General Aptitude – GATE PI General AptitudePractice Questions & PYQs

The problem states that the danger from a microbe is proportional to its toxicity, potency, and growth. We need to identify the most dangerous microbe for vaccine development. Let's analyze each microbe based on the provided image and description:

• P: High toxicity (requires more microbe mass to cause damage) and moderate potency.
• Q: Moderate toxicity and moderate potency.
• R: Low toxicity and moderate potency.
• S: Lower toxicity but higher potency.

From the image, microbe S clearly has the highest potency. Potency is defined as the probability that the microbe will overcome the human immunity system. While S has the lowest toxicity, its exceptionally high potency makes it a greater threat because it has a higher chance of successfully infecting and surviving against the body's defenses. Therefore, given that microbe S exhibits the highest potency, it represents the most significant danger, making it the primary target for vaccine development.

The system described acquires knowledge, builds a knowledge base, and applies a large, standard set of probability-based rules to make decisions in a specific problem. These are the defining characteristics of an expert system, which aims to replicate human expert problem-solving using a knowledge base and an inference engine. A Management Information System (MIS) focuses on general managerial data, not specialized rule-based reasoning. A Database Management System (DBMS) manages data storage, not knowledge acquisition or complex rule application. While the system uses probability, "probabilistic assessment system" is too general; an expert system specifically encompasses these features, including probabilistic reasoning.

To find the production quantity ($q$) that minimizes total cost, first, express the total cost ($C$) as the sum of variable cost ($V$) and fixed cost ($F$). Given $V = 4q$ and $F = \frac{100}{q}$, the total cost function is $C(q) = 4q + \frac{100}{q}$.

Next, to find the minimum cost, we differentiate $C(q)$ with respect to $q$ and set the derivative to zero.
We can rewrite $C(q)$ as $C(q) = 4q + 100q^{-1}$.
The derivative $\frac{dC}{dq}$ is:
$\frac{dC}{dq} = \frac{d}{dq}(4q) + \frac{d}{dq}(100q^{-1})$
$\frac{dC}{dq} = 4 + 100(-1)q^{-2} = 4 - 100q^{-2}$
Or,
$\frac{dC}{dq} = 4 - \frac{100}{q^2}$
Now, set $\frac{dC}{dq} = 0$ to find the optimal $q$:
$4 - \frac{100}{q^2} = 0$
$4 = \frac{100}{q^2}$
$4q^2 = 100$
$q^2 = \frac{100}{4} = 25$
$q = \sqrt{25}$
Since quantity ($q$) must be positive, $q = 5$. Thus, producing 5 units minimizes the total cost.

The problem provides a logarithmic equality: $\log(P) = \frac{1}{2}\log(Q) = \frac{1}{3}\log(R)$. We need to find the correct relationship between P, Q, and R from the given options.

First, let's establish relationships between P, Q, and R using the properties of logarithms.
From $\log(P) = \frac{1}{2}\log(Q)$:
Multiply both sides by 2: $2\log(P) = \log(Q)$
Using the logarithm property $n\log(a) = \log(a^n)$: $\log(P^2) = \log(Q)$
Since the logarithms are equal, their arguments must be equal: $P^2 = Q$.

Next, from $\log(P) = \frac{1}{3}\log(R)$:
Multiply both sides by 3: $3\log(P) = \log(R)$
Using the logarithm property $n\log(a) = \log(a^n)$: $\log(P^3) = \log(R)$
Since the logarithms are equal, their arguments must be equal: $P^3 = R$.

Now we have two key relationships: $Q = P^2$ and $R = P^3$. Let's substitute these into each option to find the true statement.

Option A: $P^2 = Q^3R^2$
Substitute $Q=P^2$ and $R=P^3$:
$P^2 = (P^2)^3 (P^3)^2$
$P^2 = P^6 \cdot P^6$
$P^2 = P^{12}$ (This is not generally true.)

Option B: $Q^2 = PR$
Substitute $Q=P^2$ and $R=P^3$:
$(P^2)^2 = P \cdot (P^3)$
$P^4 = P^4$ (This statement is TRUE.)

Option C: $Q^2 = R^3P$
Substitute $Q=P^2$ and $R=P^3$:
$(P^2)^2 = (P^3)^3 \cdot P$
$P^4 = P^9 \cdot P$
$P^4 = P^{10}$ (This is not generally true.)

Option D: $R = P^2Q^2$
Substitute $Q=P^2$ and $R=P^3$:
$P^3 = P^2 \cdot (P^2)^2$
$P^3 = P^2 \cdot P^4$
$P^3 = P^6$ (This is not generally true.)

Therefore, the relationship $Q^2 = PR$ is true.

The word "Inexplicable" means something that cannot be explained or accounted for, often implying it's mysterious or defies logic. Let's analyze the given options:

• "Incomprehensible" means something that cannot be understood or grasped.
• "Indelible" means something that cannot be erased or forgotten.
• "Inextricable" means something that cannot be untangled or separated.
• "Infallible" means something or someone that is never wrong.
  Since "Inexplicable" refers to not being able to explain, and "Incomprehensible" refers to not being able to understand, these two are the most closely related because if something cannot be understood, it often cannot be explained either.

When a verb like "contemplate" is used to show you're thinking about an action, it's usually followed by a gerund (the -ing form of a verb acting as a noun). Let's look at the options: Option 1: "$to \ visit$" is an infinitive, and "contemplate" doesn't typically take an infinitive. Option 2: "$having \ to \ visit$" suggests an obligation, which doesn't fit the meaning of just considering something. Option 3: "$visiting$" is a gerund, perfectly conveying the idea of "considering the action of visiting." Option 4: "$for \ a \ visit$" is a prepositional phrase that doesn't fit grammatically directly after "contemplated." Therefore, "$visiting$" is the most appropriate choice to complete the sentence.

The core idea here is to find a word that, like "understated" and "tentative," describes a quality that PREVENTS making a strong impression. We need a word that implies subtlety, hesitancy, or a lack of impact.

Let's look at the options:

• A. Hyperbolic: This means exaggerated. Being hyperbolic often does create a strong, albeit sometimes negative, impression. So, it doesn't fit.
• B. Restrained: This means holding back, being reserved, or controlled. If you're restrained, you're not expressing yourself fully, which aligns perfectly with being understated and tentative in failing to make a strong impression.
• C. Argumentative: Being argumentative might make an impression, not necessarily a weak one. It doesn't quite fit with the subtle nature of "understated" and "tentative."
• D. Indifferent: While indifference leads to a weak impression, "restrained" is a better stylistic match for the other words, implying a manner of presentation rather than just a state of mind.

Therefore, "restrained" is the most appropriate word because it describes a quality of holding back or being reserved, which prevents someone from making a strong impression, similar to being understated or tentative.