Rs. 2,50,000 cash is equivalent to a… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

Rs. 2,50,000 cash is equivalent to a perpetuity of Rs.7500 payable at the end of each quarter. Then the rate of interest is

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
4% p.a
B
6% p.a
C
3% p.a
D
12% p.a

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Solution

For a function to be continuous at $x = 1$ , the left-hand limit must equal the right-hand limit at that point.

When approaching $x = 1$ from the left (where $x < 1$ ), the function uses $f(x) = 2x + 1$ .

The left-hand limit at $x = 1$ :

$\lim_{x \to 1^-} f(x) = 2(1) + 1$

$= 3$

When approaching $x = 1$ from the right (where $x > 1$ ), the function uses $f(x) = ax - 1$ .

The right-hand limit at $x = 1$ :

$\lim_{x \to 1^+} f(x) = a(1) - 1$

$= a - 1$

For continuity at $x = 1$ :

$\lim_{x \to 1^-} f(x) = \lim_{x \to 1^+} f(x)$

$3 = a - 1$

$a = 4$

Therefore, $a = 4$ .

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