‘Riya Mart’ is a company manufacturing disposable crockery. They have been in business for the past five years

Question 24 of 26

Q. ‘Riya Mart’ is a company manufacturing disposable crockery. They have been in business for the past five years, but were not earning good profits. Concerned about this, the Chief Executive Officer (CEO), Verma, ordered an internal audit. The audit uncovered several issues like inventory pilferage, employees coming late and their performance not upto the mark. To stop inventory pilferage, Verma, the CEO, introduced surprise stock checks and installed an automated inventory management system to track stock movements. A biometric attendance system was also setup to keep a check on employees coming late. In addition to this, to motivate employees for better performance, they were told in advance what they are expected to do and what are their standards of performance. As a result of these steps, the inventory pilferage reduced, employees became more punctual and their performance improved.

(i) Identify and state the function of management performed by Verma, the Chief Executive Officer of the company.

(ii) State any two points of importance of the function identified in

(i) above, which are not discussed in the above para.

Dnh Dd CbseCBSE Class XII Board 2026Subjective· 3mImportance★★★★★

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Concept understanding — Controlling Definition

Controlling Definition — First Encounter

Imagine you're trying to prove that a function is continuous at a point. You've seen the epsilon-delta definition: for every $\epsilon > 0$ , there exists a $\delta > 0$ such that if $|x - c| < \delta$ , then $|f(x) - f(c)| < \epsilon$ . That's the standard definition.

Now think about what you're actually doing when you use this definition to prove continuity. You're given an arbitrary $\epsilon$ — a tolerance on the output — and you must produce a $\delta$ — a window on the input — that controls the output error. The $\delta$ you choose depends on $\epsilon$ , on the function $f$ , and on the point $c$ . The core idea: you control the input to control the output.

That's the intuition behind the term "controlling definition." It's a definition that tells you: to achieve a desired precision in the output, you must restrict the input within some range. The definition itself gives you the control — the $\delta$ — as a function of the desired precision $\epsilon$ .

The Precise Statement

A controlling definition is a definition of a limit (or continuity, or derivative) that explicitly quantifies the relationship between an output tolerance and an input restriction. For the limit $\lim_{x \to c} f(x) = L$ , the controlling definition is:

\lim_{x \to c} f(x) = L \iff \forall \epsilon > 0, \ \exists \delta > 0 \ \text{such that} \ 0 < |x - c| < \delta \implies |f(x) - L| < \epsilon

The word "controlling" highlights that $\delta$ is chosen after $\epsilon$ is given — you control the input window $\delta$ to force the output error below $\epsilon$ . The $\delta$ is not arbitrary; it must be found (or shown to exist) for every possible $\epsilon$ .

Why "Controlling" Matters

This phrasing is most common in analysis textbooks when contrasting with other equivalent definitions. For example, the "sequential definition" of a limit says: if every sequence $x_n \to c$ (with $x_n \neq c$ ) has $f(x_n) \to L$ , then the limit exists. That definition doesn't give you a direct control mechanism — it's about checking sequences.

The controlling definition is the one you actually use in proofs. It's constructive: you pick $\delta$ as a function of $\epsilon$ , often by solving inequalities. For instance, to prove $\lim_{x \to 2} (3x+1) = 7$ , you set $\delta = \epsilon/3$ . That's the control: if $|x-2| < \epsilon/3$ , then $|(3x+1)-7| = 3|x-2| < \epsilon$ . …

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The case describes Verma taking corrective actions (surprise checks, biometric system, performance standards) to fix problems — this is the controlling function of management. The final answer identifies controlling and lists two unmentioned points of its importance: judging accuracy of standards and ensuring resource efficiency.

This is a classic case study from the Business Studies syllabus on the functions of management. The key is to separate what the CEO did from the reason he did it. Verma didn't just install systems — he compared actual performance (pilferage, lateness, poor work) against a desired standard (no pilferage, punctuality, good performance) and then took corrective action. That sequence — set standards, measure actual, compare, correct — is the essence of controlling.

Notice the para explicitly says: "they were told in advance what they are expected to do and what are their standards of performance." That is the setting of standards step. The surprise checks and biometric system are the measurement and comparison steps. The reduction in pilferage and improved punctuality are the corrective action results. So the function is clearly controlling, not planning or organising.

Now, the question asks for two points of importance of controlling that are not discussed in the paragraph. The para already mentions:

Helps in reducing pilferage (part of achieving organisational goals)
Improves employee punctuality and performance (part of improving employee motivation)

So you must pick two other points from the textbook list. The most common ones that are not hinted at here are:

Judging accuracy of standards — Controlling helps verify whether the standards set during planning were realistic. If actual performance consistently falls short, it may mean the standard was too high, not that employees are lazy.
Ensuring efficient use of resources — By monitoring wastage, idle time, and costs, controlling ensures that materials, money, and labour are used optimally.

Other acceptable points (if you prefer):

Facilitating coordination (by aligning individual actions with organisational goals)
Helping in future planning (by providing feedback for better plans)

But the two above are the safest because they are textbook-standard and clearly absent from the given story.

Identify the function:

The function performed by Verma is controlling.

Reasoning: He set performance standards (told employees what was expected), measured actual performance (via surprise checks and biometric system), compared the two (found pilferage, lateness, poor performance), and took corrective action (installed systems, motivated employees). This is the complete controlling cycle.
State the function:

Controlling is the management function of monitoring organisational performance towards goals, comparing actual results with standards, and taking corrective action when deviations occur. …

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