Mohini purchases a house worth Rs. 50… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

Mohini purchases a house worth Rs. 50 lakhs and makes a down payment of Rs. 11.2 lakhs. She pays the remaining amount on monthly EMI using a reducing balance method. The bank charges 6% per annum compounded monthly for a tenure of 25 years. Her EMI is:

[Given: $(1.005)^{-300} \approx 0.224$ ]

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
Rs. 11200
B
Rs. 38800
C
Rs. 25000
D
Rs. 22400

Did you get this right?

Solution

$\dfrac{e^{2x} - 1}{e^{2x} + 1}$ can be simplified by dividing both numerator and denominator by $e^x$ :

$\dfrac{e^{2x} - 1}{e^{2x} + 1} = \dfrac{\dfrac{e^{2x}}{e^x} - \dfrac{1}{e^x}}{\dfrac{e^{2x}}{e^x} + \dfrac{1}{e^x}} = \dfrac{e^x - e^{-x}}{e^x + e^{-x}}$

Now the numerator is the derivative of the denominator.

Let $t = e^x + e^{-x}$

$\dfrac{dt}{dx} = e^x - e^{-x}$

$dt = (e^x - e^{-x})\, dx$

The integral becomes:

$\int \dfrac{dt}{t}$

$= \log|t| + C$

Substituting back $t = e^x + e^{-x}$ :

$= \log|e^x + e^{-x}| + C$

Your note

CUET UG Statistics & Applications in other years

Statistics & Applications 2024

More CUET UG Statistics & Applications questions

The rise in prices before Diwali is an example of

2025easy

Mr. X purchased a house from a company for ₹ 7,00,000 and made a down payment of ₹ 1,50,000. He repays the balance in 25 years by equal monthly installments at 9 % per annum compounded monthly. The equated monthly installment (EMI) is: [Given that : (1.0075)⁻³⁰⁰ = 0.106]

2025medium

Consider the following hypothesis $H_0: \mu = 315$ and $H_a: \mu \neq 315$ A sample of 60 provided a sample mean of 324.6. The standard deviation ($\sigma$) is 14 and level of significance $\alpha = 0.05$. Then the confidence interval is: [Given: $Z_{a/2}{\frac{14}{\sqrt60}} = 3.54$]

2025medium

With reference to sampling, which of the following are correct? (A) Simple random sampling is probability sampling (B) Snow-ball sampling is non-probability sampling (C) Stratified sampling is probability sampling (D) Cluster sampling is non-probability sampling Choose the correct answer from the options given below:

2025medium

The effective rate equivalent to a nominal rate of 12% compounded quarterly is: (Given $(1.03)^4=1.1256$)

2025medium

View all Statistics & Applications questions