# General Aptitude

 Question 1
An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

 A P B Q C R D S
GATE ME 2023      Numerical Ability
 Question 2
How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?
 A 729 B 728 C 665 D 664
GATE ME 2023      Numerical Ability
Question 2 Explanation:
Take one element {1}
$T=\phi ,S=\phi \rightarrow (\phi, \phi ) \Rightarrow 1\; pair$

$T=1,S=\phi \rightarrow (\phi, 1 ),(1,1) \Rightarrow 2\; pair$
For 1 element total pair $= 3^1$
Similarly
For 2 element total pair $= 3^2$
For 3 element total pair $= 3^3$
For 4 element total pair $= 3^4$
For 5 element total pair $= 3^5$
For 6 element total pair $= 3^6=729$

 Question 3
Which one of the sentence sequences in the given options creates a coherent narrative?

(i) I could not bring myself to knock.
(ii) There was a murmur of unfamiliar voices coming from the big drawing room and the door was firmly shut.
(iii) The passage was dark for a bit, but then it suddenly opened into a bright kitchen.
(iv) I decided I would rather wander down the passage.
 A (iv), (i), (iii), (ii) B (iii), (i), (ii), (iv) C (ii), (i), (iv), (iii) D (i), (iii), (ii), (iv)
GATE ME 2023      Verbal Ability
 Question 4
Consider the following inequalities

$p^2-4q \lt 4$
$3p+2q \lt 6$

where $p$ and $q$ are positive integers.
The value of $(p+q)$ is _______.
 A 2 B 1 C 3 D 4
GATE ME 2023      Numerical Ability
Question 4 Explanation:
\begin{aligned} p^2-4q &\lt 4 \\ p^2-4&\ lt 4q \;\;...(i)\\ 3p+2Q& \lt 6 \\ 6p-12 &\lt -4q\;\;...(ii)\\ &\text{by equation (i) + (ii)} \\ p^2+6p-16 &\lt 0 \\ (p+8)(p-2)& \lt 0 \\ \therefore \; p&\in (-8,2) \end{aligned}
Given p is positive integer
$\therefore \;p=1$
Now, from equation (i), $1-4 \lt 4q$
$q \gt \frac{-3}{4}$
from equation (ii),
$q \lt 3/2$
$\therefore \; \frac{-3}{4} \lt q \lt \frac{3}{2}$
Given q is positive integer
$\therefore \;\; q=1$
Thus $p + q = 1+1 = 2$
 Question 5
In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi's friends at school were hardworking and kind too. But the teachers drew attention to Ravi's complete lack of interest in sports. The teachers believed that, along with some of his friends who showed similar disinterest in sports, Ravi needed to engage in some sports for his overall development.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?
 A All of Ravi's friends are hardworking and kind. B No one who is not a friend of Ravi is hardworking and kind. C None of Ravi's friends are interested in sports. D Some of Ravi's friends are hardworking and kind.
GATE ME 2023      Verbal Ability

There are 5 questions to complete.