A machine costing ₹ 36000 has an… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

A machine costing ₹ 36000 has an effective life of 5 years with scrap value of ₹ 5000 following a linear method of depreciation. Which of the following statements are correct?

(A) The value of the machine after 1 year is ₹ 31000

(B) The value of the machine after 2 years is ₹ 23600

(D) The value of the machine after 4 years is ₹ 11200

Choose the correct answer from the options given below:

Official previous-year question

Held on 22 May 2025 · Verified 13 Jul 2026.

Options

A
(A), (C) and (D) only
B
(B) and (C) only
C
(B) and (D) only
D
(C) and (D) only

Did you get this right?

Solution

A lamp post stands 15 m tall. A boat of height 10 m moves away from the lamp post at a speed of 13 m/min.

Let $x$ = distance of boat from lamp post

Let $s$ = length of the boat's shadow

Given: $\frac{dx}{dt} = 13$ m/min

The lamp casts light over the boat, creating two similar triangles:

Large triangle: from lamp post top to shadow tip (height 15 m, base $x + s$ )
Small triangle: from boat top to shadow tip (height 10 m, base $s$ )

Using similar triangles:

$\frac{15}{x + s} = \frac{10}{s}$

$15s = 10(x + s)$

$15s = 10x + 10s$

$5s = 10x$

$s = 2x$

Differentiating both sides with respect to time:

$\frac{ds}{dt} = 2 \cdot \frac{dx}{dt}$

$\frac{ds}{dt} = 2 \times 13$

$\frac{ds}{dt} = 26$ m/min

The shadow increases at a rate of 26 m/min.

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