Maneesh took a loan of ₹ 9,00,800 from… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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Maneesh took a loan of ₹ 9,00,800 from bank at an interest rate of 6% per annum for 10 years. If she has to pay the loan back with the help of equal monthly installments (EMI). Then, the EMI using reduced balance method is (approx):

[Given: $(1.005)^{-120}=0.5496$ ]

Official previous-year question

Held on 2 Jun 2025 · Verified 13 Jul 2026.

Options

A
₹ 12,000
B
₹ 9,000
C
₹ 10,000
D
₹ 9,820

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Solution

For $f(x)$ to be continuous at $x = 0$ :

$\lim_{x \to 0} f(x) = f(0)$

From the given function:

$f(0) = \frac{3k}{2}$

When $x \neq 0$ :

$f(x) = \frac{\sin 3x}{x}$

Finding the limit:

$\lim_{x \to 0} \frac{\sin 3x}{x}$

$= \lim_{x \to 0} \frac{3 \sin 3x}{3x}$

$= 3 \cdot \lim_{x \to 0} \frac{\sin 3x}{3x}$

Let $u = 3x$ . When $x \to 0$ , then $u \to 0$ .

$= 3 \cdot \lim_{u \to 0} \frac{\sin u}{u}$

$= 3 \cdot 1$

$= 3$

Applying the continuity condition:

$\lim_{x \to 0} f(x) = f(0)$

$3 = \frac{3k}{2}$

$6 = 3k$

$k = 2$

Therefore, the value of $k$ is $2$ .

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