# General Aptitude

 Question 1
Consider a spherical globe rotating about an axis passing through its poles. There are three points $P$, $\mathrm{Q}$, and $\mathrm{R}$ situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let $P$, $\mathrm{Q}$, and $\mathrm{R}$ move with speeds $v_{P}, v_{Q}$, and $v_{R}$, respectively.
Which one of the following options is CORRECT?
 A $v_{P} \lt v_{R} \lt v_{Q}$ B $v_{P} \lt v_{Q} \lt v_{R}$ C $v_{P}\gt v_{R} \gt v_{Q}$ D $v_{P}=v_{R} \neq v_{Q}$
GATE CE 2023 SET-2      Numerical Ability
Question 1 Explanation: Velocity, $V=\omega r$.
Here, $\omega=$ constant.
Hence, more is the distance from the axis of rotation more will be the velocity.
$\therefore \quad \mathrm{V}_{\mathrm{P}} \gt \mathrm{V}_{\mathrm{R}} \gt \mathrm{V}_{\mathrm{Q}}$
 Question 2
If $x$ satisfies the equation $4^{8^{x}}=256$, then $x$ is equal to
 A $\frac{1}{2}$ B $\log _{16} 8$ C $\frac{2}{3}$ D $\log _{4} 8$
GATE CE 2023 SET-2      Numerical Ability
Question 2 Explanation:
$4^{8^{x}}=256$
$\rightarrow$ Taking log to the base 4 . on both side.
$8^{x}=\log _{4} 256=4$
Taking lot to the base 8 on both sides, we get
\begin{aligned} x & =\log _{8} 4 \\ & =\log _{2^{3}} 2^{2} \\ x & =\frac{2}{3} \end{aligned}

 Question 3
Based only on the following passage, which one of the options can be inferred with certainty?
When the congregation sang together, Apenyo would also join, though her little screams were not quite audible because of the group singing. But whenever there was a special number, trouble would begin; Apenyo would try singing along, much to the embarrassment of her mother. After two or three such mortifying Sunday evenings, the mother stopped going to church altogether until Apenyo became older and learnt to behave.
At home too, Apenyo never kept quiet; she hummed or made up silly songs to sing by herself, which annoyed her mother at times but most often made her become pensive. She was by now convinced that her daughter had inherited her love of singing from her father who had died unexpectedly away from home.

[Excerpt from These Hills Called Home by Temsula Ao]
 A The mother was embarrassed about her daughter's singing at home. B The mother's feelings about her daughter's singing at home were only of annoyance C The mother was not sure if Apenyo had inherited her love of singing from her father. D When Apenyo hummed at home, her mother tended to become thoughtful.
GATE CE 2023 SET-2      Verbal Ability
 Question 4
Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?
 A 16 B 4 C 120 D 720
GATE CE 2023 SET-2      Numerical Ability
Question 4 Explanation:
Let us form the pairs of Husband-wife. Now these pairs can be arranged around circular table in
\begin{aligned} & =(3-1) ! \text { ways } \\ & =2 \text { ways } \end{aligned}
Their possible internal arrangement $\mathrm{s}$
\begin{aligned} & =2 ! \times 2 ! \times 2 ! \\ & =8 \end{aligned}
Hence, total seating arrangement.
$=2 \times 8=16$
 Question 5
Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one's love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) In Elvesland, one always declares one's love by gifting a white flower.
(ii) In Elvesland, all emotions are declared by gifting flowers.
(iii) In Elvesland, sometimes one expresses one's anger by gifting a flower that is not yellow.
(iv) In Elvesland, sometimes one expresses one's love by gifting a white flower.
 A only (ii) B (i), (ii) and (iii) C (i), (iii) and (iv) D only (iv)
GATE CE 2023 SET-2      Verbal Ability

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