Question

Mr. X enters a positive integer Y in an electronic calculator and then goes on pressing the square repeatedly. Then:

• A. The display does not stabilize
• B. The display becomes closer to 0
• C. The display becomes closer to 1
• D. May not be true and the answer depends on the choice of Y

Hint:

Repeated squaring amplifies numbers >1, flattens numbers between 0 and 1, and stabilizes only if you begin at 1. Always test extreme cases in functional iteration questions.

Answer 1

The Correct Option is D

Let’s denote the function as repeatedly squaring a number: $f(x) = x^2$ applied successively. So starting with $Y$, we get $Y \rightarrow Y^2 \rightarrow Y^4 \rightarrow Y^8 \rightarrow $
Now analyze based on value of $Y$:
- If $Y>1$, say $Y = 2$, then $Y^2 = 4$, then $16$, then $256$ ... it grows without bound. Hence, display does not stabilize — it diverges.
- If $Y = 1$, then $1^2 = 1$, next square is also $1$, so display stabilizes at 1.
- If $0<Y<1$, say $Y = 0.5$, then $Y^2 = 0.25$, then $0.0625$, then $0.0039$, etc. So it approaches 0 — gets smaller and smaller.
- If $Y = 0$ or negative (but question says Y is a positive integer), not relevant.
Thus, the output behavior depends entirely on the starting value $Y$.
Since the output depends on Y (it may go to 1, diverge, or tend to 0), only (D) is correct.