \alpha$ for all $k$
D
$y(t)$ is periodic with a fundamental period $T_0 / \alpha$
2
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.

Group-I: Abuse $\rightarrow$ Insult $\rightarrow$ Ridicule

Group-II: __________$\rightarrow$ Praise $\rightarrow$ Appreciate

A
Extol
B
Prize
C
Appropriate
D
Espouse
3
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33
Had I learnt acting as a child, I__________a famous film star. Select the most appropriate option to complete the above sentence.
A
will be
B
can be
C
am going to be
D
could have been
4
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

The 12 musical notes are given as $C, C^{\#}, D, D^{\#}, E, F, F^{\#}, G, G^{\#}, A, A^{\#}$. Frequency of each note is $\sqrt[12]{2}$ times the frequency of the previous note. If the frequency of the note $C$ is 130.8 Hz , then the ratio of frequencies of notes $F^{\#}$ and $C$ is:

A
$\sqrt[6]{2}$
B
$\sqrt{2}$
C
$\sqrt[4]{2}$
D
2
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